text:
Analysis of fuel shares in the industrial sector
Roop, J.M.; Belzer, D.B.
These studies describe how fuel shares have changed over time; determine what factors are important in promoting fuel share changes; and project fuel shares to the year 1995 in the industrial sector. A general characterization of changes in fuel shares of four fuel types - coal, natural gas, oil and electricity - for the industrial sector is as follows. Coal as a major fuel source declined rapidly from 1958 to the early 1970s, with oil and natural gas substituting for coal. Coal's share of total fuels stabilized after the oil price shock of 1972-1973, and increased after the 1979 price shock. In the period since 1973, most industries and the industrial sector as a whole appear to freely substitute natural gas for oil, and vice versa. Throughout the period 1958-1981, the share of electricity as a fuel increased. These observations are derived from analyzing the fuel share patterns of more than 20 industries over the 24-year period 1958 to 1981.
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
Relativistic Guiding Center Equations
White, R. B.; Gobbin, M.
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Parallel Multigrid Equation Solver
Energy Science and Technology Software Center (OSTI)
Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.
Flavored quantum Boltzmann equations
Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545 (United States); Center for Theoretical Physics, University of California, and Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, California, 94720 (United States); Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin, 53706 (United States) and Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California, 91125 (United States); Theory Group, TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, V6T 2A3 (Canada)
We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.
Menikoff, Ralph
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ? 0, T ? 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
Generalizing the cosmic energy equation
Shtanov, Yuri; Sahni, Varun
We generalize the cosmic energy equation to the case when massive particles interact via a modified gravitational potential of the form {phi}(a,r), which is allowed to explicitly depend upon the cosmological time through the expansion factor a(t). Using the nonrelativistic approximation for particle dynamics, we derive the equation for the cosmological expansion which has the form of the Friedmann equation with a renormalized gravitational constant. The generalized Layzer-Irvine cosmic energy equation and the associated cosmic virial theorem are applied to some recently proposed modifications of the Newtonian gravitational interaction between dark-matter particles. We also draw attention to the possibility that the cosmic energy equation may be used to probe the expansion history of the universe thereby throwing light on the nature of dark matter and dark energy.
Friedmann equations from entropic force
Cai Ronggen; Cao Liming; Ohta, Nobuyoshi
In this paper, by use of the holographic principle together with the equipartition law of energy and the Unruh temperature, we derive the Friedmann equations of a Friedmann-Robertson-Walker universe.
Entropic corrections to Einstein equations
Hendi, S. H. [Physics Department, College of Sciences, Yasouj University, Yasouj 75914 (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Sheykhi, A. [Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Department of Physics, Shahid Bahonar University, P.O. Box 76175-132, Kerman (Iran, Islamic Republic of)
Considering the general quantum corrections to the area law of black hole entropy and adopting the viewpoint that gravity interprets as an entropic force, we derive the modified forms of Modified Newtonian dynamics (MOND) theory of gravitation and Einstein field equations. As two special cases we study the logarithmic and power-law corrections to entropy and find the explicit form of the obtained modified equations.
Ordinary Differential Equation System Solver
Energy Science and Technology Software Center (OSTI)
LSODE is a package of subroutines for the numerical solution of the initial value problem for systems of first order ordinary differential equations. The package is suitable for either stiff or nonstiff systems. For stiff systems the Jacobian matrix may be treated in either full or banded form. LSODE can also be used when the Jacobian can be approximated by a band matrix.
Equation of State Project Overview
Crockett, Scott
A general overview of the Equation of State (EOS) Project will be presented. The goal is to provide the audience with an introduction of what our more advanced methods entail (DFT, QMD, etc.. ) and how these models are being utilized to better constrain the thermodynamic models. These models substantially reduce our regions of interpolation between the various thermodynamic limits. I will also present a variety example of recent EOS work.
Germanium multiphase equation of state
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Crockett, Scott D.; Lorenzi-Venneri, Giulia De; Kress, Joel D.; Rudin, Sven P.
A new SESAME multiphase germanium equation of state (EOS) has been developed using the best available experimental data and density functional theory (DFT) calculations. The equilibrium EOS includes the Ge I (diamond), the Ge II (β-Sn) and the liquid phases. The foundation of the EOS is based on density functional theory calculations which are used to determine the cold curve and the Debye temperature. Results are compared to Hugoniot data through the solid-solid and solid-liquid transitions. We propose some experiments to better understand the dynamics of this element
Universal equation for Efimov states
Braaten, Eric; Hammer, H.-W.; Kusunoki, M.
Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a three-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of {sup 4}He atoms. We also extend Efimov's theory to include the effects of deep two-body bound states, which give widths to the Efimov states.
The equation of state of nuclear matter
Gandolfi, Stefano; Carlson, Joseph Allen
A brief status report of research on equation of state (EOS) of nuclear matter is provided, along with two graphs.
Product equation of state for polysulfone
Ticknor, Christopher
Here we review the new polysulfone product equation of state (EOS) made with magpie, a chemical equilibrium code.
Equation determines pressure drop in coiled tubing
Yang, Y.S.
A single equation can determine the pressure drop in wells with laminar, transitional, and turbulent incompressible fluid flow in coiled tubing or other steel tubulars. The single equation is useful, especially in computer-aided design and operations. The equation is derived and illustrated by an example.
Boundary conditions for the subdiffusion equation
Shkilev, V. P.
The boundary conditions for the subdiffusion equations are formulated using the continuous-time random walk model, as well as several versions of the random walk model on an irregular lattice. It is shown that the boundary conditions for the same equation in different models have different forms, and this difference considerably affects the solutions of this equation.
Double distributions and evolution equations
A.V. Radyushkin
Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive meson electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements < p{prime} {vert_bar}O(0,z){vert_bar}p > of quark and gluon light-cone operators. In their previous papers the authors used two types of nonperturbative functions parameterizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F{sub {zeta}}(X;t). Here they discuss in more detail the double distributions (DD's) and evolution equations which they satisfy. They propose simple models for F(x,y;t=0) DD's with correct spectral and symmetry properties which also satisfy the reduction relations connecting them to the usual parton densities f(x). In this way, they obtain self-consistent models for the {zeta}-dependence of nonforward distributions. They show that, for small {zeta}, one can easily obtain nonforward distributions (in the X > {zeta} region) from the parton densities: F{sub {zeta}} (X;t=0) {approx} f(X{minus}{zeta}/2).
Scalable Equation of State Capability
Epperly, T W; Fritsch, F N; Norquist, P D; Sanford, L A
The purpose of this techbase project was to investigate the use of parallel array data types to reduce the memory footprint of the Livermore Equation Of State (LEOS) library. Addressing the memory scalability of LEOS is necessary to run large scientific simulations on IBM BG/L and future architectures with low memory per processing core. We considered using normal MPI, one-sided MPI, and Global Arrays to manage the distributed array and ended up choosing Global Arrays because it was the only communication library that provided the level of asynchronous access required. To reduce the runtime overhead using a parallel array data structure, a least recently used (LRU) caching algorithm was used to provide a local cache of commonly used parts of the parallel array. The approach was initially implemented in a isolated copy of LEOS and was later integrated into the main trunk of the LEOS Subversion repository. The approach was tested using a simple test. Testing indicated that the approach was feasible, and the simple LRU caching had a 86% hit rate.
Darboux transformation for the NLS equation
Aktosun, Tuncay; Mee, Cornelis van der
We analyze a certain class of integral equations associated with Marchenko equations and Gel'fand-Levitan equations. Such integral equations arise through a Fourier transformation on various ordinary differential equations involving a spectral parameter. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution in terms of the unperturbed quantities and the finite-rank perturbation. We show that this result provides a fundamental approach to derive Darboux transformations for various systems of ordinary differential operators. We illustrate our theory by providing the explicit Darboux transformation for the Zakharov-Shabat system and show how the potential and wave function change when a simple discrete eigenvalue is added to the spectrum, and thus we also provide a one-parameter family of Darboux transformations for the nonlinear Schroedinger equation.
The Boltzmann equation in the difference formulation
Szoke, Abraham; Brooks III, Eugene D.
First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.
The generalized Schr�dinger�Langevin equation
Bargue�o, Pedro; Miret-Art�s, Salvador
In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called Schr�dinger�Langevin or Kostin equation. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed in terms of this generalized equation. -- Highlights: �We generalize the Kostin equation for arbitrary system�bath coupling. �This generalization is developed both in the Schr�dinger and Bohmian formalisms. �We write the generalized Kostin equation for two measurement problems. �We reformulate the generalized uncertainty principle in terms of this equation.
Fokker-Planck equation in mirror research
Post, R.F.
Open confinement systems based on the magnetic mirror principle depend on the maintenance of particle distributions that may deviate substantially from Maxwellian distributions. Mirror research has therefore from the beginning relied on theoretical predictions of non-equilibrium rate processes obtained from solutions to the Fokker-Planck equation. The F-P equation plays three roles: Design of experiments, creation of classical standards against which to compare experiment, and predictions concerning mirror based fusion power systems. Analytical and computational approaches to solving the F-P equation for mirror systems will be reviewed, together with results and examples that apply to specific mirror systems, such as the tandem mirror.
Equator Appliance: ENERGY STAR Referral (EZ 3720)
Broader source: Energy.gov [DOE]
DOE referred Equator Appliance clothes washer EZ 3720 to EPA, brand manager of the ENERGY STAR program, for appropriate action after DOE testing revealed that the model does not meet ENERGY STAR requirements.
Coherency Does Not Equate to Stability
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
for Coherency Does Not Equate to Stability LLNL BES Programs Highlight Coherency Does Not Equate to Stability As-grown nanotwin (NT) copper (A) SEM image. (B) An edge-on inverse pole figure orientation mapping (IPFOM) image, the coherent and incoherent twin boundaries are labeled as CTB and ITB (inside circles), respectively. (C) A high-resolution IPFOM image of CTBs. Some ITB segments are marked with white arrows. (D) An IPFOM image of along columnar grain boundary showing numerous ITB segments
An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like
Pierantozzi, T.; Vazquez, L.
Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case.
Equation of State from Lattice QCD Calculations (Conference)...
Office of Scientific and Technical Information (OSTI)
Conference: Equation of State from Lattice QCD Calculations Citation Details In-Document Search Title: Equation of State from Lattice QCD Calculations You are accessing a...
An Acoustic Wave Equation for Tilted Transversely Isotropic Media...
Office of Scientific and Technical Information (OSTI)
An Acoustic Wave Equation for Tilted Transversely Isotropic Media Citation Details In-Document Search Title: An Acoustic Wave Equation for Tilted Transversely Isotropic Media ...
Solving the power flow equations: a monotone operator approach...
Office of Scientific and Technical Information (OSTI)
Technical Report: Solving the power flow equations: a monotone operator approach Citation Details In-Document Search Title: Solving the power flow equations: a monotone operator ...
Equation of State Measurements by Radiography Provide Evidence...
Office of Scientific and Technical Information (OSTI)
Equation of State Measurements by Radiography Provide Evidence for a Liquid-Liquid Phase Transition in Cerium Citation Details In-Document Search Title: Equation of State ...
Nonparametric reconstruction of the dark energy equation of state...
Office of Scientific and Technical Information (OSTI)
energy equation of state from diverse data sets Citation Details In-Document Search Title: Nonparametric reconstruction of the dark energy equation of state from diverse data ...
Solves the Multigroup Neutron Diffusion Equation
Energy Science and Technology Software Center (OSTI)
GNOMER is a program which solves the multigroup neutron diffusion equation in 1D, 2D and 3D cartesian geometry. The program is designed to calculate the global core power distributions (with thermohydraulic feedbacks), as well as power distribution and homogenized cross sections over a fuel assembly.
Changing the Equation in STEM Education
Broader source: Energy.gov [DOE]
Editor's Note: This is a cross post of an announcement that the White House featured on its blog last week. Check out the video below for Secretary Chu's thoughts on how an education in math and science helps students understand the world and deal with the pressing issues of our time. Today, President Obama announced the launch of Change the Equation, a CEO-led effort to dramatically improve education in science, technology, engineering, and math (STEM), as part of his "Educate to Innovate" campaign. Change the Equation is a non-profit organization dedicated to mobilizing the business community to improve the quality of STEM education in the United States.
The quasicontinuum Fokker-Plank equation
Alexander, Francis J
We present a regularized Fokker-Planck equation with more accurate short-time and high-frequency behavior for continuous-time, discrete-state systems. The regularization preserves crucial aspects of state-space discreteness lost in the standard Kramers-Moyal expansion. We apply the method to a simple example of biochemical reaction kinetics and to a two-dimensional symmetric random walk, and suggest its application to more complex systerns.
Development of surface mine cost estimating equations
Not Available
Cost estimating equations were developed to determine capital and operating costs for five surface coal mine models in Central Appalachia, Northern Appalachia, Mid-West, Far-West, and Campbell County, Wyoming. Engineering equations were used to estimate equipment costs for the stripping function and for the coal loading and hauling function for the base case mine and for several mines with different annual production levels and/or different overburden removal requirements. Deferred costs were then determined through application of the base case depreciation schedules, and direct labor costs were easily established once the equipment quantities (and, hence, manpower requirements) were determined. The data points were then fit with appropriate functional forms, and these were then multiplied by appropriate adjustment factors so that the resulting equations yielded the model mine costs for initial and deferred capital and annual operating cost. (The validity of this scaling process is based on the assumption that total initial and deferred capital costs are proportional to the initial and deferred costs for the primary equipment types that were considered and that annual operating cost is proportional to the direct labor costs that were determined based on primary equipment quantities.) Initial capital costs ranged from $3,910,470 in Central Appalachia to $49,296,785; deferred capital costs ranged from $3,220,000 in Central Appalachia to $30,735,000 in Campbell County, Wyoming; and annual operating costs ranged from $2,924,148 in Central Appalachia to $32,708,591 in Campbell County, Wyoming. (DMC)
Solving the Schroedinger equation using Smolyak interpolants
Avila, Gustavo; Carrington, Tucker Jr.
In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased.
Sandia Equation of State Model Library
Energy Science and Technology Software Center (OSTI)
The software provides a general interface for querying thermodynamic states of material models along with implementation of both general and specific equation of state models. In particular, models are provided for the IAPWS-IF97 and IAPWS95 water standards as well as the associated water standards for viscosity, thermal conductivity, and surface tension. The interface supports implementation of models in a variety of independent variable spaces. Also, model support routines are included that allow for coupling ofmore » models and determination and representation of phase boundaries.« less
Canonical equations of ideal magnetic hydrodynamics
Gorskii, V.B.
Ideal magnetohydrodynamics is used to consider a general class of adiabatic flow in magnetic liquids. Two invariants of the canonical equations of motion--Hamiltonian and Lagrangian--are determined in terms of the canonical variables by using the approximate variational formulations. The resulting model describes adiabatic three-dimensional flow of a nonviscous compressible liquid with ideal electric conductivity and zero heat conductivity. A Clebsch transformation is used to arrive at a form of the Lagrange-Cauchy integral for a vortex flow.
Propagation of ultra-short solitons in stochastic Maxwell's equations
Kurt, Levent; Sch�fer, Tobias
We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.
Differential form of the Skornyakov-Ter-Martirosyan Equations
Pen'kov, F. M.; Sandhas, W.
The Skornyakov-Ter-Martirosyan three-boson integral equations in momentum space are transformed into differential equations. This allows us to take into account quite directly the Danilov condition providing self-adjointness of the underlying three-body Hamiltonian with zero-range pair interactions. For the helium trimer the numerical solutions of the resulting differential equations are compared with those of the Faddeev-type AGS equations.
Thermal equation of state and spin transition of magnesiosiderite...
Office of Scientific and Technical Information (OSTI)
Citation Details In-Document Search Title: Thermal equation of ... Subject: catalysis (heterogeneous), solar (photovoltaic), phonons, thermoelectric, energy storage (including ...
Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order
Favalli, Andrea; Croft, Stephen; Santi, Peter
Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclear data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This study represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.
Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Favalli, Andrea; Croft, Stephen; Santi, Peter
Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclearmore » data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This study represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.« less
Efficient Solution of the Simplified PN Equations
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Hamilton, Steven P; Evans, Thomas M
In this paper we show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy a robust set of solution strategies may be applied. Power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi's method, and a generalized Davidson method, each using algebraic and physics-based multigrid preconditioners, have been compared on C5G7 MOX test problem as well as an operational PWR model. Our results show that the most ecient approach is the generalized Davidson method, that is 30{40 times faster than traditional power iteration and 6{10 times faster thanmore » Arnoldi's method.« less
The Raychaudhuri equation in homogeneous cosmologies
Albareti, F.D.; Cembranos, J.A.R.; Cruz-Dombriz, A. de la; Dobado, A. E-mail: email@example.com E-mail: email@example.com
In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of Friedmann-Robertson-Walker as well as more general Bianchi Type I spacetimes. The fulfillment of the Focusing Theorem is mandatory in small scales since it accounts for the attractive character of gravity. However, the Focusing Theorem is not satisfied at cosmological scales due to the measured negative deceleration parameter. The study of the conditions needed for congruences convergence is not only relevant at the fundamental level but also to derive the viability conditions to be imposed on extended theories of gravity describing the different expansion regimes of the universe. We illustrate this idea for f(R) gravity theories.
Equations determine coiled tubing collapse pressure
Avakov, V.; Taliaferro, W.
A set of equations has been developed for calculating pipe collapse pressure for oval tubing such as coiled tubing. When coiled tubing is placed onto a reel, the tubing is forced into an oval shape and never again returns to perfect roundness because the coiling process exceeds the plasticity limits of the tubing. Straightening the tubing for the trip into the well does not restore roundness. The consequence of this physical property is that all coiled tubing collapse pressure calculations should be made considering oval tubing, not round tubing. Tubing collapse can occur when formation pressure against the coiled tubing exceeds the collapse resistance inherent in the coiled tubing. As coiled tubing becomes more oval in shape, it becomes more oval in shape, it becomes more susceptible to collapse from outside pressure.
Assessment of UF6 Equation of State
Brady, P; Chand, K; Warren, D; Vandersall, J
A common assumption in the mathematical analysis of flows of compressible fluids is to treat the fluid as a perfect gas. This is an approximation, as no real fluid obeys the perfect gas relationships over all temperature and pressure conditions. An assessment of the validity of treating the UF{sub 6} gas flow field within a gas centrifuge with perfect gas relationships has been conducted. The definition of a perfect gas is commonly stated in two parts: (1) the gas obeys the thermal equation of state, p = {rho}RT (thermally perfect), and, (2) the gas specific heats are constant (calorically perfect). Analysis indicates the thermally perfect assumption is valid for all flow conditions within the gas centrifuge, including shock fields. The low operating gas pressure is the primary factor in the suitability of the thermally perfect equation of state for gas centrifuge computations. UF{sub 6} is not calorically perfect, as the specific heats vary as a function of temperature. This effect is insignificant within the bulk of the centrifuge gas field, as gas temperatures vary over a narrow range. The exception is in the vicinity of shock fields, where temperature, pressure, and density gradients are large, and the variation of specific heats with temperature should be included in the technically detailed analyses. Results from a normal shock analysis incorporating variable specific heats is included herein, presented in the conventional form of shock parameters as a function of inlet Mach Number. The error introduced by assuming constant specific heats is small for a nominal UF{sub 6} shock field, such that calorically perfect shock relationships can be used for scaling and initial analyses. The more rigorous imperfect gas analysis should be used for detailed analyses.
A Reconstructed Discontinuous Galerkin Method for the Euler Equations on
Office of Scientific and Technical Information (OSTI)
Arbitrary Grids (Journal Article) | SciTech Connect Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids Citation Details In-Document Search Title: A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction,
Validity of ELTB Equation for Suitable Description of BEC
Kim, Dooyoung; Kim, Jinguanghao; Yoon, Jin-Hee
The Bose-Einstein condensation (BEC) has been found for various alkali-metal gases such as 7Li, 87Rb, Na, and H. For the description of atoms in this condensate state, the Gross-Pitaevskii (GP) equation has been widely used. However, the GP equation contains the nonlinear term, which makes this equation hard to solve. Therefore, physical quantities are usually obtained numerically, and sometimes it is difficult to extract a physical meaning from the calculated results. The nuclear theory group at Purdue University in the U.S. developed a new simple equation, the equivalent linear two-body (ELTB) equation, using the hyper-radius coordinates and tested it for one-dimensional BEC system. Their results are consistent with the numerical values from the GP equation within 4.5%.We test the validity of the ELTB equation for three-dimensional BEC system by calculating the energies per particle and the wave functions for 87Rb gas and for 7Li gas. We use the quantum-mechanical variational method for the BEC energy. Our result for 87Rb gas agrees with a numerical calculation based on the GP equation, with a relative error of 12% over a wide range of N from 100 to 10,000. The relative distances between particles for 7Li gas are consistent within a relative error of 17% for N {<=} 1300. The relatively simple form of the ELTB equation, compared with the GP equation, enables us to treat the N-body system easily and efficiently. We conclude that the ELTB equation is a powerful equation for describing BEC system because it is easy to treat.
SCIENCE ON SATURDAY- "Disastrous Equations: The Role of Mathematics...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
SCIENCE ON SATURDAY- "Disastrous Equations: The Role of Mathematics in Understanding Tsunami" Professor J. Douglas Wright, Associate Professor Department of Mathematics, Drexel ...
An Acoustic Wave Equation for Tilted Transversely Isotropic Media...
Office of Scientific and Technical Information (OSTI)
Citation Details In-Document Search Title: An Acoustic Wave Equation for Tilted Transversely Isotropic Media A finite-difference method for computing the first arrival traveltimes ...
Scientists compose complex math equations to replicate behaviors...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Climate Models: Rob Jacob Scientists compose complex math equations to replicate behaviors ... It's math in action. A global model depends on submodels Submodels can be broken into two ...
Solving the power flow equations: a monotone operator approach...
Office of Scientific and Technical Information (OSTI)
The AC power flow equations underlie all operational aspects of power systems. They are solved routinely in operational practice using the Newton-Raphson method and its variants. ...
Strategic Petroleum Reserve equation of state model development...
Office of Scientific and Technical Information (OSTI)
Strategic Petroleum Reserve equation of state model development : current performance against measured data. Citation Details In-Document Search Title: Strategic Petroleum Reserve ...
Felix Bloch, Nuclear Induction, Bloch Equations, Bloch Theorem...
Office of Scientific and Technical Information (OSTI)
Felix Bloch, Nuclear Induction, and Bloch Equations Resources with Additional Information ... for the 'development of new methods for nuclear magnetic precision measurements and ...
Stochastic finite element methods for partial differential equations...
Office of Scientific and Technical Information (OSTI)
Journal Article: Stochastic finite element methods for partial differential equations with random input data Citation Details In-Document Search Title: Stochastic finite element ...
Penetration equations Young, C.W. [Applied Research Associates...
Office of Scientific and Technical Information (OSTI)
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEFENSE; EARTH PENETRATORS; EQUATIONS; NUCLEAR WEAPONS; SOILS; ICE; ROCKS; CONCRETES; PERMAFROST; SCALING LAWS In 1967, Sandia...
Covariant functional diffusion equation for Polyakov's bosonic string
Botelho, L. C. L.
I write a covariant functional diffusion equation for Polyakov's bosonic string with the string's world-sheet area playing the role of proper time.
A Least-Squares Transport Equation Compatible with Voids
Hansen, Jon [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering; Peterson, Jacob [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering; Morel, Jim [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering; Ragusa, Jean [Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering; Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States)
Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transport equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares Sn formulation represents an excellent alternative to existing second-order Sn transport formulations
The study of nonlinear almost periodic differential equations without recourse to the H-classes of these equations
Slyusarchuk, V. E. E-mail: firstname.lastname@example.com
The well-known theorems of Favard and Amerio on the existence of almost periodic solutions to linear and nonlinear almost periodic differential equations depend to a large extent on the H-classes and the requirement that the bounded solutions of these equations be separated. The present paper provides different conditions for the existence of almost periodic solutions. These conditions, which do not depend on the H-classes of the equations, are formulated in terms of a special functional on the set of bounded solutions of the equations under consideration. This functional is used, in particular, to test whether solutions are separated. Bibliography: 24 titles. (paper)
Stochastic differential equations and numerical simulation for pedestrians
Garrison, J.C.
The mathematical foundation of the Ito interpretation of stochastic ordinary and partial differential equations is briefly explained. This provides the basis for a review of simple difference approximations to stochastic differential equations. An example arising in the theory of optical switching is discussed.
Stable Difference Schemes for the Neutron Transport Equation
Ashyralyev, Allaberen; Taskin, Abdulgafur
The initial boundary value problem for the neutron transport equation is considered. The first and second orders of accuracy difference schemes for the approximate solution of this problem are presented. In applications, the stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained. Numerical techniques are developed and algorithms are tested on an example in MATLAB.
The modified equation for spinless particles and superalgebra
Sadeghi, J.; Rostami, M.; Sadeghi, Z.
In this paper we consider modified wave equations for spinless particles in an external magnetic field. We consider 4-potentials which guarantee Lorentz' and Coulomb's conditions. The new variable for modified wave equation leads us to consider the associated Laguerre differential equation. We take advantage of the factorization method in Laguerre differential equation and solve the modified equation. In order to obtain the wave function, energy spectrum and its quantization, we will establish conditions for the orbital quantum number. We account such orbital quantum number and obtain the raising and lowering operators. If we want to have supersymmetry partners, we need to apply the shape invariance condition. This condition for the partner potential will help us find the limit of ? as ?=�?(l)
BHR equations re-derived with immiscible particle effects
Schwarzkopf, John Dennis; Horwitz, Jeremy A.
Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied to the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.
New Dirac equation from the view point of particle
Ozaydin, Fatih; Altintas, Azmi Ali; Susam, Lidya Amon; Arik, Metin; Yarman, Tolga
According to the classical approach, especially the Lorentz Invariant Dirac Equation, when particles are bound to each other, the interaction term appears as a quantity belonging to the 'field'. In this work, as a totally new approach, we propose to alter the rest masses of the particles due to their interaction, as much as their respective contributions to the static binding energy. Thus we re-write and solve the Dirac Equation for the hydrogen atom, and amazingly, obtain practically the same numerical results for the ground states, as those obtained from the Dirac Equation.
Variational principles for eigenvalues of the Klein-Gordon equation
Langer, Matthias; Tretter, Christiane
In this paper variational principles for eigenvalues of an abstract model of the Klein-Gordon equation with electromagnetic potential are established. They are used to characterize and estimate eigenvalues in cases where the essential spectrum has a gap around 0, even in the presence of complex eigenvalues. As a consequence, a comparison between eigenvalues of the Klein-Gordon equation in R{sup d} and eigenvalues of certain Schroedinger operators is obtained. The results are illustrated on examples including the Klein-Gordon equation with Coulomb and square-well potential.
The fundamental solution of the unidirectional pulse propagation equation
Babushkin, I.; Bergé, L.
The fundamental solution of a variant of the three-dimensional wave equation known as "unidirectional pulse propagation equation" (UPPE) and its paraxial approximation is obtained. It is shown that the fundamental solution can be presented as a projection of a fundamental solution of the wave equation to some functional subspace. We discuss the degree of equivalence of the UPPE and the wave equation in this respect. In particular, we show that the UPPE, in contrast to the common belief, describes wave propagation in both longitudinal and temporal directions, and, thereby, its fundamental solution possesses a non-causal character.
Exact solution of the self-consistent Vlasov equation
Morawetz, K.
An analytical solution of the self-consistent Vlasov equation is presented. The time evolution is entirely determined by the initial distribution function. The largest Lyapunov exponent is calculated analytically. For special parameters of the potential a positive Lyapunov exponent is possible. This model may serve as a check for numerical codes solving self-consistent Vlasov equations. The here presented method is also applicable for any system with an analytical solution of the Hamilton equation for the form factor of the potential. {copyright} {ital 1997} {ital The American Physical Society}
Equator Appliance: ENERGY STAR Referral (EZ 3720 CEE)
Broader source: Energy.gov [DOE]
DOE referred the matter of Equator clothes washer model EZ 3720 CEE to the EPA for appropriate action after DOE testing showed that the model does not meet the ENERGY STAR specification.
Electrolux Gibson Air Conditioner and Equator Clothes Washer...
Broader source: Energy.gov (indexed) [DOE]
ENERGY STAR program has revealed that an Electrolux Gibson air conditioner (model GAH105Q2T1) and an Equator clothes washer (model EZ 3720 CEE), both of which claimed ENERGY STAR...
Development of one-equation transition/turbulence models
Edwards, J.R.; Roy, C.J.; Blottner, F.G.; Hassan, H.A.
This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity--transport equation for nonturbulent fluctuation growth based on that proposed by Warren and Hassan is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittency function based on the work of Dhawan and Narasimha. The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the grid-dependence of selected predictions is analyzed.
Stochastic finite element methods for partial differential equations with
Office of Scientific and Technical Information (OSTI)
random input data (Journal Article) | SciTech Connect Journal Article: Stochastic finite element methods for partial differential equations with random input data Citation Details In-Document Search Title: Stochastic finite element methods for partial differential equations with random input data Authors: Gunzburger, Max D [1] ; Webster, Clayton G [1] ; Zhang, Guannan [1] + Show Author Affiliations ORNL Publication Date: 2014-01-01 OSTI Identifier: 1159494 DOE Contract Number:
Adjoint Fokker-Planck equation and runaway electron dynamics (Journal
Office of Scientific and Technical Information (OSTI)
Article) | SciTech Connect Adjoint Fokker-Planck equation and runaway electron dynamics Citation Details In-Document Search This content will become publicly available on January 13, 2017 Title: Adjoint Fokker-Planck equation and runaway electron dynamics Authors: Liu, Chang [1] ; Brennan, Dylan P. [1] ; Bhattacharjee, Amitava [1] ; Boozer, Allen H. [2] + Show Author Affiliations Princeton University, Princeton, New Jersey 08544, USA Columbia University, New York, New York 10027, USA
Notes on the Lumped Backward Master Equation for the Neutron
Office of Scientific and Technical Information (OSTI)
Extinction/Survival Probability (Technical Report) | SciTech Connect Technical Report: Notes on the Lumped Backward Master Equation for the Neutron Extinction/Survival Probability Citation Details In-Document Search Title: Notes on the Lumped Backward Master Equation for the Neutron Extinction/Survival Probability The expected or mean neutron number (or density) provides an adequate characterization of the neutron population and its dynamical excursions in most neutronic applications, in
Renormalization group equations in a model of generalized hidden local
Office of Scientific and Technical Information (OSTI)
symmetry and restoration of chiral symmetry (Journal Article) | SciTech Connect Renormalization group equations in a model of generalized hidden local symmetry and restoration of chiral symmetry Citation Details In-Document Search Title: Renormalization group equations in a model of generalized hidden local symmetry and restoration of chiral symmetry We study possible restoration patterns of chiral symmetry in a generalized hidden local symmetry model, which is a low-energy effective theory
Renormalization group functional equations (Journal Article) | SciTech
Office of Scientific and Technical Information (OSTI)
Connect group functional equations Citation Details In-Document Search Title: Renormalization group functional equations Authors: Curtright, Thomas L. ; Zachos, Cosmas K. Publication Date: 2011-03-16 OSTI Identifier: 1100055 Type: Publisher's Accepted Manuscript Journal Name: Physical Review D Additional Journal Information: Journal Volume: 83; Journal Issue: 6; Journal ID: ISSN 1550-7998 Publisher: American Physical Society Sponsoring Org: USDOE Country of Publication: United States
Multifractal analysis of time series generated by discrete Ito equations
Telesca, Luciano; Czechowski, Zbigniew; Lovallo, Michele
In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.
Multibump solutions for quasilinear elliptic equations with critical growth
Liu, Jiaquan; Wang, Zhi-Qiang; Wu, Xian
The current paper is concerned with constructing multibump solutions for a class of quasilinear Schr�dinger equations with critical growth. This extends the classical results of Coti Zelati and Rabinowitz [Commun. Pure Appl. Math. 45, 1217�1269 (1992)] for semilinear equations as well as recent work of Liu, Wang, and Guo [J. Funct. Anal. 262, 4040�4102 (2012)] for quasilinear problems with subcritical growth. The periodicity of the potentials is used to glue ground state solutions to construct multibump bound state solutions.
Optimization of High-order Wave Equations for Multicore CPUs
Energy Science and Technology Software Center (OSTI)
This is a simple benchmark to guage the performance of a high-order isotropic wave equation grid. The code is optimized for both SSE and AVX and is parallelized using OpenMP (see Optimization section). Structurally, the benchmark begins, reads a few command-line parameters, allocates and pads the four arrays (current, last, next wave fields, and the spatially varying but isotropic velocity), initializes these arrays, then runs the benchmark proper. The code then benchmarks the naive, SSEmore » (if supported), and AVX (if supported implementations) by applying the wave equation stencil 100 times and taking the average performance. Boundary conditions are ignored and would noiminally be implemented by the user. THus, the benchmark measures only the performance of the wave equation stencil and not a full simulation. The naive implementation is a quadruply (z,y,x, radius) nested loop that can handle arbitrarily order wave equations. The optimized (SSE/AVX) implentations are somewhat more complex as they operate on slabs and include a case statement to select an optimized inner loop depending on wave equation order.« less
Handbook of Industrial Engineering Equations, Formulas, and Calculations
Badiru, Adedeji B; Omitaomu, Olufemi A
The first handbook to focus exclusively on industrial engineering calculations with a correlation to applications, Handbook of Industrial Engineering Equations, Formulas, and Calculations contains a general collection of the mathematical equations often used in the practice of industrial engineering. Many books cover individual areas of engineering and some cover all areas, but none covers industrial engineering specifically, nor do they highlight topics such as project management, materials, and systems engineering from an integrated viewpoint. Written by acclaimed researchers and authors, this concise reference marries theory and practice, making it a versatile and flexible resource. Succinctly formatted for functionality, the book presents: Basic Math Calculations; Engineering Math Calculations; Production Engineering Calculations; Engineering Economics Calculations; Ergonomics Calculations; Facility Layout Calculations; Production Sequencing and Scheduling Calculations; Systems Engineering Calculations; Data Engineering Calculations; Project Engineering Calculations; and Simulation and Statistical Equations. It has been said that engineers make things while industrial engineers make things better. To make something better requires an understanding of its basic characteristics and the underlying equations and calculations that facilitate that understanding. To do this, however, you do not have to be computational experts; you just have to know where to get the computational resources that are needed. This book elucidates the underlying equations that facilitate the understanding required to improve design processes, continuously improving the answer to the age-old question: What is the best way to do a job?
Properties of the Boltzmann equation in the classical approximation
Epelbaum, Thomas; Gelis, François; Tanji, Naoto; Wu, Bin
We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.
Properties of the Boltzmann equation in the classical approximation
Tanji, Naoto; Epelbaum, Thomas; Gelis, Francois; Wu, Bin
We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.
Non-stochastic matrix Schr�dinger equation for open systems
Joubert-Doriol, Lo�c; Ryabinkin, Ilya G.; Izmaylov, Artur F.
We propose an extension of the Schr�dinger equation for a quantum system interacting with environment. This extension describes dynamics of a collection of auxiliary wavefunctions organized as a matrix m, from which the system density matrix can be reconstructed as ?{sup ^}=mm{sup �}. We formulate a compatibility condition, which ensures that the reconstructed density satisfies a given quantum master equation for the system density. The resulting non-stochastic evolution equation preserves positive-definiteness of the system density and is applicable to both Markovian and non-Markovian system-bath treatments. Our formalism also resolves a long-standing problem of energy loss in the time-dependent variational principle applied to mixed states of closed systems.
Properties of the Boltzmann equation in the classical approximation
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Epelbaum, Thomas; Gelis, François; Tanji, Naoto; Wu, Bin
We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since onemore » has also access to the non-approximated result for comparison.« less
Multi-time Schr�dinger equations cannot contain interaction potentials
Petrat, S�ren; Tumulka, Roderich
Multi-time wave functions are wave functions that have a time variable for every particle, such as ?(t{sub 1},x{sub 1},...,t{sub N},x{sub N}). They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schr�dinger equations, one for each time variable. These Schr�dinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for non-interacting particles, it is a challenge to set up consistent multi-time equations with interaction. We prove for a wide class of multi-time Schr�dinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently [S. Petrat and R. Tumulka, �Multi-time wave functions for quantum field theory,� Ann. Physics (to be published)]. We also prove the following result: When a cut-off length ? > 0 is introduced (in the sense that the multi-time wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multi-time Schr�dinger equations with interaction potentials of range ? are consistent; however, in the desired limit ? ? 0 of removing the cut-off, the resulting multi-time equations are interaction-free, which supports the conclusion expressed in the title.
Equation of State Measurements by Radiography Provide Evidence for a
Office of Scientific and Technical Information (OSTI)
Liquid-Liquid Phase Transition in Cerium (Journal Article) | SciTech Connect Equation of State Measurements by Radiography Provide Evidence for a Liquid-Liquid Phase Transition in Cerium Citation Details In-Document Search Title: Equation of State Measurements by Radiography Provide Evidence for a Liquid-Liquid Phase Transition in Cerium Authors: Lipp, M J ; Jenei, Z ; Ruddle, D ; Aracne-Ruddle, C ; Cynn, H ; Evans, W J ; Kono, Y ; Kenney-Benson, C ; Park, C Publication Date: 2013-08-26 OSTI
Equation of state measurements by radiography provide evidence for a
Office of Scientific and Technical Information (OSTI)
liquid-liquid phase transition in cerium (Journal Article) | SciTech Connect Equation of state measurements by radiography provide evidence for a liquid-liquid phase transition in cerium Citation Details In-Document Search Title: Equation of state measurements by radiography provide evidence for a liquid-liquid phase transition in cerium Authors: Lipp, M.J. ; Jenei, Zs. ; Ruddle, D. ; Aracne-Ruddle, C. ; Cynn, H. ; Evans, W.J. ; Kono, Y. ; Kenney-Benson, C. ; Park, C. [1] ; CIW) [2] + Show
Illite Dissolution Rates and Equation (100 to 280 dec C)
DOE Data Explorer [Office of Scientific and Technical Information (OSTI)]
Carroll, Susan
The objective of this suite of experiments was to develop a useful kinetic dissolution expression for illite applicable over an expanded range of solution pH and temperature conditions representative of subsurface conditions in natural and/or engineered geothermal reservoirs. Using our new data, the resulting rate equation is dependent on both pH and temperature and utilizes two specific dissolution mechanisms (a �neutral� and a �basic� mechanism). The form of this rate equation should be easily incorporated into most existing reactive transport codes for to predict rock-water interactions in EGS shear zones.
Equations of state and phase diagrams of hydrogen isotopes
Urlin, V. D.
A new form of the semiempirical equation of state proposed for the liquid phase of hydrogen isotopes is based on the assumption that its structure is formed by cells some of which contain hydrogen molecules and others contain hydrogen atoms. The values of parameters in the equations of state of the solid (molecular and atomic) phases as well as of the liquid phase of hydrogen isotopes (protium and deuterium) are determined. Phase diagrams, shock adiabats, isentropes, isotherms, and the electrical conductivity of compressed hydrogen are calculated. Comparison of the results of calculations with available experimental data in a wide pressure range demonstrates satisfactory coincidence.
Thermodynamically constrained correction to ab initio equations of state
French, Martin; Mattsson, Thomas R.
We show how equations of state generated by density functional theory methods can be augmented to match experimental data without distorting the correct behavior in the high- and low-density limits. The technique is thermodynamically consistent and relies on knowledge of the density and bulk modulus at a reference state and an estimation of the critical density of the liquid phase. We apply the method to four materials representing different classes of solids: carbon, molybdenum, lithium, and lithium fluoride. It is demonstrated that the corrected equations of state for both the liquid and solid phases show a significantly reduced dependence of the exchange-correlation functional used.
Illite Dissolution Rates and Equation (100 to 280 dec C)
DOE Data Explorer [Office of Scientific and Technical Information (OSTI)]
Carroll, Susan
The objective of this suite of experiments was to develop a useful kinetic dissolution expression for illite applicable over an expanded range of solution pH and temperature conditions representative of subsurface conditions in natural and/or engineered geothermal reservoirs. Using our new data, the resulting rate equation is dependent on both pH and temperature and utilizes two specific dissolution mechanisms (a �neutral� and a �basic� mechanism). The form of this rate equation should be easily incorporated into most existing reactive transport codes for to predict rock-water interactions in EGS shear zones.
Illite Dissolution Rates and Equation (100 to 280 dec C)
DOE Data Explorer [Office of Scientific and Technical Information (OSTI)]
Carroll, Susan
The objective of this suite of experiments was to develop a useful kinetic dissolution expression for illite applicable over an expanded range of solution pH and temperature conditions representative of subsurface conditions in natural and/or engineered geothermal reservoirs. Using our new data, the resulting rate equation is dependent on both pH and temperature and utilizes two specific dissolution mechanisms (a "neutral" and a "basic" mechanism). The form of this rate equation should be easily incorporated into most existing reactive transport codes for to predict rock-water interactions in EGS shear zones.
Equation of State measurements of hydrogen isotopes on Nova
Collins, G. W., LLNL
High intensity lasers can be used to perform measurements of materials at extremely high pressures if certain experimental issues can be overcome. We have addressed those issues and used the Nova laser to shock-compress liquid deuterium and obtain measurements of density and pressure on the principal Hugoniot at pressures from 300 kbar to more than 2 Mbar. The data are compared with a number of equation of state models. The data indicate that the effect of molecular dissociation of the deuterium into a monatomic phase may have a significant impact on the equation of state near 1 Mbar.
Ideal solar cell equation in the presence of photon recycling
Lan, Dongchen Green, Martin A.
Previous derivations of the ideal solar cell equation based on Shockley's p-n junction diode theory implicitly assume negligible effects of photon recycling. This paper derives the equation in the presence of photon recycling that modifies the values of dark saturation and light-generated currents, using an approach applicable to arbitrary three-dimensional geometries with arbitrary doping profile and variable band gap. The work also corrects an error in previous work and proves the validity of the reciprocity theorem for charge collection in such a more general case with the previously neglected junction depletion region included.
Levinson theorem for the Dirac equation in D+1 dimensions
Gu Xiaoyan; Ma Zhongqi; Dong Shihai
In terms of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation with a spherically symmetric potential in D+1 dimensions is uniformly established as a relation between the total number of bound states and the sum of the phase shifts of the scattering states at E={+-}M with a given angular momentum. The critical case, where the Dirac equation has a half bound state, is analyzed in detail. A half bound state is a zero-momentum solution if its wave function is finite but does not decay fast enough at infinity to be square integrable.
Simplified P N Equations Steven P. Hamilton, Thomas M. Evans
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Efficient Solution of the Simplified P N Equations Steven P. Hamilton, Thomas M. Evans Oak Ridge National Laboratory December 29, 2014 CASL-U-2014-0352-000 Efficient solution of the simplified P N equations $ Steven P. Hamilton a,1,∗ , Thomas M. Evans a,1 a Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN 37831 U.S.A. Abstract In this paper we show new solver strategies for the multigroup SP N equa- tions for nuclear reactor analysis. By forming the complete matrix over space,
Dirac equation in low dimensions: The factorization method
S�nchez-Monroy, J.A.; Quimbay, C.J.
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein�Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials. - Highlights: � The low-dimensional Dirac equation in the presence of static potentials is solved. � The factorization method is generalized for energy-dependent Hamiltonians. � The shape invariance is generalized for energy-dependent Hamiltonians. � The stability of the Dirac sea is related to the existence of supersymmetric partner Hamiltonians.
Solves Poisson's Equation in Axizymmetric Geometry on a Rectangular Mesh
Energy Science and Technology Software Center (OSTI)
DATHETA4.0 computes the magnetostatic field produced by multiple point current sources in the presence of perfect conductors in axisymmetric geometry. DATHETA4.0 has an interactive user interface and solves Poisson''s equation using the ADI method on a rectangular finite-difference mesh. DATHETA4.0 uncludes models specific to applied-B ion diodes.
Gravitational lens equation for embedded lenses; magnification and ellipticity
Chen, B.; Kantowski, R.; Dai, X.
We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches the observer. We call this deflector an embedded lens because the deflecting mass is part of the mean density. The embedded lens equation differs from the conventional lens equation because the deflector mass is not simply an addition to the cosmic mean. We prescribe an iteration scheme to solve this new lens equation and use it to compare our results with standard linear lensing theory. We also compute analytic expressions for the lowest order corrections to image amplifications and distortions caused by incorporating the lensing mass into the mean. We use these results to estimate the effect of embedding on strong lensing magnifications and ellipticities and find only small effects, <1%, contrary to what we have found for time delays and for weak lensing, {approx}5%.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
National Lab Uses OGJ Data to Develop Cost Equations
Brown, Daryl R.; Cabe, James E.; Stout, Tyson E.
For the past 30 years, the Oil and Gas Journal (OGJ) has published data on the costs of onshore and offshore oil and gas pipelines and related equipment. This article describes the methodology employed and resulting equations developed for conceptual capital cost estimating of onshore pipelines. Also described are cost trends uncovered during the course of the analysis.
Development of a One-Equation Transition/Turbulence Model
This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity - transport equation for non-turbulent fluctuation growth based on that proposed by Warren and Hassan (Journal of Aircraft, Vol. 35, No. 5) is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittence function based on the work of Dhawan and Narasimha (Journal of Fluid Mechanics, Vol. 3, No. 4). The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the spatial accuracy of selected predictions is analyzed.
Vorticity Preserving Flux Corrected Transport Scheme for the Acoustic Equations
Lung, Tyler B.; Roe, Phil; Morgan, Nathaniel R.
Long term research goals are to develop an improved cell-centered Lagrangian Hydro algorithm with the following qualities: 1. Utilizes Flux Corrected Transport (FCT) to achieve second order accuracy with multidimensional physics; 2. Does not rely on the one-dimensional Riemann problem; and 3. Implements a form of vorticity control. Short term research goals are to devise and implement a 2D vorticity preserving FCT solver for the acoustic equations on an Eulerian mesh: 1. Develop a flux limiting mechanism for systems of governing equations with symmetric wave speeds; 2. Verify the vorticity preserving properties of the scheme; and 3. Compare the performance of the scheme to traditional MUSCL-Hancock and other algorithms.
Boltzmann equation solver adapted to emergent chemical non-equilibrium
Birrell, Jeremiah; Wilkening, Jon; Rafelski, Johann
We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature T(t) and phase space occupation factor ?(t). In this first paper we address (effectively) massless fermions and derive dynamical equations for T(t) and ?(t) such that the zeroth order term of the basis alone captures the particle number density and energy density of each particle distribution. We validate our method and illustrate the reduced computational cost and the ability to easily represent final state chemical non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component (e{sup �}-annihilation)
Eternal inflation and a thermodynamic treatment of Einstein's equations
Ghersi, José Tomás Gálvez; Geshnizjani, Ghazal; Shandera, Sarah; Piazza, Federico E-mail: firstname.lastname@example.com E-mail: firstname.lastname@example.com
In pursuing the intriguing resemblance of the Einstein equations to thermodynamic equations, most sharply seen in systems possessing horizons, we suggest that eternal inflation of the stochastic type may be a fruitful phenomenon to explore. We develop a thermodynamic first law for quasi-de Sitter space, valid on the horizon of a single observer's Hubble patch and explore consistancy with previous proposals for horizons of various types in dynamic and static situations. We use this framework to demonstrate that for the local observer fluctuations of the type necessary for stochastic eternal inflation fall within the regime where the thermodynamic approach is believed to apply. This scenario is interesting because of suggestive parallels with black hole evaporation.
Numerical solution of three-dimensional magnetic differential equations
Reiman, A.H.; Greenside, H.S.
A computer code is described that solves differential equations of the form B . del f = h for a single-valued solution f, given a toroidal three-dimensional divergence-free field B and a single-valued function h. The code uses a new algorithm that Fourier decomposes a given function in a set of flux coordinates in which the field lines are straight. The algorithm automatically adjusts the required integration lengths to compensate for proximity to low order rational surfaces. Applying this algorithm to the Cartesian coordinates defines a transformation to magnetic coordinates, in which the magnetic differential equation can be accurately solved. Our method is illustrated by calculating the Pfirsch-Schlueter currents for a stellarator.
Quantum Markovian master equation for scattering from surfaces
Li, Haifeng; Shao, Jiushu; Azuri, Asaf; Pollak, Eli Alicki, Robert
We propose a semi-phenomenological Markovian Master equation for describing the quantum dynamics of atom-surface scattering. It embodies the Lindblad-like structure and can describe both damping and pumping of energy between the system and the bath. It preserves positivity and correctly accounts for the vanishing of the interaction of the particle with the surface when the particle is distant from the surface. As a numerical test, we apply it to a model of an Ar atom scattered from a LiF surface, allowing for interaction only in the vertical direction. At low temperatures, we find that the quantum mechanical average energy loss is smaller than the classical energy loss. The numerical results obtained from the space dependent friction master equation are compared with numerical simulations for a discretized bath, using the multi-configurational time dependent Hartree methodology. The agreement between the two simulations is quantitative.
Higher order matrix differential equations with singular coefficient matrices
Fragkoulis, V. C.; Kougioumtzoglou, I. A.; Pantelous, A. A.; Pirrotta, A.
In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.
Scientists compose complex math equations to replicate behaviors of Earth
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
systems | Argonne National Laboratory Rob Jacob talks about climate models Climate Models: Rob Jacob Scientists compose complex math equations to replicate behaviors of Earth systems By Angela Hardin * December 16, 2015 Tweet EmailPrint Whenever news breaks about what Earth's climate is expected to be like decades into the future or how much rainfall various regions around the country or the world are likely to receive, those educated estimates are generated by a global climate model. But
Method of comparison equations for Schwarzschild black holes
Casadio, Roberto; Luzzi, Mattia
We employ the method of comparison equations to study the propagation of a massless minimally coupled scalar field on the Schwarzschild background. In particular, we show that this method allows us to obtain explicit approximate expressions for the radial modes with energy below the peak of the effective potential which are fairly accurate over the whole region outside the horizon. This case can be of particular interest, for example, for the problem of black hole evaporation.
Time-periodic solutions of the Benjamin-Ono equation
Ambrose , D.M.; Wilkening, Jon
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one of the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.
Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach
Toutounji, Mohamad
This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.
Development and Application of Compatible Discretizations of Maxwell's Equations
White, D; Koning, J; Rieben, R
We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we have designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve.
Real-time nonlinear optimization as a generalized equation.
Zavala, V. M.; Anitescu, M. (Mathematics and Computer Science)
We establish results for the problem of tracking a time-dependent manifold arising in real-time optimization by casting this as a parametric generalized equation. We demonstrate that if points along a solution manifold are consistently strongly regular, it is possible to track the manifold approximately by solving a single linear complementarity problem (LCP) at each time step. We derive sufficient conditions guaranteeing that the tracking error remains bounded to second order with the size of the time step even if the LCP is solved only approximately. We use these results to derive a fast, augmented Lagrangian tracking algorithm and demonstrate the developments through a numerical case study.
Heart simulation with surface equations for using on MCNP code
Rezaei-Ochbelagh, D.; Salman-Nezhad, S.; Asadi, A.; Rahimi, A.
External photon beam radiotherapy is carried out in a way to achieve an 'as low as possible' a dose in healthy tissues surrounding the target. One of these surroundings can be heart as a vital organ of body. As it is impossible to directly determine the absorbed dose by heart, using phantoms is one way to acquire information around it. The other way is Monte Carlo method. In this work we have presented a simulation of heart geometry by introducing of different surfaces in MCNP code. We used 14 surface equations in order to determine human heart modeling. Those surfaces are borders of heart walls and contents.
CDF Solutions of Buckley-Leverett Equation with Uncertain Parameters
Wang, Peng; Tartakovsky, Daniel M.; Jarman, Kenneth D.; Tartakovsky, Alexandre M.
The Buckley-Leverett (nonlinear advection) equation is often used to describe two-phase flow in porous media. We develop a new probabilistic method to quantify parametric uncertainty in the Buckley-Leverett model. Our approach is based on the concept of fine-grained cumulative density function (CDF) and provides a full statistical description of the system states. Hence, it enables one to obtain not only average system response but also the probability of rare events, which is critical for risk assessment. We obtain a closed-form, semi-analytical solution and test it against the results from Monte Carlo simulations.
Fire Intensity Data for Validation of the Radiative Transfer Equation
Blanchat, Thomas K.; Jernigan, Dann A.
A set of experiments and test data are outlined in this report that provides radiation intensity data for the validation of models for the radiative transfer equation. The experiments were performed with lightly-sooting liquid hydrocarbon fuels that yielded fully turbulent fires 2 m diameter). In addition, supplemental measurements of air flow and temperature, fuel temperature and burn rate, and flame surface emissive power, wall heat, and flame height and width provide a complete set of boundary condition data needed for validation of models used in fire simulations.
The Equation of State of LLM-105 (2,6-diamino-3,5-dinitropyrazine...
Office of Scientific and Technical Information (OSTI)
The Equation of State of LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide) Citation Details In-Document Search Title: The Equation of State of LLM-105 (2,6-diamino-3,5-dinitropyraz...
Thermal equation of state and stability of (Mg[subscript 0.06...
Office of Scientific and Technical Information (OSTI)
Thermal equation of state and stability of (Mgsubscript 0.06Fesubscript 0.94)O Citation Details In-Document Search Title: Thermal equation of state and stability of ...
Synthesis and equation of state of perovskite in the (Mg,Fe)...
Office of Scientific and Technical Information (OSTI)
Synthesis and equation of state of perovskite in the (Mg,Fe)subscript 3Alsubscript ... Citation Details In-Document Search Title: Synthesis and equation of state of perovskite ...
Equations of state in the Fe-FeSi system at high pressures and...
Office of Scientific and Technical Information (OSTI)
Equations of state in the Fe-FeSi system at high pressures and temperatures Citation Details In-Document Search Title: Equations of state in the Fe-FeSi system at high pressures ...
Wong's equations and the small x effective action in QCD (Journal...
Office of Scientific and Technical Information (OSTI)
Wong's equations and the small x effective action in QCD Citation Details In-Document Search Title: Wong's equations and the small x effective action in QCD We propose a new form ...
A new high pressure and temperature equation of state of fcc...
Office of Scientific and Technical Information (OSTI)
new high pressure and temperature equation of state of fcc cobalt Citation Details In-Document Search Title: A new high pressure and temperature equation of state of fcc cobalt ...
Phase Diagram and Equation of State of Magnesium to High Pressures...
Office of Scientific and Technical Information (OSTI)
Phase Diagram and Equation of State of Magnesium to High Pressures and High Temperatures Citation Details In-Document Search Title: Phase Diagram and Equation of State of Magnesium ...
Higher-order Schrödinger and Hartree–Fock equations
Carles, Rémi; Lucha, Wolfgang; Moulay, Emmanuel
The domain of validity of the higher-order Schrödinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then, the Cauchy theory for higher-order Hartree–Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for physics.
Necessary Optimality Conditions for Some Control Problems of Elliptic Equations with Venttsel Boundary Conditions
Luo Yousong
In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a control will be minimized. A constraint on the solution of the state equation is also considered.
Thermodynamics of the polaron master equation at finite bias
Krause, Thilo Brandes, Tobias; Schaller, Gernot; Esposito, Massimiliano
We study coherent transport through a double quantum dot. Its two electronic leads induce electronic matter and energy transport and a phonon reservoir contributes further energy exchanges. By treating the system-lead couplings perturbatively, whereas the coupling to vibrations is treated non-perturbatively in a polaron-transformed frame, we derive a thermodynamic consistent low-dimensional master equation. When the number of phonon modes is finite, a Markovian description is only possible when these couple symmetrically to both quantum dots. For a continuum of phonon modes however, also asymmetric couplings can be described with a Markovian master equation. We compute the electronic current and dephasing rate. The electronic current enables transport spectroscopy of the phonon frequency and displays signatures of Franck-Condon blockade. For infinite external bias but finite tunneling bandwidths, we find oscillations in the current as a function of the internal bias due to the electron-phonon coupling. Furthermore, we derive the full fluctuation theorem and show its identity to the entropy production in the system.
Possible ambiguities in the equation of state for neutron stars
Cheoun, Myung-Ki; Miyatsu, Tsuyoshi; Ryu, C. Y.; Deliduman, Cemsinan; G�ng�r, Can; Kele?, Vildan; Kajino, Toshitaka; Mathews, Grant J.
We addressed possible ambiguities on the properties of neutron stars (NSs) estimated in theoretical sides. First, roles of hyperons inside the NS are discussed through various relativistic mean field (RMF) theories. In particular, the extension of SU(6) spin-flavor symmetry to SU(3) flavor symmetry is shown to give rise to the increase of hyperon threshold density, similarly to the Fock term effects in RMF theories. As a result, about 2.0 solar mass is obtained with the hyperons. Second, the effect by the modified f(R) gravity, which leaves a room for the dark energy in the Einstein equation to be taken into account, is discussed for the NS in a strong magnetic field (MF). Our results show that the modified gravity with the Kaluza-Klein electro-magnetism theory expanded in terms of a length scale parameter may reasonably describe the NS in strong MF, so called magnetar. Even the super-soft equation of state is shown to be revived by the modified f(R) gravity.
Nonparametric reconstruction of the dark energy equation of state
Heitmann, Katrin; Holsclaw, Tracy; Alam, Ujjaini; Habib, Salman; Higdon, David; Sanso, Bruno; Lee, Herbie
The major aim of ongoing and upcoming cosmological surveys is to unravel the nature of dark energy. In the absence of a compelling theory to test, a natural approach is to first attempt to characterize the nature of dark energy in detail, the hope being that this will lead to clues about the underlying fundamental theory. A major target in this characterization is the determination of the dynamical properties of the dark energy equation of state w. The discovery of a time variation in w(z) could then lead to insights about the dynamical origin of dark energy. This approach requires a robust and bias-free method for reconstructing w(z) from data, which does not rely on restrictive expansion schemes or assumed functional forms for w(z). We present a new non parametric reconstruction method for the dark energy equation of state based on Gaussian Process models. This method reliably captures nontrivial behavior of w(z) and provides controlled error bounds. We demollstrate the power of the method on different sets of simulated supernova data. The GP model approach is very easily extended to include diverse cosmological probes.
On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations
Christov, Ivan C.
We propose a hierarchy of nonlinearly dispersive generalized Korteweg�de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (�peakompactons�) are presented.
On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Christov, Ivan C.
We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves ("peakompactons") are presented.
Equation of State for Supercooled Water at Pressures up to 400 MPa
Holten, Vincent; Sengers, Jan V.; Anisimov, Mikhail A.
An equation of state is presented for the thermodynamic properties of cold and supercooled water. It is valid for temperatures from the homogeneous ice nucleation temperature up to 300 K and for pressures up to 400 MPa, and can be extrapolated up to 1000 MPa. The equation of state is compared with experimental data for the density, expansion coefficient, isothermal compressibility, speed of sound, and heat capacity. Estimates for the accuracy of the equation are given. The melting curve of ice I is calculated from the phase-equilibrium condition between the proposed equation and an existing equation of state for ice I.
Fraga, Eduardo S.; Kurkela, Aleksi; Vuorinen, Aleksi
Lattice quantum chromodynamics (QCD) studies of the thermodynamics of hot quark-gluon plasma demonstrate the importance of accounting for the interactions of quarks and gluons if one wants to investigate the phase structure of strongly interacting matter. Motivated by this observation and using state-of-the-art results from perturbative QCD, we construct a simple, effective equation of state (EOS) for cold quark matter that consistently incorporates the effects of interactions and furthermore includes a built-in estimate of the inherent systematic uncertainties. This goes beyond the MIT bag model description in a crucial way, yet leads to an EOS that is equally straightforward to use. We also demonstrate that, at moderate densities, our EOS can be made to smoothly connect to hadronic EOSs, with the two exhibiting very similar behavior near the matching region. The resulting hybrid stars are seen to have masses similar to those predicted by the purely nucleonic EOSs.
The isobaric multiplet mass equation for A?71 revisited
Lam, Yi Hua; Blank, Bertram; Smirnova, Nadezda A.; Bueb, Jean Bernard; Antony, Maria Susai
Accurate mass determination of short-lived nuclides by Penning-trap spectrometers and progress in the spectroscopy of proton-rich nuclei have triggered renewed interest in the isobaric multiplet mass equation (IMME). The energy levels of the members of T=1/2,1,3/2, and 2 multiplets and the coefficients of the IMME are tabulated for A?71. The new compilation is based on the most recent mass evaluation (AME2011) and it includes the experimental results on energies of the states evaluated up to end of 2011. Taking into account the error bars, a significant deviation from the quadratic form of the IMME for the A=9,35 quartets and the A=32 quintet is observed.
Levinson theorem for the Dirac equation in one dimension
Ma Zhongqi; Dong Shihai; Wang Luya
The Levinson theorem for the (1+1)-dimensional Dirac equation with a symmetric potential is proved with the Sturm-Liouville theorem. The half-bound states at the energies E={+-}M, whose wave function is finite but does not decay at infinity fast enough to be square integrable, are discussed. The number n{sub {+-}} of bound states is equal to the sum of the phase shifts at the energies E={+-}M:{delta}{sub {+-}}(M)+{delta}{sub {+-}}(-M)=(n{sub {+-}}+a){pi}, where the subscript {+-} denotes the parity and the constant a is equal to -1/2 when no half-bound state occurs, to 0 when one half-bound state occurs at E=M or at E=-M, and to 1/2 when two half-bound states occur at both E={+-}M.
SESAME 7363: A new Li(6)D equation of state
Sheppard, Daniel Glen; Kress, Joel David; Crockett, Scott; Collins, Lee A.; Greeff, Carl William
A new Equation of State (EOS) for Lithium 6 Deuteride (6LiD) was created, sesame 7363. This EOS was released to the user community under "eos-developmental" as sesame 97363. The construction of this new EOS is a modification of a previously released EOS, sesame 73601. Sesame 7360 is too stiff (5-10% excess pressure) at high compressions and high temperatures (ρ = 4-110g/cm3, T = 30-10,000 eV) compared to orbital-free density-functional theory. Sesame 7363 is softer and gives a better representation of the physics over this range without compromising the agreement with the experimental and simulation data that sesame 7360 was based on.
Polynomial solutions of the Monge-Amp�re equation
Aminov, Yu A
The question of the existence of polynomial solutions to the Monge-Amp�re equation z{sub xx}z{sub yy}?z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a�polynomial. It is proved that if f is a�polynomial of the second degree, which is positive for all values of its arguments and has a�positive squared part, then no polynomial solution exists. On the other hand, a�solution which is not polynomial but is analytic in the whole of the x,�y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction of such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.
The one-dimensional Gross-Pitaevskii equation and its some excitation states
Prayitno, T. B.
We have derived some excitation states of the one-dimensional Gross-Pitaevskii equation coupled by the gravitational potential. The methods that we have used here are taken by pursuing the recent work of Kivshar et. al. by considering the equation as a macroscopic quantum oscillator. To obtain the states, we have made the appropriate transformation to reduce the three-dimensional Gross-Pitaevskii equation into the one-dimensional Gross-Pitaevskii equation and applying the time-independent perturbation theory in the general solution of the one-dimensional Gross-Pitaevskii equation as a linear superposition of the normalized eigenfunctions of the Schrödinger equation for the harmonic oscillator potential. Moreover, we also impose the condition by assuming that some terms in the equation should be so small in order to preserve the use of the perturbation method.
Opal equation-of-state tables for astrophysical applications
Rogers, F.J.; Swenson, F.J.; Iglesias, C.A.
OPAL opacities have recently helped to resolve a number of long-standing discrepancies between theory and observation. This success has made it important to provide the associated equation-of-state (EOS) data. The OPAL EOS is based on an activity expansion of the grand canonical partition function of the plasma in terms of its fundamental constituents (electrons and nuclei). The formation of composite particles and many-body effects on the internal bound states occur naturally in this approach. Hence, pressure ionization is a consequence of the theory. In contrast, commonly used approaches, all of which are based on minimization of free energy, are forced to assert the effect of the plasma on composite particles and must rely on an ad hoc treatment of pressure ionization. Another advantage of the OPAL approach is that it provides a systematic expansion in the Coulomb coupling parameter that includes subtle quantum effects generally not considered in other EOS calculations. Tables have been generated that provide pressure, internal energy, entropy, and a variety of derivative quantities. These tables cover a fairly broad range of conditions and compositions applicable to general stellar-evolution calculations for stars more massive than {approximately}0.8 {ital M}{sub {circle_dot}}. An interpolation code is provided along with the tables to facilitate their use. {copyright} {ital 1996 The American Astronomical Society.}
Equations of state and phase transitions in stellar matter
Raduta, Ad. R. [IFIN-HH, Bucharest POB-MG 6 (Romania); Gulminelli, F.; Aymard, F. [CNRS, UMR6534, LPC and ENSICAEN, UMR6534, LPC, F-14050 Caen cedex (France); Oertel, M. [LUTH, CNRS, Observatoire de Paris, Universite Paris Diderot, 92195 Meudon (France); Margueron, J. [IPN, IN2P3-CNRS, Universite Paris-Sud, F-91406 Orsay cedex (France)
Realistic description of core-collapsing supernovae evolution and structure of proto-neutron stars chiefly depends on microphysics input in terms of equations of state, chemical composition and weak interaction rates. At sub-saturation densities the main uncertainty comes from the symmetry energy. Within a nuclear statistical equilibrium (NSE) model with consistent treatment of clusterized and unbound components we investigate the meaning of symmetry energy in the case of dis-homogeneous systems, as the one thought to constitute the neutron star crust, and its sensitivity to the isovector properties of the effective interaction. At supra-saturation densities the situation is much more difficult because of the poor knowledge of nucleon-hyperon and hyperon-hyperon interactions and thermodynamic behavior in terms of phase transitions. Within a simple (np?) model we show that compressed baryonic matter with strangeness manifests a complex phase diagram with first and second order phase transitions. The fact that both are explored under strangeness chemical equilibrium and survive Coulomb suggests that they might have sizable consequences on star evolution. An example in this sense is the drastic reduction of the neutrino-mean free path in the vicinity of the critical point obtained within RPA which would lead to a less rapid star cooling.
Nuclear processing - a simple cost equation or a complex problem?
Banfield, Z.; Banford, A.W.; Hanson, B.C.; Scully, P.J.
BNFL has extensive experience of nuclear processing plant from concept through to decommissioning, at all stages of the fuel cycle. Nexia Solutions (formerly BNFL's R and D Division) has always supported BNFL in development of concept plant, including the development of costed plant designs for the purpose of economic evaluation and technology selection. Having undertaken such studies over a number of years, this has enabled Nexia Solutions to develop a portfolio of costed plant designs for a broad range of nuclear processes, throughputs and technologies. This work has led to an extensive understanding of the relationship of the cost of nuclear processing plant, and how this can be impacted by scale of process, and the selection of design philosophy. The relationship has been seen to be non linear and so simplistic equations do not apply, the relationship is complex due to the variety of contributory factors. This is particularly evident when considering the scale of a process, for example how step changes in design occurs with increasing scale, how the applicability of technology options can vary with scale etc... This paper will explore the contributory factor of scale to nuclear processing plant costs. (authors)
Test plan for validation of the radiative transfer equation.
Ricks, Allen Joseph; Grasser, Thomas W.; Kearney, Sean Patrick; Jernigan, Dann A.; Blanchat, Thomas K.
As the capabilities of numerical simulations increase, decision makers are increasingly relying upon simulations rather than experiments to assess risks across a wide variety of accident scenarios including fires. There are still, however, many aspects of fires that are either not well understood or are difficult to treat from first principles due to the computational expense. For a simulation to be truly predictive and to provide decision makers with information which can be reliably used for risk assessment the remaining physical processes must be studied and suitable models developed for the effects of the physics. A set of experiments are outlined in this report which will provide soot volume fraction/temperature data and heat flux (intensity) data for the validation of models for the radiative transfer equation. In addition, a complete set of boundary condition measurements will be taken to allow full fire predictions for validation of the entire fire model. The experiments will be performed with a lightly-sooting liquid hydrocarbon fuel fire in the fully turbulent scale range (2 m diameter).
Wave�vortex interactions in the nonlinear Schr�dinger equation
Guo, Yuan B�hler, Oliver
This is a theoretical study of wave�vortex interaction effects in the two-dimensional nonlinear Schr�dinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wave�vortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wave�vortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.
An Improved Reaction Rate Equation for Simulating the Ignition and Growth of Reaction in High Explosives
Murphy, M J
We describe an improved reaction rate equation for simulating ignition and growth of reaction in high explosives. It has been implemented into CALE and ALE3D as an alternate to the baseline the Lee-Tarver reactive flow model. The reactive flow model treats the explosive in two phases (unreacted/reactants and reacted/products) with a reaction rate equation to determine the fraction reacted, F. The improved rate equation has fewer parameters, is continuous with continuous derivative, results in a unique set of reaction rate parameters for each explosive while providing the same functionality as the baseline rate equation. The improved rate equation uses a cosine function in the ignition term and a sine function in the growth and completion terms. The improved rate equation is simpler with fewer parameters.
An asymptotic expansion of the solution of a�matrix difference equation of general form
Sgibnev, M S
An asymptotic expansion of the solution of an inhomogeneous matrix difference equation of general form is obtained. The case when there is no bound on the differences of the arguments is considered. The effect of the roots of the characteristic equation is taken into account. An integral estimate with a�submultiplicative weight is established for the remainder in terms of the submultiplicative moment of the free term of the equation. Bibliography: 14 titles.
Solitary waves in nonlinear Dirac equation. From field theory to Dirac materials
Saxena, Avadh
This report describes the implementation of nonlinear Dirac equations in the calculation of solitary waves. Conclusions and comments on quantum elasticity are also included.
A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model
Office of Scientific and Technical Information (OSTI)
(Technical Report) | SciTech Connect Technical Report: A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model Citation Details In-Document Search Title: A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model We introduce a novel approach for the hyperbolization of the well-known two-phase six equation flow model. The six-equation model has been frequently used in many two-phase flow applications such as bubbly fluid flows in nuclear reactors. One
A Bme Solution Of The Stochastic Three-Dimensional Laplace Equation...
Solution Of The Stochastic Three-Dimensional Laplace Equation Representing A Geothermal Field Subject To Site-Specific Information Abstract This work develops a model of the...
The thermal equation of state of (Mg, Fe)SiO[subscript 3] bridgmanite...
Office of Scientific and Technical Information (OSTI)
thermal equation of state of (Mg, Fe)SiOsubscript 3 bridgmanite (perovskite) and implications for lower mantle structures Citation Details In-Document Search Title: The thermal ...
Equation of state and phase diagram of FeO (Journal Article)...
Office of Scientific and Technical Information (OSTI)
high temperature behavior of FeO, including its phase diagram and equation of state, is essential knowledge for understanding the properties and evolution of Earth's deep interior. ...
Optimization of the Direct Discrete Method Using the Solution of the Adjoint Equation and its Application in the Multi-Group Neutron Diffusion Equation
Ayyoubzadeh, Seyed Mohsen; Vosoughi, Naser
Obtaining the set of algebraic equations that directly correspond to a physical phenomenon has been viable in the recent direct discrete method (DDM). Although this method may find its roots in physical and geometrical considerations, there are still some degrees of freedom that one may suspect optimize-able. Here we have used the information embedded in the corresponding adjoint equation to form a local functional, which in turn by its minimization, yield suitable dual mesh positioning.
A parametric approach to supersymmetric quantum mechanics in the solution of Schr�dinger equation
Tezcan, Cevdet; Sever, Ramazan
We study exact solutions of the Schr�dinger equation for some potentials. We introduce a parametric approach to supersymmetric quantum mechanics to calculate energy eigenvalues and corresponding wave functions exactly. As an application we solve Schr�dinger equation for the generalized Morse potential, modified Hulthen potential, deformed Rosen-Morse potential and Poschl-Teller potential. The method is simple and effective to get the results.
Explicit solutions of the radiative transport equation in the P{sub 3} approximation
Liemert, André Kienle, Alwin
Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiative transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.
Symmetry operators for Dirac's equation on two-dimensional spin manifolds
Fatibene, Lorenzo; McLenaghan, Raymond G.; Smith, Shane N.; Rastelli, Giovanni
It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence 2 Killing tensors. The role of these operators in the theory of separation of variables for the Dirac equation is studied.
Free-complement local-Schr�dinger-equation method for solving the Schr�dinger equation of atoms and molecules: Basic theories and features
Nakatsuji, Hiroshi Nakashima, Hiroyuki
The free-complement (FC) method is a general method for solving the Schr�dinger equation (SE): The produced wave function has the potentially exact structure as the solution of the Schr�dinger equation. The variables included are determined either by using the variational principle (FC-VP) or by imposing the local Schr�dinger equations (FC-LSE) at the chosen set of the sampling points. The latter method, referred to as the local Schr�dinger equation (LSE) method, is integral-free and therefore applicable to any atom and molecule. The purpose of this paper is to formulate the basic theories of the LSE method and explain their basic features. First, we formulate three variants of the LSE method, the AB, HS, and H{sup T}Q methods, and explain their properties. Then, the natures of the LSE methods are clarified in some detail using the simple examples of the hydrogen atom and the Hooke�s atom. Finally, the ideas obtained in this study are applied to solving the SE of the helium atom highly accurately with the FC-LSE method. The results are very encouraging: we could get the world�s most accurate energy of the helium atom within the sampling-type methodologies, which is comparable to those obtained with the FC-VP method. Thus, the FC-LSE method is an easy and yet a powerful integral-free method for solving the Schr�dinger equation of general atoms and molecules.
Statistically designed study of the variables and parameters of carbon dioxide equations of state
Donohue, M.D.; Naiman, D.Q.; Jin, Gang; Loehe, J.R.
Carbon dioxide is used widely in enhanced oil recovery (EOR) processes to maximize the production of crude oil from aging and nearly depleted oil wells. Carbon dioxide also is encountered in many processes related to oil recovery. Accurate representations of the properties of carbon dioxide, and its mixtures with hydrocarbons, play a critical role in a number of enhanced oil recovery operations. One of the first tasks of this project was to select an equation of state to calculate the properties of carbon dioxide and its mixtures. The equations simplicity, accuracy, and reliability in representing phase behavior and thermodynamic properties of mixtures containing carbon dioxide with hydrocarbons at conditions relevant to enhanced oil recovery were taken into account. We also have determined the thermodynamic properties that are important to enhanced oil recovery and the ranges of temperature, pressure and composition that are important. We chose twelve equations of state for preliminary studies to be evaluated against these criteria. All of these equations were tested for pure carbon dioxide and eleven were tested for pure alkanes and their mixtures with carbon dioxide. Two equations, the ALS equation and the ESD equation, were selected for detailed statistical analysis. 54 refs., 41 figs., 36 tabs.
Equation of State from Lattice QCD Calculations (Conference) | SciTech
Office of Scientific and Technical Information (OSTI)
Connect Conference: Equation of State from Lattice QCD Calculations Citation Details In-Document Search Title: Equation of State from Lattice QCD Calculations We provide a status report on the calculation of the Equation of State (EoS) of QCD at finite temperature using lattice QCD. Most of the discussion will focus on comparison of recent results obtained by the HotQCD and Wuppertal-Budapest collaborations. We will show that very significant progress has been made towards obtaining high
Real-time and imaginary-time quantum hierarchal Fokker-Planck equations
Office of Scientific and Technical Information (OSTI)
(Journal Article) | SciTech Connect Real-time and imaginary-time quantum hierarchal Fokker-Planck equations Citation Details In-Document Search Title: Real-time and imaginary-time quantum hierarchal Fokker-Planck equations We consider a quantum mechanical system represented in phase space (referred to hereafter as "Wigner space"), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time,
A stochastic multi-symplectic scheme for stochastic Maxwell equations with additive noise
Hong, Jialin; Zhang, Liying
In this paper we investigate a stochastic multi-symplectic method for stochastic Maxwell equations with additive noise. Based on the stochastic version of variational principle, we find a way to obtain the stochastic multi-symplectic structure of three-dimensional (3-D) stochastic Maxwell equations with additive noise. We propose a stochastic multi-symplectic scheme and show that it preserves the stochastic multi-symplectic conservation law and the local and global stochastic energy dissipative properties, which the equations themselves possess. Numerical experiments are performed to verify the numerical behaviors of the stochastic multi-symplectic scheme.
Error propagation equations for estimating the uncertainty in high-speed wind tunnel test results
Clark, E.L.
Error propagation equations, based on the Taylor series model, are derived for the nondimensional ratios and coefficients most often encountered in high-speed wind tunnel testing. These include pressure ratio and coefficient, static force and moment coefficients, dynamic stability coefficients, and calibration Mach number. The error equations contain partial derivatives, denoted as sensitivity coefficients, which define the influence of free-steam Mach number, M{infinity}, on various aerodynamic ratios. To facilitate use of the error equations, sensitivity coefficients are derived and evaluated for five fundamental aerodynamic ratios which relate free-steam test conditions to a reference condition.
Surface harmonics method equations for solving the time-dependent neutron transport problems and their verification
Boyarinov, V. F.; Kondrushin, A. E.; Fomichenko, P. A.
Finite-difference time-dependent equations of Surface Harmonics method have been obtained for plane geometry. Verification of these equations has been carried out by calculations of tasks from 'Benchmark Problem Book ANL-7416'. The capacity and efficiency of the Surface Harmonics method have been demonstrated by solution of the time-dependent neutron transport equation in diffusion approximation. The results of studies showed that implementation of Surface Harmonics method for full-scale calculations will lead to a significant progress in the efficient solution of the time-dependent neutron transport problems in nuclear reactors. (authors)
Imaginary Time Step Method to Solve the Dirac Equation with Nonlocal Potential
Zhang Ying [State Key Lab Nucl. Phys. and Tech., School of Physics, Peking University, Beijing 100871 (China); Liang Haozhao [State Key Lab Nucl. Phys. and Tech., School of Physics, Peking University, Beijing 100871 (China); Institut de Physique Nucleaire, IN2P3-CNRS and Universite Paris-Sud, F-91406 Orsay France (France); Meng Jie [State Key Lab Nucl. Phys. and Tech., School of Physics, Peking University, Beijing 100871 (China); Department of Physics, University of Stellenbosch, Stellenbosch (South Africa)
The imaginary time step (ITS) method is applied to solve the Dirac equation with nonlocal potentials in coordinate space. Taking the nucleus {sup 12}C as an example, even with nonlocal potentials, the direct ITS evolution for the Dirac equation still meets the disaster of the Dirac sea. However, following the recipe in our former investigation, the disaster can be avoided by the ITS evolution for the corresponding Schroedinger-like equation without localization, which gives the convergent results exactly the same with those obtained iteratively by the shooting method with localized effective potentials.
Numerical simulation of scattering of acoustic waves by inelastic bodies using hypersingular boundary integral equation
Daeva, S.G.; Setukha, A.V.
A numerical method for solving a problem of diffraction of acoustic waves by system of solid and thin objects based on the reduction the problem to a boundary integral equation in which the integral is understood in the sense of finite Hadamard value is proposed. To solve this equation we applied piecewise constant approximations and collocation methods numerical scheme. The difference between the constructed scheme and earlier known is in obtaining approximate analytical expressions to appearing system of linear equations coefficients by separating the main part of the kernel integral operator. The proposed numerical scheme is tested on the solution of the model problem of diffraction of an acoustic wave by inelastic sphere.
Validity of equation-of-motion approach to kondo problem in the large N
Office of Scientific and Technical Information (OSTI)
limit (Journal Article) | SciTech Connect SciTech Connect Search Results Journal Article: Validity of equation-of-motion approach to kondo problem in the large N limit Citation Details In-Document Search Title: Validity of equation-of-motion approach to kondo problem in the large N limit The Anderson impurity model for Kondo problem is investigated for arbitrary orbit-spin degeneracy N of the magnetic impurity by the equation of motion method (EOM). By employing a new decoupling scheme, a
Quasiparticle description of (2+1)- flavor lattice QCD equation of state
Chandra, Vinod; Ravishankar, V.
A quasiparticle model has been employed to describe the (2+1)-flavor lattice QCD equation of state with physical quark masses. The interaction part of the equation of state has been mapped to the effective fugacities of otherwise noninteracting quasigluons and quasiquarks. The mapping is found to be exact for the equation of state. The model leads to nontrivial dispersion relations for quasipartons. The dispersion relations, effective quasiparticle number densities, and trace anomaly have been investigated employing the model. A virial expansion for the equation of state has further been obtained to investigate the role of interactions in quark-gluon plasma. Finally, Debye screening in quark-gluon plasma has been studied employing the model.
Equation of state and phase diagram of Fe-16Si alloy as a candidate...
Office of Scientific and Technical Information (OSTI)
SciTech Connect Search Results Journal Article: Equation of state and phase diagram of Fe-16Si alloy as a candidate component of Earths core Citation Details In-Document Search ...
Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system
Brett, Tobias Galla, Tobias
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.
Electrolux Gibson Air Conditioner and Equator Clothes Washer Fail DOE Energy Star Testing
Broader source: Energy.gov [DOE]
DOE testing in support of the ENERGY STAR program has revealed that an Electrolux Gibson air conditioner (model GAH105Q2T1) and an Equator clothes washer (model EZ 3720 CEE), both of which claimed...
Equation of state of pyrite to 80 GPa and 2400 K (Journal Article...
Office of Scientific and Technical Information (OSTI)
Citation Details In-Document Search Title: Equation of state of pyrite to 80 GPa and 2400 K Authors: Thompson, Elizabeth C. ; Chidester, Bethany A. ; Fischer, Rebecca A. ; Myers, ...
Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves
Webb, G. M.; Brio, M.; Zank, G. P.
A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in {beta}{approx}1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a{sub g}{sup 2}=V{sub A}{sup 2} where a{sub g} is the gas sound speed and V{sub A} is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation.
A Novel Hyperbolization Procedure for The Two-Phase Six-Equation...
Office of Scientific and Technical Information (OSTI)
A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model Citation Details In-Document Search Title: A Novel Hyperbolization Procedure for The Two-Phase...
New Improved Equations For Na-K, Na-Li And Sio2 Geothermometers...
Improved Equations For Na-K, Na-Li And Sio2 Geothermometers By Outlier Detection And Rejection Jump to: navigation, search OpenEI Reference LibraryAdd to library Journal Article:...
Effects of the Fe[superscript 3+] spin transition on the equation...
Office of Scientific and Technical Information (OSTI)
Title: Effects of the Fesuperscript 3+ spin transition on the equation of state of bridgmanite Authors: Mao, Zhu ; Lin, Jung-Fu ; Yang, Jing ; Inoue, Toru ; Prakapenka, Vitali B. ...
A Novel Hyperbolization Procedure for The Two-Phase Six-Equation...
Office of Scientific and Technical Information (OSTI)
Technical Report: A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model Citation Details In-Document Search Title: A Novel Hyperbolization Procedure for The ...
Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential
Fa, Kwok Sau
An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations, which includes short, intermediate and long-time memory effects described by the waiting time probability density function. Analytical expression for the correlation function is obtained and analyzed, which can be used to describe, for instance, internal motions of proteins. The result shows that the generalized diffusion equation has a broad application and it may be used to describe different kinds of systems. - Highlights: • Calculation of the correlation function. • The correlation function is connected to the survival probability. • The model can be applied to the internal dynamics of proteins.
H–J–B Equations of Optimal Consumption-Investment and Verification Theorems
Nagai, Hideo
We consider a consumption-investment problem on infinite time horizon maximizing discounted expected HARA utility for a general incomplete market model. Based on dynamic programming approach we derive the relevant H–J–B equation and study the existence and uniqueness of the solution to the nonlinear partial differential equation. By using the smooth solution we construct the optimal consumption rate and portfolio strategy and then prove the verification theorems under certain general settings.
Equations Governing Space-Time Variability of Liquid Water Path in Stratus Clouds
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Equations Governing Space-Time Variability of Liquid Water Path in Stratus Clouds K. Ivanova Pennsylvania State University University Park, Pennsylvania T. P. Ackerman Pacific Northwest National Laboratory Richland, Washington M. Ausloos University of Liège B-4000 Liège, Belgium Abstract We present a method on how to derive an underlying mathematical (statistical or model free) equation for a liquid water path (LWP) signal directly from empirical data. The evolution of the probability density
Analytical continuation from bound to resonant states in the Dirac equation
Office of Scientific and Technical Information (OSTI)
with quadrupole-deformed potentials (Journal Article) | SciTech Connect Analytical continuation from bound to resonant states in the Dirac equation with quadrupole-deformed potentials Citation Details In-Document Search This content will become publicly available on August 27, 2016 Title: Analytical continuation from bound to resonant states in the Dirac equation with quadrupole-deformed potentials Authors: Xu, Xu-Dong ; Zhang, Shi-Sheng ; Signoracci, A. J. ; Smith, M. S. ; Li, Z. P.
An analysis of the standard system of differential equations describing multi-speed flows of multi-phase media is performed. It is proved that the Cauchy problem, as posed in most best-estimate thermal-hydraulic codes, results in unstable solutions and potentially unreliable description of many physical phenomena. A system of equations, free from instability effects, is developed allowing more rigorous numerical modeling.
Investigating the Nuclear Equation of State through N/Z Equilibration
Yennello, S.; Keksis, A.; Bell, E.
The equilibration of the N/Z degree of freedom during heavy-ion collisions can be a discriminating observables for helping to understand the nuclear equation of state. Equilibration can be investigated by examining the ratios of isotopes produced in these reactions. The isotope ratio method and the tracer method yield consistent results. The quasiprojectiles produced in deep inelastic collisions are predicted to be sensitive to the density dependence of the equation of state.
Equations of state in the Fe-FeSi system at high pressures and temperatures
Office of Scientific and Technical Information (OSTI)
(Journal Article) | SciTech Connect SciTech Connect Search Results Journal Article: Equations of state in the Fe-FeSi system at high pressures and temperatures Citation Details In-Document Search Title: Equations of state in the Fe-FeSi system at high pressures and temperatures Authors: Fischer, Rebecca A. ; Campbell, Andrew J. ; Caracas, Razvan ; Reaman, Daniel M. ; Heinz, Dion L. ; Dera, Przemyslaw ; Prakapenka, Vitali B. [1] ; UC) [2] ; Claude-Bernard) [2] + Show Author Affiliations
Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle
Barletti, Luigi
The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained, their asymptotic form corresponding to significant physical regimes is investigated. In particular, the diffusive regime, the Maxwell-Boltzmann regime (high temperature), the collimation regime and the degenerate gas limit (vanishing temperature) are considered.
Exact solution to the Schrödinger's equation with pseudo-Gaussian potential
Iacob, Felix; Lute, Marina
We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.
A New 2D-Transport, 1D-Diffusion Approximation of the Boltzmann Transport equation
Larsen, Edward
The work performed in this project consisted of the derivation, implementation, and testing of a new, computationally advantageous approximation to the 3D Boltz- mann transport equation. The solution of the Boltzmann equation is the neutron flux in nuclear reactor cores and shields, but solving this equation is difficult and costly. The new �2D/1D� approximation takes advantage of a special geometric feature of typical 3D reactors to approximate the neutron transport physics in a specific (ax- ial) direction, but not in the other two (radial) directions. The resulting equation is much less expensive to solve computationally, and its solutions are expected to be sufficiently accurate for many practical problems. In this project we formulated the new equation, discretized it using standard methods, developed a stable itera- tion scheme for solving the equation, implemented the new numerical scheme in the MPACT code, and tested the method on several realistic problems. All the hoped- for features of this new approximation were seen. For large, difficult problems, the resulting 2D/1D solution is highly accurate, and is calculated about 100 times faster than a 3D discrete ordinates simulation.
A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit
Gamba, Irene M.; Haack, Jeffrey R.
We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation.
Bound state solution of Dirac equation for 3D harmonics oscillator plus trigonometric scarf noncentral potential using SUSY QM approach
Cari, C. Suparmi, A.
Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.
An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations
Sun, Wenjun; Jiang, Song; Xu, Kun
The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transport equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach.
Stability and error analysis of nodal expansion method for convection-diffusion equation
Deng, Z.; Rizwan-Uddin; Li, F.; Sun, Y.
The development, and stability and error analyses of nodal expansion method (NEM) for one dimensional steady-state convection diffusion equation is presented. Following the traditional procedure to develop NEM, the discrete formulation of the convection-diffusion equation, which is similar to the standard finite difference scheme, is derived. The method of discrete perturbation analysis is applied to this discrete form to study the stability of the NEM. The scheme based on the NEM is found to be stable for local Peclet number less than 4.644. A maximum principle is proved for the NEM scheme, followed by an error analysis carried out by applying the Maximum principle together with a carefully constructed comparison function. The scheme for the convection diffusion equation is of second-order. Numerical experiments are carried and the results agree with the conclusions of the stability and error analyses. (authors)
Equation of state of hot polarized nuclear matter and heavy-ion fusion reactions
Ghodsi, O. N.; Gharaei, R.
We employ the equation of state of hot polarized nuclear matter to simulate the repulsive force caused by the incompressibility effects of nuclear matter in the fusion reactions of heavy colliding ions. The results of our studies reveal that temperature effects of compound nuclei have significant importance in simulating the repulsive force on the fusion reactions for which the temperature of the compound nucleus increases up to about 2 MeV. Since the equation of state of hot nuclear matter depends upon the density and temperature of the nuclear matter, it has been suggested that, by using this equation of state, one can simulate simultaneously both the effects of the precompound nucleons' emission and the incompressibility of nuclear matter to calculate the nuclear potential in fusion reactions within a static formalism such as the double-folding (DF) model.
Multi-time Schrödinger equations cannot contain interaction potentials
Petrat, Sören; Tumulka, Roderich
Multi-time wave functions are wave functions that have a time variable for every particle, such as ϕ(t{sub 1},x{sub 1},...,t{sub N},x{sub N}). They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schrödinger equations, one for each time variable. These Schrödinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for non-interacting particles, it is a challenge to set up consistent multi-time equations with interaction. We prove for a wide class of multi-time Schrödinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently [S. Petrat and R. Tumulka, "Multi-time wave functions for quantum field theory," Ann. Physics (to be published)]. We also prove the following result: When a cut-off length δ > 0 is introduced (in the sense that the multi-time wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multi-time Schrödinger equations with interaction potentials of range δ are consistent; however, in the desired limit δ → 0 of removing the cut-off, the resulting multi-time equations are interaction-free, which supports the conclusion expressed in the title.
First-principles high-pressure unreacted equation of state and heat of
Office of Scientific and Technical Information (OSTI)
formation of crystal 2,6-diamino-3, 5-dinitropyrazine-1-oxide (LLM-105) (Journal Article) | SciTech Connect Journal Article: First-principles high-pressure unreacted equation of state and heat of formation of crystal 2,6-diamino-3, 5-dinitropyrazine-1-oxide (LLM-105) Citation Details In-Document Search Title: First-principles high-pressure unreacted equation of state and heat of formation of crystal 2,6-diamino-3, 5-dinitropyrazine-1-oxide (LLM-105) Authors: Manaa, M R ; Kuo, I W ; Fried, L
Verification of the history-score moment equations for weight-window variance reduction
Solomon, Clell J; Sood, Avneet; Booth, Thomas E; Shultis, J. Kenneth
The history-score moment equations that describe the moments of a Monte Carlo score distribution have been extended to weight-window variance reduction, The resulting equations have been solved deterministically to calculate the population variance of the Monte Carlo score distribution for a single tally, Results for one- and two-dimensional one-group problems are presented that predict the population variances to less than 1% deviation from the Monte Carlo for one-dimensional problems and between 1- 2% for two-dimensional problems,
Trigonometric and hyperbolic functions method for constructing analytic solutions to nonlinear plane magnetohydrodynamics equilibrium equations
Moawad, S. M.
In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.
Thermal equation of state and stability of (Mg[subscript 0.06]Fe[subscript
Office of Scientific and Technical Information (OSTI)
0.94])O (Journal Article) | SciTech Connect SciTech Connect Search Results Journal Article: Thermal equation of state and stability of (Mg[subscript 0.06]Fe[subscript 0.94])O Citation Details In-Document Search Title: Thermal equation of state and stability of (Mg[subscript 0.06]Fe[subscript 0.94])O Authors: Wicks, June K. ; Jackson, Jennifer M. ; Sturhahn, Wolfgang ; Zhuravlev, Kirill K. ; Tkachev, Sergey N. ; Prakapenka, Vitali B. [1] ; UC) [2] ; CIT) [2] + Show Author Affiliations
Validity of equation-of-motion approach to kondo problem in the large N
Office of Scientific and Technical Information (OSTI)
limit (Journal Article) | SciTech Connect Validity of equation-of-motion approach to kondo problem in the large N limit Citation Details In-Document Search Title: Validity of equation-of-motion approach to kondo problem in the large N limit × You are accessing a document from the Department of Energy's (DOE) SciTech Connect. This site is a product of DOE's Office of Scientific and Technical Information (OSTI) and is provided as a public service. Visit OSTI to utilize additional information
A New Lifshitz Transition and the Equation of State of Osmium (Journal
Office of Scientific and Technical Information (OSTI)
Article) | SciTech Connect A New Lifshitz Transition and the Equation of State of Osmium Citation Details In-Document Search Title: A New Lifshitz Transition and the Equation of State of Osmium × You are accessing a document from the Department of Energy's (DOE) SciTech Connect. This site is a product of DOE's Office of Scientific and Technical Information (OSTI) and is provided as a public service. Visit OSTI to utilize additional information resources in energy science and technology. A
Phase Diagram and Equation of State of Magnesium to High Pressures and High
Office of Scientific and Technical Information (OSTI)
Temperatures (Journal Article) | SciTech Connect Phase Diagram and Equation of State of Magnesium to High Pressures and High Temperatures Citation Details In-Document Search Title: Phase Diagram and Equation of State of Magnesium to High Pressures and High Temperatures Authors: Stinton, G W ; MacLeod, S G ; Cynn, H ; Errandonea, D ; Evans, W J ; Proctor, J E ; Meng, Y ; McMahon, M I Publication Date: 2014-01-21 OSTI Identifier: 1188628 Report Number(s): LLNL-JRNL-648674 DOE Contract Number:
Effects of the Fe[superscript 3+] spin transition on the equation of state
Office of Scientific and Technical Information (OSTI)
of bridgmanite (Journal Article) | SciTech Connect SciTech Connect Search Results Journal Article: Effects of the Fe[superscript 3+] spin transition on the equation of state of bridgmanite Citation Details In-Document Search Title: Effects of the Fe[superscript 3+] spin transition on the equation of state of bridgmanite Authors: Mao, Zhu ; Lin, Jung-Fu ; Yang, Jing ; Inoue, Toru ; Prakapenka, Vitali B. [1] ; UC) [2] ; CHPSTAR- China) [2] ; Ehime U) [2] + Show Author Affiliations (Texas) (
Equation of state and phase diagram of Fe-16Si alloy as a candidate
Office of Scientific and Technical Information (OSTI)
component of Earth's core (Journal Article) | SciTech Connect SciTech Connect Search Results Journal Article: Equation of state and phase diagram of Fe-16Si alloy as a candidate component of Earth's core Citation Details In-Document Search Title: Equation of state and phase diagram of Fe-16Si alloy as a candidate component of Earth's core The outer core of the Earth contains several weight percent of one or more unknown light elements, which may include silicon. Therefore it is critical to
Constraining the equation of state of superhadronic matter from heavy-ion collisions
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Pratt, Scott; Sorensen, Paul; Sangaline, Evan; Wang, Hui
The equation of state of QCD matter for temperatures near and above the quark-hadron transition (~165 MeV) is inferred within a Bayesian framework through the comparison of data from the Relativistic Heavy Ion Collider and from the Large Hadron Collider to theoretical models. State-of-the-art statistical techniques are applied to simultaneously analyze multiple classes of observables while varying 14 independent model parameters. Thus, the resulting posterior distribution over possible equations of state is consistent with results from lattice gauge theory.
Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials
Arnold, J.; Kosson, D.S.; Garrabrants, A.; Meeussen, J.C.L.; Sloot, H.A. van der
A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.
Group-invariant solutions of semilinear Schr�dinger equations in multi-dimensions
Anco, Stephen C.; Feng, Wei; Department of Mathematics, Zhejiang University of Technology, Hangzhou 310014
Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr�dinger equations in dimensions n ? 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr�dinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether's theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr�dinger equations involving an extra modulation term with a parameter m = 2?n ? 0 is discussed.
Equation of state for high explosives detonation products with explicit polar and ionic species
Bastea, S; Glaesemann, K R; Fried, L E
We introduce a new thermodynamic theory for detonation products that includes polar and ionic species. The new formalism extends the domain of validity of the previously developed EXP6 equation of state library and opens the possibility of new applications. We illustrate the scope of the new approach on PETN detonation properties and water ionization models.
Derivation of quantum mechanics from the Boltzmann equation for the Planch aether
Winterberg, F.
The Planck aether hypothesis assumes that space is densely filled with an equal number of locally interacting positive and negative Planck masses obeying an exactly nonrelativistic law of motion. The Planck masses can be described by a quantum mechanical two-component nonrelativistic operator field equation having the form of a two-component nonlinear Schroedinger equation, with a spectrum of quasiparticles obeying Lorentz invariance as a dynamic symmetry for energies small compared to the Planck energy. We show that quantum mechanics itself can be derived from the Newtonian mechanics of the Planck aether as an approximate solution of Boltzmann`s equation for the locally interacting positive and negative Planck masses, and that the validity of the nonrelativistic Schroedinger equation depends on Lorentz invariance as a dynamic symmetry. We also show how the many-body Schroedinger wave function can be factorized into a product of quasiparticles of the Planck aether with separable quantum potentials. Finally, we present a possible explanation of wave function collapse as a kind of enhanced gravitational collapse in the presence of the negative Planck masses.
The One and Two Loops Renormalization Group Equations in the Standard Model
Juarez W, S. Rebeca; Solis R, H. Gabriel; Kielanowski, P.
In the context of the Standard Model (SM), we compare the analytical and the numerical solutions of the Renormalization Group Equations (RGE) for the relevant couplings to one and two loops. This information will be an important ingredient for the precise evaluation of boundary values on the physical Higgs Mass.
Scaling of magneto-quantum-radiative hydrodynamic equations: from laser-produced plasmas to astrophysics
Cross, J. E.; Gregori, G.; Reville, B.
We introduce the equations of magneto-quantum-radiative hydrodynamics. By rewriting them in a dimensionless form, we obtain a set of parameters that describe scale-dependent ratios of characteristic hydrodynamic quantities. We discuss how these dimensionless parameters relate to the scaling between astrophysical observations and laboratory experiments.
Neutron skin thickness and neutron star equations of state: a strong relationship
Menezes, D. P.; Avancini, S. S.; Marinelli, J. R.; Watanabe de Moraes, M. M.; Providencia, C.
A density dependent hadronic model and a common parametrization of the non-linear Walecka model are used to obtain the lead neutron skin thickness through its proton and neutron density profiles. The neutron skin thickness is known to reflect the equation of state properties. A direct correlation between the neutron skin thickness and the slope of the symmetry energy is found.
On the solution of the continuity equation for precipitating electrons in solar flares
Emslie, A. Gordon; Holman, Gordon D.; Litvinenko, Yuri E. E-mail: firstname.lastname@example.com
Electrons accelerated in solar flares are injected into the surrounding plasma, where they are subjected to the influence of collisional (Coulomb) energy losses. Their evolution is modeled by a partial differential equation describing continuity of electron number. In a recent paper, Dobranskis and Zharkova claim to have found an 'updated exact analytical solution' to this continuity equation. Their solution contains an additional term that drives an exponential decrease in electron density with depth, leading them to assert that the well-known solution derived by Brown, Syrovatskii and Shmeleva, and many others is invalid. We show that the solution of Dobranskis and Zharkova results from a fundamental error in the application of the method of characteristics and is hence incorrect. Further, their comparison of the 'new' analytical solution with numerical solutions of the Fokker-Planck equation fails to lend support to their result. We conclude that Dobranskis and Zharkova's solution of the universally accepted and well-established continuity equation is incorrect, and that their criticism of the correct solution is unfounded. We also demonstrate the formal equivalence of the approaches of Syrovatskii and Shmeleva and Brown, with particular reference to the evolution of the electron flux and number density (both differential in energy) in a collisional thick target. We strongly urge use of these long-established, correct solutions in future works.
Numerical solution of the Stratonovich- and Ito�Euler equations: Application to the stochastic piston problem
Zhang, Zhongqiang; Yang, Xiu; Lin, Guang; Karniadakis, George Em
We consider a piston with a velocity perturbed by Brownian motion moving into a straight tube filled with a perfect gas at rest. The shock generated ahead of the piston can be located by solving the one-dimensional Euler equations driven by white noise using the Stratonovich or Ito formulations. We approximate the Brownian motion with its spectral truncation and subsequently apply stochastic collocation using either sparse grid or the quasi-Monte Carlo (QMC) method. In particular, we first transform the Euler equations with an unsteady stochastic boundary into stochastic Euler equations over a fixed domain with a time-dependent stochastic source term. We then solve the transformed equations by splitting them up into two parts, i.e., a �deterministic part� and a �stochastic part�. Numerical results verify the Stratonovich�Euler and Ito�Euler models against stochastic perturbation results, and demonstrate the efficiency of sparse grid and QMC for small and large random piston motions, respectively. The variance of shock location of the piston grows cubically in the case of white noise in contrast to colored noise reported in [1], where the variance of shock location grows quadratically with time for short times and linearly for longer times.
A new three-equation model for the CO{sub 2} laser
Stanghini, M.; Basso, M.; Genesio, R.; Tesi, A.; Meucci, R.; Ciofini, M.
Three rate equations describing the single-mode CO{sub 2} laser dynamics are derived by applying the theory of linear filters to an improved four-level model. The model is studied in the case of periodic modulations of the losses and compared with the outcome of an experiment, revealing a good agreement.
FWAVE V1.0 a framework for finite difference wave equation modeling
Energy Science and Technology Software Center (OSTI)
FWAVE provides a computation framework for the rapid prototyping and efficient use of finite difference wave equation solutions. The user provides single grid Fortran solver components that are integrated using opaque handles to C++ distributed data structures. Permits the scientific researcher to make of clusters and parallel computers by concentrating only on the numerical schemes.
SciCADE 95: International conference on scientific computation and differential equations
This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included.
The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature
Bertolami, O.; Gomes, C. E-mail: firstname.lastname@example.com
We derive the Layzer-Irvine equation for alternative gravitational theories with non-minimal coupling between curvature and matter for an homogeneous and isotropic Universe. As an application, we study the case of Abell 586, a relaxed and spherically symmetric galaxy cluster, assuming some matter density profiles.
Adaptice-step time integration package for stiff, nonstiff and multi-rate systems of ordinary differential equations (ODEs)
Energy Science and Technology Software Center (OSTI)
ARKode is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/ALgebraic equation Solvers [1]. The ARKode solver library provides an adaptive-step time integration package for stiff, nonstiff and multi-rate systems of ordinary differential equations (ODEs) using Runge Kutta methods [2].
Fast multiscale Gaussian beam methods for wave equations in bounded convex domains
Bao, Gang; Department of Mathematics, Michigan State University, East Lansing, MI 48824 ; Lai, Jun; Qian, Jianliang
Motivated by fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beam methods which were originally designed for pure initial-value problems of wave equations, we develop fast multiscale Gaussian beam methods for initial boundary value problems of wave equations in bounded convex domains in the high frequency regime. To compute the wave propagation in bounded convex domains, we have to take into account reflecting multiscale Gaussian beams, which are accomplished by enforcing reflecting boundary conditions during beam propagation and carrying out suitable reflecting beam summation. To propagate multiscale beams efficiently, we prove that the ratio of the squared magnitude of beam amplitude and the beam width is roughly conserved, and accordingly we propose an effective indicator to identify significant beams. We also prove that the resulting multiscale Gaussian beam methods converge asymptotically. Numerical examples demonstrate the accuracy and efficiency of the method.
On lower bounds for possible blow-up solutions to the periodic Navier-Stokes equation
Cortissoz, Jean C. Montero, Julio A. Pinilla, Carlos E.
We show a new lower bound on the H{sup .3/2} (T{sup 3}) norm of a possible blow-up solution to the Navier-Stokes equation, and also comment on the extension of this result to the whole space. This estimate can be seen as a natural limiting result for Leray's blow-up estimates in L{sup p}(R{sup 3}), 3 < p < ?. We also show a lower bound on the blow-up rate of a possible blow-up solution of the Navier-Stokes equation in H{sup .5/2} (T{sup 3}), and give the corresponding extension to the case of the whole space.
Numerical solution of the time dependent neutron transport equation by the method of the characteristics
Talamo, Alberto
This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.
Deterministic proton transport solving a one dimensional Fokker-Planck equation
Marr, D.; Prael, R.; Adams, K.; Alcouffe, R.
The transport of protons through matter is characterized by many interactions which cause small deflections and slight energy losses. The few which are catastrophic or cause large angle scattering can be viewed as extinction for many applications. The transport of protons at this level of approximation can be described by a Fokker Planck Equation. This equation is solved using a deterministic multigroup differencing scheme with a highly resolved set of discrete ordinates centered around the beam direction which is adequate to properly account for deflections and energy losses due to multiple Coulomb scattering. Comparisons with LAHET for a large variety of problems ranging from 800 MeV protons on a copper step wedge to 10 GeV protons on a sandwich of material are presented. The good agreement with the Monte Carlo code shows that the solution method is robust and useful for approximate solutions of selected proton transport problems.
The Conforming Virtual Element Method for the convection-diffusion-reaction equation with variable coeffcients.
Manzini, Gianmarco; Cangiani, Andrea; Sutton, Oliver
This document describes the conforming formulations for virtual element approximation of the convection-reaction-diffusion equation with variable coefficients. Emphasis is given to construction of the projection operators onto polynomial spaces of appropriate order. These projections make it possible the virtual formulation to achieve any order of accuracy. We present the construction of the internal and the external formulation. The difference between the two is in the way the projection operators act on the derivatives (laplacian, gradient) of the partial differential equation. For the diffusive regime we prove the well-posedness of the external formulation and we derive an estimate of the approximation error in the H1-norm. For the convection-dominated case, the streamline diffusion stabilization (aka SUPG) is also discussed.
Dynamical mass generation in unquenched QED using the Dyson-Schwinger equations
Kızılersü, Ayse; Sizer, Tom; Pennington, Michael R.; Williams, Anthony G.; Williams, Richard
We present a comprehensive numerical study of dynamical mass generation for unquenched QED in four dimensions, in the absence of four-fermion interactions, using the Dyson-Schwinger approach. We begin with an overview of previous investigations of criticality in the quenched approximation. To this we add an analysis using a new fermion-antifermion-boson interaction ansatz, the Kizilersu-Pennington (KP) vertex, developed for an unquenched treatment. After surveying criticality in previous unquenched studies, we investigate the performance of the KP vertex in dynamical mass generation using a renormalized fully unquenched system of equations. This we compare with the results for two hybrid vertices incorporating the Curtis-Pennington vertex in the fermion equation. We conclude that the KP vertex is as yet incomplete, and its relative gauge-variance is due to its lack of massive transverse components in its design.
A fast, high-order solver for the Grad�Shafranov equation
Pataki, Andras; Cerfon, Antoine J.; Freidberg, Jeffrey P.; Greengard, Leslie; O�Neil, Michael
We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives. Smooth arbitrary plasma cross-sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver. Equilibria with large Shafranov shifts can be computed without difficulty. Spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution. A fusion-relevant example of an equilibrium with a pressure pedestal is also presented.
Vortices at the magnetic equator generated by hybrid Alfv�n resonant waves
Hiraki, Yasutaka
We performed three-dimensional magnetohydrodynamic simulations of shear Alfv�n waves in a full field line system with magnetosphere-ionosphere coupling and plasma non-uniformities. Feedback instability of the Alfv�n resonant modes showed various nonlinear features under the field line cavities: (i) a secondary flow shear instability occurs at the magnetic equator, (ii) trapping of the ionospheric Alfv�n resonant modes facilitates deformation of field-aligned current structures, and (iii) hybrid Alfv�n resonant modes grow to cause vortices and magnetic oscillations around the magnetic equator. Essential features in the initial brightening of auroral arc at substorm onsets could be explained by the dynamics of Alfv�n resonant modes, which are the nature of the field line system responding to a background rapid change.
Improved master equation approach to quantum transport: From Born to self-consistent Born approximation
Jin, Jinshuang; Li, Jun; Liu, Yu; Li, Xin-Qi; Yan, YiJing
Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.
Low-dimensional weakly interacting Bose gases: Nonuniversal equations of state
Astrakharchik, G. E.; Boronat, J.; Mazzanti, F.; Kurbakov, I. L.; Lozovik, Yu. E.
The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. We propose to use the concept of energy-dependent s-wave scattering length for obtaining estimations of nonuniversal terms in the energy expansion. We test this approach by making a comparison to exactly solvable one-dimensional problems and find that the generated terms have the correct structure. The applicability to two-dimensional systems is analyzed by comparing with results of Monte Carlo simulations. The prediction for the nonuniversal behavior is qualitatively correct and the densities, at which the deviations from the universal equation of state become visible, are estimated properly. Finally, the possibility of observing the nonuniversal terms in experiments with trapped gases is also discussed.
Observational constraints on dark energy with a fast varying equation of state
Felice, Antonio De; Nesseris, Savvas
We place observational constraints on models with the late-time cosmic acceleration based on a number of parametrizations allowing fast transitions for the equation of state of dark energy. In addition to the model of Linder and Huterer where the dark energy equation of state w monotonically grows or decreases in time, we propose two new parametrizations in which w has an extremum. We carry out the likelihood analysis with the three parametrizations by using the observational data of supernovae type Ia, cosmic microwave background, and baryon acoustic oscillations. Although the transient cosmic acceleration models with fast transitions can give rise to the total chi square smaller than that in the ?-Cold-Dark-Matter (?CDM) model, these models are not favored over ?CDM when one uses the Akaike information criterion which penalizes the extra degrees of freedom present in the parametrizations.
Manufactured solutions for the three-dimensional Euler equations with relevance to Inertial Confinement Fusion
Waltz, J.; Canfield, T.R.; Morgan, N.R.; Risinger, L.D.; Wohlbier, J.G.
We present a set of manufactured solutions for the three-dimensional (3D) Euler equations. The purpose of these solutions is to allow for code verification against true 3D flows with physical relevance, as opposed to 3D simulations of lower-dimensional problems or manufactured solutions that lack physical relevance. Of particular interest are solutions with relevance to Inertial Confinement Fusion (ICF) capsules. While ICF capsules are designed for spherical symmetry, they are hypothesized to become highly 3D at late time due to phenomena such as Rayleigh–Taylor instability, drive asymmetry, and vortex decay. ICF capsules also involve highly nonlinear coupling between the fluid dynamics and other physics, such as radiation transport and thermonuclear fusion. The manufactured solutions we present are specifically designed to test the terms and couplings in the Euler equations that are relevant to these phenomena. Example numerical results generated with a 3D Finite Element hydrodynamics code are presented, including mesh convergence studies.
Equations of state and transport properties of mixtures in the warm dense regime
Hou, Yong; Dai, Jiayu; Kang, Dongdong; Ma, Wen; Yuan, Jianmin
We have performed average-atom molecular dynamics to simulate the CH and LiH mixtures in the warm dense regime, and obtained equations of state and the ionic transport properties. The electronic structures are calculated by using the modified average-atom model, which have included the broadening of energy levels, and the ion-ion pair potentials of mixtures are constructed based on the temperature-dependent density functional theory. The ionic transport properties, such as ionic diffusion and shear viscosity, are obtained through the ionic velocity correlation functions. The equations of state and transport properties for carbon, hydrogen and lithium, hydrogen mixtures in a wide region of density and temperature are calculated. Through our computing the average ionization degree, average ion-sphere diameter and transition properties in the mixture, it is shown that transport properties depend not only on the ionic mass but also on the average ionization degree.
Generalized conditional symmetries and related solutions of the Grad-Shafranov equation
Cimpoiasu, Rodica
The generalized conditional symmetry (GCS) method is applied to a specific case of the Grad–Shafranov (GS) equation, in cylindrical geometry assuming the existence of an axial symmetry. We investigate the conditions that yield the GS equation admitting a special class of second-order GCSs. The determining system for the unknown arbitrary functions is solved in several special cases and new exact solutions, including solitary waves, different in form and structure from the ones obtained using other nonclassical symmetry methods, are pointed out. Several plots of the level sets or flux surfaces of the new solutions as well as surfaces with vanishing flow are displayed. The obtained solutions can be useful for studying plasma equilibrium, transport phenomena, and magnetohydrodynamic stability.
Dynamical mass generation in unquenched QED using the Dyson-Schwinger equations
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Kızılersü, Ayse; Sizer, Tom; Pennington, Michael R.; Williams, Anthony G.; Williams, Richard
We present a comprehensive numerical study of dynamical mass generation for unquenched QED in four dimensions, in the absence of four-fermion interactions, using the Dyson-Schwinger approach. We begin with an overview of previous investigations of criticality in the quenched approximation. To this we add an analysis using a new fermion-antifermion-boson interaction ansatz, the Kizilersu-Pennington (KP) vertex, developed for an unquenched treatment. After surveying criticality in previous unquenched studies, we investigate the performance of the KP vertex in dynamical mass generation using a renormalized fully unquenched system of equations. This we compare with the results for two hybrid vertices incorporating themore » Curtis-Pennington vertex in the fermion equation. We conclude that the KP vertex is as yet incomplete, and its relative gauge-variance is due to its lack of massive transverse components in its design.« less
The Equations of Motion of Compact Binaries in the Neighborhood of Supermassive Black Hole
Gorbatsievich, Alexander; Bobrik, Alexey
By the use of Einstein-Infeld-Hoffmann method, the equations of motion of a binary star system in the field of a supermassive black hole are derived. In spite of the fact that the motion of a binary system as a whole can be relativistic or even ultra-relativistic with respect to the supermassive black hole, it is shown, that under the assumption of non-relativistic relative motion of the stars in binary system, the motion of the binary system as a whole satisfies the Mathisson-Papapetrou equations with additional terms depending on quadrupole moments. Exemplary case of ultrarelativistic motion of a binary neutron star in the vicinity of non-rotating black hole is considered. It it shown that the motion of binary's center of mass may considerably differ from geodesic motion.
Grating formation by a high power radio wave in near-equator ionosphere
Singh, Rohtash; Sharma, A. K.; Tripathi, V. K.
The formation of a volume grating in the near-equator regions of ionosphere due to a high power radio wave is investigated. The radio wave, launched from a ground based transmitter, forms a standing wave pattern below the critical layer, heating the electrons in a space periodic manner. The thermal conduction along the magnetic lines of force inhibits the rise in electron temperature, limiting the efficacy of heating to within a latitude of few degrees around the equator. The space periodic electron partial pressure leads to ambipolar diffusion creating a space periodic density ripple with wave vector along the vertical. Such a volume grating is effective to cause strong reflection of radio waves at a frequency one order of magnitude higher than the maximum plasma frequency in the ionosphere. Linearly mode converted plasma wave could scatter even higher frequency radio waves.
The quantum equations of state of plasma under the influence of a weak magnetic field
Hussein, N. A.; Eisa, D. A.; Eldin, M. G.
The aim of this paper is to calculate the magnetic quantum equations of state of plasma, the calculation is based on the magnetic binary Slater sum in the case of low density. We consider only the thermal equilibrium plasma in the case of n{lambda}{sub ab}{sup 3} Much-Less-Than 1, where {lambda}{sub ab}{sup 2}=( Planck-Constant-Over-Two-Pi {sup 2}/m{sub ab}KT) is the thermal De Broglie wave length between two particles. The formulas contain the contributions of the magnetic field effects. Using these results we compute the magnetization and the magnetic susceptibility. Our equation of state is compared with others.
Non-perturbative effects for the Quark-Gluon Plasma equation of state
Begun, V. V. Gorenstein, M. I. Mogilevsky, O. A.
The non-perturbative effects for the Quark-Gluon Plasma (QGP) equation of state (EoS) are considered. The modifications of the bag model EoS are constructed to satisfy the main qualitative features observed for the QGP EoS in the lattice QCD calculations. A quantitative comparison with the lattice results is done for the SU(3) gluon plasma and for the QGP with dynamical quarks. Our analysis advocates a negative value of the bag constant B.
CONTRACTOR REPORT SAND97-2426 Unlimited Release UC-705 Penetration Equations
Office of Scientific and Technical Information (OSTI)
CONTRACTOR REPORT SAND97-2426 Unlimited Release * UC-705 Penetration Equations C. W. Young Applied Research Associates, Inc. 4300 San Mateo Blvd. NE, Suite A-220 Albuquerque NM 871 10 Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000. Approved for public release; distribution
SCIENCE ON SATURDAY- "Disastrous Equations: The Role of Mathematics in
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Understanding Tsunami" | Princeton Plasma Physics Lab 26, 2013, 9:30am Science On Saturday MBG Auditorium SCIENCE ON SATURDAY- "Disastrous Equations: The Role of Mathematics in Understanding Tsunami" Professor J. Douglas Wright, Associate Professor Department of Mathematics, Drexel University Presentation: PDF icon SOS26JAN2013_JDWright.pdf Science on Saturday is a series of lectures given by scientists, mathematicians, and other professionals involved in cutting-edge
Equivalence of integral and differential methods of generating accurately solvable potentials of the steady Schroedinger equation
Samsonov, B.F.
It is proven that the well-known nonlocal (i.e., based on integral transformations) methods of generating accurately solvable potentials of the one-dimensional steady Schroedinger equation are equivalent to multiple use of the local (i.e., based on a differential transformation) method known as the Darboux transformation. New accurately solvable potentials with a hydrogen-like spectrum are obtained, and several functions of the lowest states of the discrete spectrum are presented.
Jiang, Yan-Fei; Stone, James M.; Davis, Shane W.
We describe a new algorithm for solving the coupled frequency-integrated transfer equation and the equations of magnetohydrodynamics in the regime that light-crossing time is only marginally shorter than dynamical timescales. The transfer equation is solved in the mixed frame, including velocity-dependent source terms accurate to O(v/c). An operator split approach is used to compute the specific intensity along discrete rays, with upwind monotonic interpolation used along each ray to update the transport terms, and implicit methods used to compute the scattering and absorption source terms. Conservative differencing is used for the transport terms, which ensures the specific intensity (as well as energy and momentum) are conserved along each ray to round-off error. The use of implicit methods for the source terms ensures the method is stable even if the source terms are very stiff. To couple the solution of the transfer equation to the MHD algorithms in the ATHENA code, we perform direct quadrature of the specific intensity over angles to compute the energy and momentum source terms. We present the results of a variety of tests of the method, such as calculating the structure of a non-LTE atmosphere, an advective diffusion test, linear wave convergence tests, and the well-known shadow test. We use new semi-analytic solutions for radiation modified shocks to demonstrate the ability of our algorithm to capture the effects of an anisotropic radiation field accurately. Since the method uses explicit differencing of the spatial operators, it shows excellent weak scaling on parallel computers.
Viscosity Solutions of HJB Equations with Unbounded Data and Characteristic Points
Motta, Monica
We study a class of infinite horizon and exit-time control problems for nonlinear systems with unbounded data using the dynamic programming approach. We prove local optimality principles for viscosity super- and subsolutions of degenerate Hamilton-Jacobi equations in a very general setting. We apply these results to characterize the (possibly multiple) discontinuous solutions of Dirichlet and free boundary value problems as suitable value functions for the above-mentioned control problems.
Real-time and imaginary-time quantum hierarchal Fokker-Planck equations
Tanimura, Yoshitaka
We consider a quantum mechanical system represented in phase space (referred to hereafter as "Wigner space"), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for the hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first- and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and system-bath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material.
Nonlinear periodic waves solutions of the nonlinear self-dual network equations
Laptev, Denis V. Bogdan, Mikhail M.
The new classes of periodic solutions of nonlinear self-dual network equations describing the breather and soliton lattices, expressed in terms of the Jacobi elliptic functions have been obtained. The dependences of the frequencies on energy have been found. Numerical simulations of soliton lattice demonstrate their stability in the ideal lattice and the breather lattice instability in the dissipative lattice. However, the lifetime of such structures in the dissipative lattice can be extended through the application of ac driving terms.
Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action
Dvirny, A. I.; Slyn'ko, V. I. E-mail: firstname.lastname@example.com
Inverse theorems to Lyapunov's direct method are established for quasihomogeneous systems of differential equations with impulsive action. Conditions for the existence of Lyapunov functions satisfying typical bounds for quasihomogeneous functions are obtained. Using these results, we establish conditions for an equilibrium of a nonlinear system with impulsive action to be stable, using the properties of a quasihomogeneous approximation to the system. The results are illustrated by an example of a large-scale system with homogeneous subsystems. Bibliography: 30 titles. (paper)
Non-homogeneous solutions of a Coulomb Schr�dinger equation as basis set for scattering problems
Del Punta, J. A.; Ambrosio, M. J.; Gasaneo, G.; Zaytsev, S. A.; Ancarani, L. U.
We introduce and study two-body Quasi Sturmian functions which are proposed as basis functions for applications in three-body scattering problems. They are solutions of a two-body non-homogeneous Schr�dinger equation. We present different analytic expressions, including asymptotic behaviors, for the pure Coulomb potential with a driven term involving either Slater-type or Laguerre-type orbitals. The efficiency of Quasi Sturmian functions as basis set is numerically illustrated through a two-body scattering problem.
Argonne OutLoud: Changing the bio-energy equation (April 12, 2012) |
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Argonne National Laboratory Changing the bio-energy equation (April 12, 2012) Share Description Argonne OutLoud public lecture series. Episode 1: Argonomist Cristina Negri talks about phytoremediation for polluted soil and water. Speakers Cristina Negri Duration 00:55:11 Topic Community Education Outreach Environment Environmental science & technology Land reclamation Water quality Video ID http://youtu.be/vlMUJOs4vh0 Credit Argonne National Laboratory Cristina Negri
The tunneling solutions of the time-dependent Schroedinger equation for a square-potential barrier
Elci, A.; Hjalmarson, H. P.
The exact tunneling solutions of the time-dependent Schroedinger equation with a square-potential barrier are derived using the continuous symmetry group G{sub S} for the partial differential equation. The infinitesimal generators and the elements for G{sub S} are represented and derived in the jet space. There exist six classes of wave functions. The representative (canonical) wave functions for the classes are labeled by the eigenvalue sets, whose elements arise partially from the reducibility of a Lie subgroup G{sub LS} of G{sub S} and partially from the separation of variables. Each eigenvalue set provides two or more time scales for the wave function. The ratio of two time scales can act as the duration of an intrinsic clock for the particle motion. The exact solutions of the time-dependent Schroedinger equation presented here can produce tunneling currents that are orders of magnitude larger than those produced by the energy eigenfunctions. The exact solutions show that tunneling current can be quantized under appropriate boundary conditions and tunneling probability can be affected by a transverse acceleration.
Coughlin, Eric R.; Begelman, Mitchell C. E-mail: email@example.com
We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.
A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics
Shao, Yan-Lin Faltinsen, Odd M.
We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods, e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.
Unified Einstein-Virasoro Master Equation in the General Non-Linear Sigma Model
Boer, J. de; Halpern, M.B.
The Virasoro master equation (VME) describes the general affine-Virasoro construction $T=L^abJ_aJ_b+iD^a \\dif J_a$ in the operator algebra of the WZW model, where $L^ab$ is the inverse inertia tensor and $D^a $ is the improvement vector. In this paper, we generalize this construction to find the general (one-loop) Virasoro construction in the operator algebra of the general non-linear sigma model. The result is a unified Einstein-Virasoro master equation which couples the spacetime spin-two field $L^ab$ to the background fields of the sigma model. For a particular solution $L_G^ab$, the unified system reduces to the canonical stress tensors and conventional Einstein equations of the sigma model, and the system reduces to the general affine-Virasoro construction and the VME when the sigma model is taken to be the WZW action. More generally, the unified system describes a space of conformal field theories which is presumably much larger than the sum of the general affine-Virasoro construction and the sigma model with its canonical stress tensors. We also discuss a number of algebraic and geometrical properties of the system, including its relation to an unsolved problem in the theory of $G$-structures on manifolds with torsion.
Discontinuous Galerkin solution of the Navier-Stokes equations on deformable domains
Persson, P.-O.; Bonet, J.; Peraire, J.
We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain, By writing the Navier-Stokes equations as a conservation law for the independent variables in the reference configuration, the complexity introduced by variable geometry is reduced to solving a transformed conservation law in a fixed reference configuration, The spatial discretization is carried out using the Discontinuous Galerkin method on unstructured meshes of triangles, while the time integration is performed using an explicit Runge-Kutta method, For general domain changes, the standard scheme fails to preserve exactly the free-stream solution which leads to some accuracy degradation, especially for low order approximations. This situation is remedied by adding an additional equation for the time evolution of the transformation Jacobian to the original conservation law and correcting for the accumulated metric integration errors. A number of results are shown to illustrate the flexibility of the approach to handle high order approximations on complex geometries.
A Vorticity-Divergence Global Semi-Lagrangian Spectral Model for the Shallow Water Equations
Drake, JB
The shallow water equations modeling flow on a sphere are useful for the development and testing of numerical algorithms for atmospheric climate and weather models. A new formulation of the shallow water equations is derived which exhibits an advective form for the vorticity and divergence. This form is particularly well suited for numerical computations using a semi-Lagrangian spectral discretization. A set of test problems, standard for the shallow water equations on a sphere, are solved and results compared with an Eulerian spectral model. The semi-Lagrangian transport method was introduced into atmospheric modeling by Robert, Henderson, and Turnbull. A formulation based on a three time level integration scheme in conjunction with a finite difference spatial discretization was studied by Ritchie. Two time level grid point schemes were derived by Bates et al. Staniforth and Cote survey developments of the application of semi-Lagrangian transport (SLT) methods for shallow water models and for numerical weather prediction. The spectral (or spherical harmonic transform) method when combined with a SLT method is particularly effective because it allows for long time steps avoiding the Courant-Friedrichs-Lewy (CFL) restriction of Eulerian methods, while retaining accurate (spectral) treatment of the spatial derivatives. A semi-implicit, semi-Lagrangian formulation with spectral spatial discretization is very effective because the Helmholz problem arising from the semi-implicit time integration can be solved cheaply in the course of the spherical harmonic transform. The combination of spectral, semi-Lagrangian transport with a semi-implicit time integration schemes was first proposed by Ritchie. A advective formulation using vorticity and divergence was introduced by Williamson and Olson. They introduce the vorticity and divergence after the application of the semi-Lagrangian discretization. The semi-Lagrangian formulation of Williamson and Olson and Bates et al. has the property that the metric terms of the advective form are treated discretely requiring a delicate spherical vector addition of terms at the departure point and arrival point. In their formulation, the metric terms associated with the advection operator do not appear explicitly. The spherical geometry associated with the combination of vector quantities at arrival and departure points treats the metric terms and is derived in Bates et al. The formulation derived in this paper avoids this vector addition. It is possible to do this because our formulation is based entirely on a scalar, advective form of the momentum equations. This new form is made possible by the generalization of a vector identity to spherical geometry. In Section 2 the standard form of the shallow water equations in spherical geometry are given. Section 3 presents the vector identities needed to derive an advective form of the vorticity and divergence equations. The semi-implicit time integration and semi-Lagrangian transport method are described in Section 4. The SLT interpolation scheme is described in Section 5. Section 6 completes the development of the discrete model with the description of the semi-implicit spectral equations. A discussion of results on several standard test problems is contained in Section 7.
Nonlinear diffusion acceleration for the multigroup transport equation discretized with S{sub N} and continuous FEM with rattlesnake
Wang, Y.
Nonlinear diffusion acceleration (NDA) can improve the performance of a neutron transport solver significantly especially for the multigroup eigenvalue problems. The high-order transport equation and the transport-corrected low-order diffusion equation form a nonlinear system in NDA, which can be solved via a Picard iteration. The consistency of the correction of the low-order equation is important to ensure the stabilization and effectiveness of the iteration. It also makes the low-order equation preserve the scalar flux of the high-order equation. In this paper, the consistent correction for a particular discretization scheme, self-adjoint angular flux (SAAF) formulation with discrete ordinates method (S{sub N}) and continuous finite element method (CFEM) is proposed for the multigroup neutron transport equation. Equations with the anisotropic scatterings and a void treatment are included. The Picard iteration with this scheme has been implemented and tested with RattleS{sub N}ake, a MOOSE-based application at INL. Convergence results are presented. (authors)
Final Report for "Extending BOUT++ for Solution of Edge Plasma Equations for Use in Whole Device Simulation of Tokamaks"
Ammar H Hakim
In this Phase I project we have extended the BOUT++ code to solve edge fluid equations. We added a simple neutral fluid model, created a mesh generator as well as collected a set of difficult test problems for benchmarking edge codes. The work in this project should be useful as a starting point to build a complete set of edge fluid equations in BOUT++ that would enhance its ability to not only perform edge turbulence calculations, but also allow the coupled transport-turbulence equations evolved in an efficient manner.
The Equation of State of LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide)
Office of Scientific and Technical Information (OSTI)
(Conference) | SciTech Connect Conference: The Equation of State of LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide) Citation Details In-Document Search Title: The Equation of State of LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide) Authors: Zaug, J M ; Stavrou, E ; Kalkan, B Publication Date: 2015-02-25 OSTI Identifier: 1184137 Report Number(s): LLNL-PROC-667859 DOE Contract Number: DE-AC52-07NA27344 Resource Type: Conference Resource Relation: Conference: Presented at: The Equation of
Smoothed particle hydrodynamics model for Landau-Lifshitz Navier-Stokes and advection-diffusion equations
Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre M.
We propose a novel Smoothed Particle Hydrodynamics (SPH) discretization of the fully-coupled Landau-Lifshitz-Navier-Stokes (LLNS) and advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations are found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for the coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study the formation of the so-called giant fluctuations of the front between light and heavy fluids with and without gravity, where the light fluid lays on the top of the heavy fluid. We find that the power spectra of the simulated concentration field is in good agreement with the experiments and analytical solutions. In the absence of gravity the the power spectra decays as the power -4 of the wave number except for small wave numbers which diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations resulting in the much weaker dependence of the power spectra on the wave number. Finally the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlying a light fluid. The front dynamics is shown to agree well with the analytical solutions.
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Qin, Hong; Burby, Joshua W; Davidson, Ronald C
It is commonly believed that energy-momentum conservation is the result of space-time symmetry. However, for classical particle-field systems, e.g., Klimontovich-Maxwell and Klimontovich- Poisson systems, such a connection hasn't been formally established. The difficulty is due to the fact that particles and the electromagnetic fields reside on different manifolds. To establish the connection, the standard Euler-Lagrange equation needs to be generalized to a weak form. Using this technique, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived.
Soliton stability and collapse in the discrete nonpolynomial Schroedinger equation with dipole-dipole interactions
Gligoric, Goran; Hadzievski, Ljupco; Maluckov, Aleksandra; Malomed, Boris A.
The stability and collapse of fundamental unstaggered bright solitons in the discrete Schroedinger equation with the nonpolynomial on-site nonlinearity, which models a nearly one-dimensional Bose-Einstein condensate trapped in a deep optical lattice, are studied in the presence of the long-range dipole-dipole (DD) interactions. The cases of both attractive and repulsive contact and DD interaction are considered. The results are summarized in the form of stability-collapse diagrams in the parametric space of the model, which demonstrate that the attractive DD interactions stabilize the solitons and help to prevent the collapse. Mobility of the discrete solitons is briefly considered too.
Effects of bounded space in the solutions of time-space fractional diffusion equation
Allami, M. H. [Laser and Plasma Research Institute, Shahid Beheshti University, Tehran (Iran, Islamic Republic of); Shokri, B. [Laser and Plasma Research Institute, Shahid Beheshti University, Tehran (Iran, Islamic Republic of); Physics Department, Shahid Beheshti University, G.C., Tehran (Iran, Islamic Republic of)
By using a recently proposed numerical method, the fractional diffusion equation with memory in a finite domain is solved for different asymmetry parameters and fractional orders. Some scaling laws are revisited in this condition, such as growth rate in a distance from pulse perturbation, the time when the perturbative peak reaches the other points, and advectionlike behavior as a result of asymmetry and memory. Conditions for negativity and instability of solutions are shown. Also up-hill transport and its time-space region are studied.
Inverse scattering transform for the focusing nonlinear Schr�dinger equation with nonzero boundary conditions
Biondini, Gino; Kova?i?, Gregor
The inverse scattering transform for the focusing nonlinear Schr�dinger equation with non-zero boundary conditions at infinity is presented, including the determination of the analyticity of the scattering eigenfunctions, the introduction of the appropriate Riemann surface and uniformization variable, the symmetries, discrete spectrum, asymptotics, trace formulae and the so-called theta condition, and the formulation of the inverse problem in terms of a Riemann-Hilbert problem. In addition, the general behavior of the soliton solutions is discussed, as well as the reductions to all special cases previously discussed in the literature.
(U) A Gruneisen Equation of State for TPX. Application in FLAG
Fredenburg, David A.; Aslam, Tariq Dennis; Bennett, Langdon Stanford
A Gruneisen equation of state (EOS) is developed for the polymer TPX (poly 4-methyl-1-pentene) within the LANL hydrocode FLAG. Experimental shock Hugoniot data for TPX is fit to a form of the Gruneisen EOS, and the necessary parameters for implementing the TPX EOS in FLAG are presented. The TPX EOS is further validated through one-dimensional simulations of recent double-shock experiments, and a comparison is made between the new Gruneisen EOS for TPX and the EOS representation for TPX used in the LANL Common Model.
Optimal recovery of the solution of the heat equation from inaccurate data
Magaril-Il'yaev, G G; Osipenko, Konstantin Yu
The problem of optimal recovery of the solution of the heat equation in the entire space at a fixed instant of time from inaccurate observations of this solution at some other instants of time is investigated. Explicit expressions for an optimal recovery method and its error are given. The solution of a similar problem with a priori information about the temperature distribution at some instants of time is also given. In all cases the optimal method uses information about at most two observations. Bibliography: 22 titles.
Stabilization of the solution of a�doubly nonlinear parabolic equation
Andriyanova, � R; Mukminov, F Kh
The method of Galerkin approximations is employed to prove the existence of a�strong global (in time) solution of a�doubly nonlinear parabolic equation in an unbounded domain. The second integral identity is established for Galerkin approximations, and passing to the limit in it an estimate for the decay rate of the norm of the solution from below is obtained. The estimates characterizing the decay rate of the solution as x?? obtained here are used to derive an upper bound for the decay rate of the solution with respect to time; the resulting estimate is pretty close to the lower one. Bibliography: 17 titles.
Photon equation of motion with application to the electron's anomalous magnetic moment
Ritchie, A B
The photon equation of motion previously applied to the Lamb shift is here applied to the anomalous magnetic moment of the electron. Exact agreement is obtained with the QED result of Schwinger. The photon theory treats the radiative correction to the photon in the presence of the electron rather than its inverse as in standard QED. The result is found to be first-order in the photon-electron interaction rather than second-order as in standard QED, introducing an ease of calculation hitherto unavailable.
Hamiltonian field description of the one-dimensional Poisson-Vlasov equations
Morrison, P.J.
The one-dimensional Poisson-Vlasov equations are cast into Hamiltonian form. A Poisson Bracket in terms of the phase space density, as sole dynamical variable, is presented. This Poisson bracket is not of the usual form, but possesses the commutator properties of antisymmetry, bilinearity, and nonassociativity by virtue of the Jacobi requirement. Clebsch potentials are seen to yield a conventional (canonical) formulation. This formulation is discretized by expansion in terms of an arbitrary complete set of basis functions. In particular, a wave field representation is obtained.
Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
Lamata, L.; Leon, J.; Schaetz, T.; Solano, E.
We present a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle are associated with the respective ionic variables. We show also how to simulate the simplified 1+1 case, requiring the manipulation of only two internal levels and one motional degree of freedom. Moreover, we study relevant quantum-relativistic effects, like the Zitterbewegung and Klein's paradox, the transition from massless to massive fermions, and the relativistic and nonrelativistic limits, via the tuning of controllable experimental parameters.
A dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain
Valilyev, O.V.; Paolucci, S.
A dynamically adaptive multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution. High resolution computations are performed only in regions where sharp transitions occur. The scheme handles general boundary conditions. The method is applied to the solution of the one-dimensional Burgers equation with small viscosity, a moving shock problem, and a nonlinear thermoacoustic wave problem. The results indicate that the method is very accurate and efficient. 16 refs., 9 figs., 2 tab.
Validation of a zero-equation turbulence model for complex indoor airflow simulation
Srebric, J.; Chen, Q.; Glicksman, L.R.
The design of an indoor environment requires a tool that can quickly predict the three-dimensional distributions of air velocity, temperature, and contaminant concentrations in the room on a desktop computer. This investigation has tested a zero-equation turbulence model for the prediction of the indoor environment in an office with displacement ventilation, with a heater and infiltration and with forced convection and a partition wall. The computed air velocity and temperature distributions agree well with the measured data. The computing time for each case is less than seven minutes on a PC Pentium II, 350 MHz.
Momentum space iterative solution of the time-dependent Schrödinger equation
Kiss, G. Zs.; Borbély, S.; Nagy, L.
We present a novel approach, the iterative solution of the time-dependent Schrödinger equation (iTDSE model), for the investigation of atomic systems interacting with external laser fields. This model is the extension of the momentum-space strong-field approximation (MSSFA) [1], in which the Coulomb potential was considered only as a first order perturbation. In the iTDSE approach higher order terms were gradually introduced until convergence was achieved. Benchmark calculations were done on the hydrogen atom, and the obtained results were compared to the direct numerical solution [2].
Dissipation in a rotating frame: Master equation, effective temperature, and Lamb shift
Verso, Alvise; Ankerhold, Joachim
Motivated by recent realizations of microwave-driven nonlinear resonators in superconducting circuits, the impact of environmental degrees of freedom is analyzed as seen from a rotating frame. A system plus reservoir model is applied to consistently derive in the weak coupling limit the master equation for the reduced density in the moving frame and near the first bifurcation threshold. The concept of an effective temperature is introduced to analyze to what extent a detailed balance relation exists. Explicit expressions are also found for the Lamb-shift. Results for ohmic baths are in agreement with experimental findings, while for structured environments population inversion is predicted that may qualitatively explain recent observations.
The role of electron equation of state in heating partition of protons in a collisionless plasma
Parashar, Tulasi N.; Vasquez, Bernard J.; Markovskii, Sergei A.
One of the outstanding questions related to the solar wind is the heating of solar wind plasma. Addressing this question requires a self consistent treatment of the kinetic physics of a collisionless plasma. A hybrid code (with particle ions and fluid electrons) is one of the most convenient computational tools, which allows us to explore self consistent ion kinetics, while saving us computational time as compared to the full particle in cell codes. A common assumption used in hybrid codes is that of isothermal electrons. In this paper, we discuss the role that the equation of state for electrons could potentially play in determining the ion kinetics.
Equations of State of Anhydrous AlF3 and AlI3: Modeling of Extreme...
Office of Scientific and Technical Information (OSTI)
Condition Halide Chemistry Citation Details In-Document Search Title: Equations of State of Anhydrous AlF3 and AlI3: Modeling of Extreme Condition Halide Chemistry Authors: ...
Symmetries of Einstein's field equations with a perfect fluid source as examples of Lie--Baecklund symmetries
Stephani, H.
The framework of Lie--Baecklund (or generalized) symmetries is used to give a unifying view of some of the known symmetries of Einstein's field equations for the vacuum or perfect fluid case (with a ..mu.. = p or a ..mu..+3p = 0 equation of state). These symmetries occur if space-time admits one or two Killing vectors (orthogonal or parallel, respectively, to the four-velocity in the perfect fluid case).
Zakharov-Kuznetsov equation in a magnetized plasma with two temperature superthermal electrons
Saini, N. S. Chahal, B. S.; Bains, A. S.; Bedi, C.
A nonlinear Zakharov-Kuznetsov (ZK) equation for ion-acoustic solitary waves (IASWs) in a magnetized plasmas containing kappa distributed cold and hot electrons is derived by using reductive perturbation method. From the solution of ZK equation, the characteristics of IASWs have been studied under the influence of various plasma parameters. Existence domain of physical parameters is determined. It has been observed that the present plasma system supports the existence of both positive as well as negative potential solitons. The combined effects of cold to hot electron temperature ratio (?), density ratio of cold electrons to ions (f), superthermality of cold and hot electrons (?{sub c},?{sub h}), strength of magnetic field (via ?{sub i}), and obliqueness (?) significantly influence the profile of IASWs. The physical parameters play a great role to modify the width and amplitude of the solitary structures. The stability analysis is also presented in this investigation and parametric range is determined to check the presence of stable and unstable solitons. The findings of this study are important to the physics of electrostatic wave structures in the Saturn's magnetosphere where two temperature electrons with kappa distribution exist.
Dromion-like structures and stability analysis in the variable coefficients complex Ginzburg–Landau equation
Wong, Pring; Pang, Li-Hui; Huang, Long-Gang; Li, Yan-Qing; Lei, Ming; Liu, Wen-Jun
The study of the complex Ginzburg–Landau equation, which can describe the fiber laser system, is of significance for ultra-fast laser. In this paper, dromion-like structures for the complex Ginzburg–Landau equation are considered due to their abundant nonlinear dynamics. Via the modified Hirota method and simplified assumption, the analytic dromion-like solution is obtained. The partial asymmetry of structure is particularly discussed, which arises from asymmetry of nonlinear and dispersion terms. Furthermore, the stability of dromion-like structures is analyzed. Oscillation structure emerges to exhibit strong interference when the dispersion loss is perturbed. Through the appropriate modulation of modified exponent parameter, the oscillation structure is transformed into two dromion-like structures. It indicates that the dromion-like structure is unstable, and the coherence intensity is affected by the modified exponent parameter. Results in this paper may be useful in accounting for some nonlinear phenomena in fiber laser systems, and understanding the essential role of modified Hirota method.
Time-local view of nonequilibrium statistical mechanics. II. Generalized Langevin equations
Der, R.
On a semiphenomenological level, generalized Langevin equations are usually obtained by adding a random force (RF) term to macroscopic deterministic equations assumed to be known. Here this procedure is made rigorous by conveniently redefining the RF, which is shown to be colored noise weakly correlated with the observables at earlier times due to the finite lifetime of microscopic events. Corresponding fluctuation-dissipation theorems are derived. Explicit expressions for the spectral density of the fluctuations are obtained in a particularly simple form, with the deviation of the line shape from the Lorentzian being related most explicitly to the spectral density of the RF. Well-known low-frequency expressions and the Einstein relation of (generalized) Brownian motion theory are modified so as to include lifetime effects. New sum rules are obtained relating dissipative quantities to contour integrals (in the complex frequency domain) over spectral densities or corresponding response functions. The Heisenberg dynamics of a complete set of macroobservables is shown to be equivalent to a generalized Orstein-Uhlenbeck stochastic process which is a non-Markovian process due to the lifetime effects.
Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems
Hykes, J. M.; Ferrer, R. M.
The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is {sup 98}Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)
Implementation of two-equation soot flamelet models for laminar diffusion flames
Carbonell, D.; Oliva, A.; Perez-Segarra, C.D.
The two-equation soot model proposed by Leung et al. [K.M. Leung, R.P. Lindstedt, W.P. Jones, Combust. Flame 87 (1991) 289-305] has been derived in the mixture fraction space. The model has been implemented using both Interactive and Non-Interactive flamelet strategies. An Extended Enthalpy Defect Flamelet Model (E-EDFM) which uses a flamelet library obtained neglecting the soot formation is proposed as a Non-Interactive method. The Lagrangian Flamelet Model (LFM) is used to represent the Interactive models. This model uses direct values of soot mass fraction from flamelet calculations. An Extended version (E-LFM) of this model is also suggested in which soot mass fraction reaction rates are used from flamelet calculations. Results presented in this work show that the E-EDFM predict acceptable results. However, it overpredicts the soot volume fraction due to the inability of this model to couple the soot and gas-phase mechanisms. It has been demonstrated that the LFM is not able to predict accurately the soot volume fraction. On the other hand, the extended version proposed here has been shown to be very accurate. The different flamelet mathematical formulations have been tested and compared using well verified reference calculations obtained solving the set of the Full Transport Equations (FTE) in the physical space. (author)
A Discontinuous Petrov-Galerkin Methodology for Adaptive Solutions to the Incompressible Navier-Stokes Equations
Roberts, Nathan V.; Demkowiz, Leszek; Moser, Robert
The discontinuous Petrov-Galerkin methodology with optimal test functions (DPG) of Demkowicz and Gopalakrishnan [18, 20] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. Whereas Bubnov-Galerkin methods use identical trial and test spaces, Petrov-Galerkin methods allow these function spaces to differ. In DPG, test functions are computed on the fly and are chosen to realize the supremum in the inf-sup condition; the method is equivalent to a minimum residual method. For well-posed problems with sufficiently regular solutions, DPG can be shown to converge at optimal rates—the inf-sup constants governing the convergence are mesh-independent, and of the same order as those governing the continuous problem [48]. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. We employ DPG to solve the steady incompressible Navier-Stokes equations in two dimensions, building on previous work on the Stokes equations, and focusing particularly on the usefulness of the approach for automatic adaptivity starting from a coarse mesh. We apply our approach to a manufactured solution due to Kovasznay as well as the lid-driven cavity flow, backward-facing step, and flow past a cylinder problems.
Implementation of an interactive matching scheme for the Kapchinskij-Vladimirskij equations in the WARP code
Chilton, Sven H.
The WARP code is a robust electrostatic particle-in-cell simulation package used to model charged particle beams with strong space-charge forces. A fundamental operation associated with seeding detailed simulations of a beam transport channel is to generate initial conditions where the beam distribution is matched to the structure of a periodic focusing lattice. This is done by solving for periodic, matched solutions to a coupled set of ODEs called the Kapchinskij-Vladimirskij (KV) envelope equations, which describe the evolution of low-order beam moments subject to applied lattice focusing, space-charge defocusing, and thermal defocusing forces. Recently, an iterative numerical method was developed (Lund, Chilton, and Lee, Efficient computation of matched solutions to the KV envelope equations for periodic focusing lattices, Physical Review Special Topics-Accelerators and Beams 9, 064201 2006) to generate matching conditions in a highly flexible, convergent, and fail-safe manner. This method is extended and implemented in the WARP code as a Python package to vastly ease the setup of detailed simulations. In particular, the Python package accommodates any linear applied lattice focusing functions without skew coupling, and a more general set of beam parameter specifications than its predecessor. Lattice strength iteration tools were added to facilitate the implementation of problems with specific applied focusing strengths.
Implementation of an iterative matching scheme for the Kapchinskij-Vladimirskij equations in the WARP code
Chilton, Sven; Chilton, Sven H.
The WARP code is a robust electrostatic particle-in-cell simulation package used to model charged particle beams with strong space-charge forces. A fundamental operation associated with seeding detailed simulations of a beam transport channel is to generate initial conditions where the beam distribution is matched to the structure of a periodic focusing lattice. This is done by solving for periodic, matched solutions to a coupled set of ODEs called the Kapchinskij-Vladimirskij (KV) envelope equations, which describe the evolution of low-order beam moments subject to applied lattice focusing, space-charge defocusing, and thermal defocusing forces. Recently, an iterative numerical method was developed (Lund, Chilton, and Lee, Efficient computation of matched solutions to the KV envelope equations for periodic focusing lattices, Physical Review Special Topics-Accelerators and Beams 9, 064201 2006) to generate matching conditions in a highly flexible, convergent, and fail-safe manner. This method is extended and implemented in the WARP code as a Python package to vastly ease the setup of detailed simulations. In particular, the Python package accommodates any linear applied lattice focusing functions without skew coupling, and a more general set of beam parameter specifications than its predecessor. Lattice strength iteration tools were added to facilitate the implementation of problems with specific applied focusing strengths.
Measurements of the equations of state and spectrum of nonideal xenon plasma under shock compression
Zheng, J.; Gu, Y. J.; Chen, Z. Y.; Chen, Q. F.
Experimental equations of state on generation of nonideal xenon plasma by intense shock wave compression was presented in the ranges of pressure of 2-16 GPa and temperature of 31-50 kK, and the xenon plasma with the nonideal coupling parameter {Gamma} range from 0.6-2.1 was generated. The shock wave was produced using the flyer plate impact and accelerated up to {approx}6 km/s with a two-stage light gas gun. Gaseous specimens were shocked from two initial pressures of 0.80 and 4.72 MPa at room temperature. Time-resolved spectral radiation histories were recorded by using a multiwavelength channel pyrometer. The transient spectra with the wavelength range of 460-700 nm were recorded by using a spectrometer to evaluate the shock temperature. Shock velocity was measured and particle velocity was determined by the impedance matching methods. The equations of state of xenon plasma and ionization degree have been discussed in terms of the self-consistent fluid variational theory.
First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Hu, S. X.; Collins, L. A.; Goncharov, V. N.; Kress, J. D.; McCrory, R. L.; Skupsky, S.
Obtaining an accurate equation of state (EOS) of polystyrene (CH) is crucial to reliably design inertial confinement fusion (ICF) capsules using CH/CH-based ablators. Thus, with first-principles calculations, we have investigated the extended EOS of CH over a wide range of plasma conditions (ρ = 0.1 to 100 g/cm3 and T = 1,000 to 4,000,000 K). When compared with the widely used SESAME-EOS table, the first-principles equation of state (FPEOS) of CH has shown significant differences in the low-temperature regime, in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic target implosionsmore » on OMEGA using the FPEOS table of CH have predicted ~5% reduction in implosion velocity and ~30% decrease in neutron yield in comparison with the usual SESAME simulations. This is attributed to the ~10% lower mass ablation rate of CH predicted by FPEOS. Simulations using CH-FPEOS show better agreement with measurements of Hugoniot temperature and scattered lights from ICF implosions.« less
First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions
Hu, S. X.; Collins, L. A.; Goncharov, V. N.; Kress, J. D.; McCrory, R. L.; Skupsky, S.
Obtaining an accurate equation of state (EOS) of polystyrene (CH) is crucial to reliably design inertial confinement fusion (ICF) capsules using CH/CH-based ablators. Thus, with first-principles calculations, we have investigated the extended EOS of CH over a wide range of plasma conditions (ρ = 0.1 to 100 g/cm3 and T = 1,000 to 4,000,000 K). When compared with the widely used SESAME-EOS table, the first-principles equation of state (FPEOS) of CH has shown significant differences in the low-temperature regime, in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic target implosions on OMEGA using the FPEOS table of CH have predicted ~5% reduction in implosion velocity and ~30% decrease in neutron yield in comparison with the usual SESAME simulations. This is attributed to the ~10% lower mass ablation rate of CH predicted by FPEOS. Simulations using CH-FPEOS show better agreement with measurements of Hugoniot temperature and scattered lights from ICF implosions.
Cluster virial expansion for the equation of state of partially ionized hydrogen plasma
Omarbakiyeva, Y. A.; Fortmann, C.; Ramazanov, T. S.; Roepke, G.
We study the contribution of electron-atom interaction to the equation of state for partially ionized hydrogen plasma using the cluster-virial expansion. We use the Beth-Uhlenbeck approach to calculate the second virial coefficient for the electron-atom (bound cluster) pair from the corresponding scattering phase shifts and binding energies. Experimental scattering cross-sections as well as phase shifts calculated on the basis of different pseudopotential models are used as an input for the Beth-Uhlenbeck formula. By including Pauli blocking and screening in the phase shift calculation, we generalize the cluster-virial expansion in order to cover also near solid density plasmas. We present results for the electron-atom contribution to the virial expansion and the corresponding equation of state, i.e. pressure, composition, and chemical potential as a function of density and temperature. These results are compared with semiempirical approaches to the thermodynamics of partially ionized plasmas. Avoiding any ill-founded input quantities, the Beth-Uhlenbeck second virial coefficient for the electron-atom interaction represents a benchmark for other, semiempirical approaches.
Equation-based languages – A new paradigm for building energy modeling, simulation and optimization
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Wetter, Michael; Bonvini, Marco; Nouidui, Thierry S.
Most of the state-of-the-art building simulation programs implement models in imperative programming languages. This complicates modeling and excludes the use of certain efficient methods for simulation and optimization. In contrast, equation-based modeling languages declare relations among variables, thereby allowing the use of computer algebra to enable much simpler schematic modeling and to generate efficient code for simulation and optimization. We contrast the two approaches in this paper. We explain how such manipulations support new use cases. In the first of two examples, we couple models of the electrical grid, multiple buildings, HVAC systems and controllers to test a controller thatmore » adjusts building room temperatures and PV inverter reactive power to maintain power quality. In the second example, we contrast the computing time for solving an optimal control problem for a room-level model predictive controller with and without symbolic manipulations. As a result, exploiting the equation-based language led to 2, 200 times faster solution« less
A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Hybrid Grids
Xiaodong Liu; Lijun Xuan; Hong Luo; Yidong Xia
A reconstructed discontinuous Galerkin (rDG(P1P2)) method, originally introduced for the compressible Euler equations, is developed for the solution of the compressible Navier- Stokes equations on 3D hybrid grids. In this method, a piecewise quadratic polynomial solution is obtained from the underlying piecewise linear DG solution using a hierarchical Weighted Essentially Non-Oscillatory (WENO) reconstruction. The reconstructed quadratic polynomial solution is then used for the computation of the inviscid fluxes and the viscous fluxes using the second formulation of Bassi and Reay (Bassi-Rebay II). The developed rDG(P1P2) method is used to compute a variety of flow problems to assess its accuracy, efficiency, and robustness. The numerical results demonstrate that the rDG(P1P2) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to the large eddy simulation (LES) and direct numerical simulation (DNS) of compressible turbulent flows.
Detecting breast microcalcifications using super-resolution and wave-equation ultrasound imaging: a numerical phantom study
Huang, Lianjie; Simonetti, Francesco; Huthwaite, Peter; Rosenberg, Robert; Williamson, Michael
Ultrasound image resolution and quality need to be significantly improved for breast microcalcification detection. Super-resolution imaging with the factorization method has recently been developed as a promising tool to break through the resolution limit of conventional imaging. In addition, wave-equation reflection imaging has become an effective method to reduce image speckles by properly handling ultrasound scattering/diffraction from breast heterogeneities during image reconstruction. We explore the capabilities of a novel super-resolution ultrasound imaging method and a wave-equation reflection imaging scheme for detecting breast microcalcifications. Super-resolution imaging uses the singular value decomposition and a factorization scheme to achieve an image resolution that is not possible for conventional ultrasound imaging. Wave-equation reflection imaging employs a solution to the acoustic-wave equation in heterogeneous media to backpropagate ultrasound scattering/diffraction waves to scatters and form images of heterogeneities. We construct numerical breast phantoms using in vivo breast images, and use a finite-difference wave-equation scheme to generate ultrasound data scattered from inclusions that mimic microcalcifications. We demonstrate that microcalcifications can be detected at full spatial resolution using the super-resolution ultrasound imaging and wave-equation reflection imaging methods.
Algorithmically scalable block preconditioner for fully implicit shallow water equations in CAM-SE
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Lott, P Aaron; Woodward, Carol; Evans, Katherine J
Performing accurate and efficient numerical simulation of global atmospheric climate models is challenging due to the disparate length and time scales over which physical processes interact. Implicit solvers enable the physical system to be integrated with a time step commensurate with processes being studied. The dominant cost of an implicit time step is the ancillary linear system solves, so we have developed a preconditioner aimed at improving the efficiency of these linear system solves. Our preconditioner is based on an approximate block factorization of the linearized shallow-water equations and has been implemented within the spectral element dynamical core within themore » Community Atmospheric Model (CAM-SE). In this paper we discuss the development and scalability of the preconditioner for a suite of test cases with the implicit shallow-water solver within CAM-SE.« less
Equation-of-State Test Suite for the DYNA3D Code
Benjamin, Russell D.
This document describes the creation and implementation of a test suite for the Equationof- State models in the DYNA3D code. A customized input deck has been created for each model, as well as a script that extracts the relevant data from the high-speed edit file created by DYNA3D. Each equation-of-state model is broken apart and individual elements of the model are tested, as well as testing the entire model. The input deck for each model is described and the results of the tests are discussed. The intent of this work is to add this test suite to the validation suite presently used for DYNA3D.
Accelerating Time Integration for the Shallow Water Equations on the Sphere Using GPUs
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Archibald, R.; Evans, K. J.; Salinger, A.
The push towards larger and larger computational platforms has made it possible for climate simulations to resolve climate dynamics across multiple spatial and temporal scales. This direction in climate simulation has created a strong need to develop scalable time-stepping methods capable of accelerating throughput on high performance computing. This work details the recent advances in the implementation of implicit time stepping on a spectral element cube-sphere grid using graphical processing units (GPU) based machines. We demonstrate how solvers in the Trilinos project are interfaced with ACME and GPU kernels can significantly increase computational speed of the residual calculations in themore » implicit time stepping method for the shallow water equations on the sphere. We show the optimization gains and data structure reorganization that facilitates the performance improvements.« less
Collapse for the higher-order nonlinear Schrödinger equation
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Achilleos, V.; Diamantidis, S.; Frantzeskakis, D. J.; Horikis, T. P.; Karachalios, N. I.; Kevrekidis, P. G.
We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schrodinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zero-state, from collapse. The numerical simulations, performed for a wide class of initial data, aremore » found to be in very good agreement with the analytical results, and reveal long-time stability properties of localized solutions. The role of the higher-order effects to the transient dynamics is also revealed in these simulations.« less
Differential total absorptivity solution to the radiative transfer equation for mixtures of combustion gases and soot
Bressloff, N.W.; Moss, J.B.; Rubini, P.A.
The differential total absorptivity (DTA) solution to the radiative transfer equation, originally devised for combustion gases in the discrete transfer radiation model, is extended to mixtures of gaseous combustion products and soot. The method is compared to other solution techniques for representative mixtures across single lines of sight and across a layer bounded by solid walls. Intermediate soot loadings are considered such that the total radiance is not dominated by either the gaseous or soot components. The DTA solution is shown to yield excellent accuracy relative to a narrow-band solution, with a considerable saving in computational cost. Thus, explicit treatment of the source temperature dependence of absorption is successfully demonstrated without the need for spectral integration.
Relativistic equation of state at subnuclear densities in the Thomas-Fermi approximation
Zhang, Z. W.; Shen, H., E-mail: firstname.lastname@example.com [School of Physics, Nankai University, Tianjin 300071 (China)
We study the non-uniform nuclear matter using the self-consistent Thomas-Fermi approximation with a relativistic mean-field model. The non-uniform matter is assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons. At each temperature T, proton fraction Y{sub p} , and baryon mass density ? {sub B}, we determine the thermodynamically favored state by minimizing the free energy with respect to the radius of the Wigner-Seitz cell, while the nucleon distribution in the cell can be determined self-consistently in the Thomas-Fermi approximation. A detailed comparison is made between the present results and previous calculations in the Thomas-Fermi approximation with a parameterized nucleon distribution that has been adopted in the widely used Shen equation of state.
A node-centered local refinement algorithm for poisson's equation in complex geometries
McCorquodale, Peter; Colella, Phillip; Grote, David P.; Vay, Jean-Luc
This paper presents a method for solving Poisson's equation with Dirichlet boundary conditions on an irregular bounded three-dimensional region. The method uses a nodal-point discretization and adaptive mesh refinement (AMR) on Cartesian grids, and the AMR multigrid solver of Almgren. The discrete Laplacian operator at internal boundaries comes from either linear or quadratic (Shortley-Weller) extrapolation, and the two methods are compared. It is shown that either way, solution error is second order in the mesh spacing. Error in the gradient of the solution is first order with linear extrapolation, but second order with Shortley-Weller. Examples are given with comparison with the exact solution. The method is also applied to a heavy-ion fusion accelerator problem, showing the advantage of adaptivity.
Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Zhang, Yang; Chong, Edwin K. P.; Hannig, Jan; Estep, Donald
We inmore » troduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N , the number of nodes in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.« less
Predictions of the equation of state of cerium yield interesting insights into experimental results
Cherne, Frank J; Jensen, Brian J; Rigg, Paulo A; Elkin, Vyacheslav M
There has been much interest in the past in understanding the dynamic properties of phase changing materials. In this paper we begin to explore the dynamic properties of the complex material of cerium. Cerium metal is a good candidate material to explore capabilities in determining a dynamic phase diagram on account of its low dynamic phase boundaries, namely, the {gamma}-{alpha}, and {alpha}-liquid phase boundaries. Here we present a combination of experimental results with calculated results to try to understand the dynamic behavior of the material. Using the front surface impact technique, we performed a series of experiments which displayed a rarefaction shock upon release. These experiments show that the reversion shock stresses occur at different magnitudes, allowing us to plot out the {gamma}-{alpha} phase boundary. Applying a multiphase equation of state a broader understanding of the experimental results will be discussed.
The fixed hypernode method for the solution of the many body Schroedinger equation
Pederiva, F; Kalos, M H; Reboredo, F; Bressanini, D; Guclu, D; Colletti, L; Umrigar, C J
We propose a new scheme for an approximate solution of the Schroedinger equation for a many-body interacting system, based on the use of pairs of walkers. Trial wavefunctions for these pairs are combinations of standard symmetric and antisymmetric wavefunctions. The method consists in applying a fixed-node restriction in the enlarged space, and computing the energy of the antisymmetric state from the knowledge of the exact ground state energy for the symmetric state. We made two conjectures: first, that this fixed-hypernode energy is an upper bound to the true fermion energy; second that this bound would necessarily be lower than the usual fixed-node energy using the same antisymmetric trial function. The first conjecture is true, and is proved in this paper. The second is not, and numerical and analytical counterexamples are given. The question of whether the fixed-hypernode energy can be better than the usual bound remains open.
The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schroedinger equation
Leung Shingyu; Qian Jianliang
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.
Accelerated molecular dynamics and equation-free methods for simulating diffusion in solids.
Deng, Jie; Zimmerman, Jonathan A.; Thompson, Aidan Patrick; Brown, William Michael; Plimpton, Steven James; Zhou, Xiao Wang; Wagner, Gregory John; Erickson, Lindsay Crowl
Many of the most important and hardest-to-solve problems related to the synthesis, performance, and aging of materials involve diffusion through the material or along surfaces and interfaces. These diffusion processes are driven by motions at the atomic scale, but traditional atomistic simulation methods such as molecular dynamics are limited to very short timescales on the order of the atomic vibration period (less than a picosecond), while macroscale diffusion takes place over timescales many orders of magnitude larger. We have completed an LDRD project with the goal of developing and implementing new simulation tools to overcome this timescale problem. In particular, we have focused on two main classes of methods: accelerated molecular dynamics methods that seek to extend the timescale attainable in atomistic simulations, and so-called 'equation-free' methods that combine a fine scale atomistic description of a system with a slower, coarse scale description in order to project the system forward over long times.
Wave chaos in the stadium: Statistical properties of short-wave solutions of the Helmholtz equation
McDonald, S.W.; Kaufman, A.N.
We numerically investigate statistical properties of short-wavelength normal modes and the spectrum for the Helmholtz equation in a two-dimensional stadium-shaped region. As the geometrical optics rays within this boundary (billiards) are nonintegrable, this wave problem serves as a simple model for the study of quantum chaos. The local spatial correlation function
Theoretical analysis of integral neutron transport equation using collision probability method with quadratic flux approach
Shafii, Mohammad Ali Meidianti, Rahma Wildian, Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto
Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.
Equation of motion coupled cluster methods for electron attachment and ionization potential in polyacenes
Bhaskaran-Nair, Kiran; Kowalski, Karol; Jarrell, Mark; Moreno, Juana; Shelton, William A.
Polyacenes have attracted considerable attention due to their use in organic based optoelectronic materials. Polyacenes are polycyclic aromatic hydrocarbons composed of fused benzene rings. Key to understanding and design of new functional materials is an understanding of their excited state properties starting with their electron affinity (EA) and ionization potential (IP). We have developed a highly accurate and com- putationally e*fficient EA/IP equation of motion coupled cluster singles and doubles (EA/IP-EOMCCSD) method that is capable of treating large systems and large basis set. In this study we employ the EA/IP-EOMCCSD method to calculate the electron affinity and ionization potential of naphthalene, anthracene, tetracene, pentacene, hex- acene and heptacene. We have compared our results with other previous theoretical studies and experimental data. Our EA/IP results are in very good agreement with experiment and when compared with the other theoretical investigations our results represent the most accurate calculations as compared to experiment.
A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics
Brunovsky, Pavol; Cerny, Ales; Winkler, Michael
We consider the ordinary differential equation x{sup 2} u'' = axu'+bu-c(u'-1){sup 2}, x Element-Of (0,x{sub 0}), with a Element-Of R, b Element-Of R , c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b<0 then no continuous solutions exist, whereas if a+b>0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x{sub 0}={infinity} which is such that 0{<=}u(x){<=}x for all x>0, and that this solution is strictly increasing and concave.
Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport
Litvinenko, Yuri E.; Effenberger, Frederic
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.
Excitation Energies Through the Locally Renormalized Equation-of-Motion Formalism: Singles and Doubles Model
Kowalski, Karol
The stationary conditions obtained from approximate coupled-cluster functional derived from the Numerator-Denominator connected Expansion (NDC) [K. Kowalski, P. Piecuch, J Chem. Phys. 122 (2005) 074107] are employed to calculate the linear response of cluster amplitudes. A simple scheme that involves singly and doubly excited amplitudes, termed locally renormalized equation-of-motion approach with singles and doubles (LR-EOMCCSD), is compared with other excited-state methods that include up to two-body operators in the wavefunction expansion. In particular, the impact of the local denominators on the excitation energies is discussed in detail. Several benchmark calculations on the CH+, C?, N?, O?, CIOCI molecules are presented to illustrate the performance of the LR-EOMCCSD approach.
Accuracy of the Frensley inflow boundary condition for Wigner equations in simulating resonant tunneling diodes
Jiang Haiyan; Cai Wei; Tsu, Raphael
In this paper, the accuracy of the Frensley inflow boundary condition of the Wigner equation is analyzed in computing the I-V characteristics of a resonant tunneling diode (RTD). It is found that the Frensley inflow boundary condition for incoming electrons holds only exactly infinite away from the active device region and its accuracy depends on the length of contacts included in the simulation. For this study, the non-equilibrium Green's function (NEGF) with a Dirichlet to Neumann mapping boundary condition is used for comparison. The I-V characteristics of the RTD are found to agree between self-consistent NEGF and Wigner methods at low bias potentials with sufficiently large GaAs contact lengths. Finally, the relation between the negative differential conductance (NDC) of the RTD and the sizes of contact and buffer in the RTD is investigated using both methods.
Locally Renormalized Coupled-Cluster Equations for Singly and Doubly Excited Clusters
Kowalski, Karol
The Numerator-Denominator Connected (NDC) Expansion for the Coupled-Cluster (CC) method [K. Kowalski, P. Piecuch, J. Chem. Phys. 122 (2005) 074107], is used to construct a new set of stationary conditions for approximate coupled-cluster approaches. Several CC approximations based on models involving singles and doubles (CCSD) as well as singles, doubles, and triples (CCSDT) are developed and discussed in the context of ground-state applications. The resulting locally-renormalized CCSD (LR-CCSD) and CCSDT (LR-CCSDT) equations are shown to regularize the expressions for the cluster amplitudes in the challenging situations that occur when the orbital energy differences approach zero. Affordable schemes for handling the local denominators (all-holes-Jn coupling), that naturally appear in locally renormalized formalisms, are also discussed.
Isothermal Multiphase Flash Calculations with the PC-SAFT Equation of State
Justo-Garcia, Daimler N.; Garcia-Sanchez, Fernando; Romero-Martinez, Ascencion
A computational approach for isothermal multiphase flash calculations with the PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory) equation of state is presented. In the framework of the study of fluid phase equilibria of multicomponent systems, the general multiphase problem is the single most important calculation which consists of finding the correct number and types of phases and their corresponding equilibrium compositions such that the Gibbs energy of the system is a minimum. For solving this problem, the system Gibbs energy was minimized using a rigorous method for thermodynamic stability analysis to find the most stable state of the system. The efficiency and reliability of the approach to predict and calculate complex phase equilibria are illustrated by solving three typical problems encountered in the petroleum industry.
Robustness of Quadratic Hedging Strategies in Finance via Backward Stochastic Differential Equations with Jumps
Di Nunno, Giulia; Khedher, Asma; Vanmaele, Michèle
We consider a backward stochastic differential equation with jumps (BSDEJ) which is driven by a Brownian motion and a Poisson random measure. We present two candidate-approximations to this BSDEJ and we prove that the solution of each candidate-approximation converges to the solution of the original BSDEJ in a space which we specify. We use this result to investigate in further detail the consequences of the choice of the model to (partial) hedging in incomplete markets in finance. As an application, we consider models in which the small variations in the price dynamics are modeled with a Poisson random measure with infinite activity and models in which these small variations are modeled with a Brownian motion or are cut off. Using the convergence results on BSDEJs, we show that quadratic hedging strategies are robust towards the approximation of the market prices and we derive an estimation of the model risk.
Prediction of explosive cylinder tests using equations of state from the PANDA code
Kerley, G.I.; Christian-Frear, T.L.
The PANDA code is used to construct tabular equations of state (EOS) for the detonation products of 24 explosives having CHNO compositions. These EOS, together with a reactive burn model, are used in numerical hydrocode calculations of cylinder tests. The predicted detonation properties and cylinder wall velocities are found to give very good agreement with experimental data. Calculations of flat plate acceleration tests for the HMX-based explosive LX14 are also made and shown to agree well with the measurements. The effects of the reaction zone on both the cylinder and flat plate tests are discussed. For TATB-based explosives, the differences between experiment and theory are consistently larger than for other compositions and may be due to nonideal (finite dimameter) behavior.
Accelerating Time Integration for the Shallow Water Equations on the Sphere Using GPUs
Archibald, R.; Evans, K. J.; Salinger, A.
The push towards larger and larger computational platforms has made it possible for climate simulations to resolve climate dynamics across multiple spatial and temporal scales. This direction in climate simulation has created a strong need to develop scalable time-stepping methods capable of accelerating throughput on high performance computing. This work details the recent advances in the implementation of implicit time stepping on a spectral element cube-sphere grid using graphical processing units (GPU) based machines. We demonstrate how solvers in the Trilinos project are interfaced with ACME and GPU kernels can significantly increase computational speed of the residual calculations in the implicit time stepping method for the shallow water equations on the sphere. We show the optimization gains and data structure reorganization that facilitates the performance improvements.
Three-dimensional nonlinear Schroedinger equation in electron-positron-ion magnetoplasmas
Sabry, R.; Moslem, W. M.; El-Shamy, E. F.; Shukla, P. K.
Three-dimensional ion-acoustic envelope soliton excitations in electron-positron-ion magnetoplasmas are interpreted. This is accomplished through the derivation of three-dimensional nonlinear Schroedinger equation, where the nonlinearity is balancing with the dispersive terms. The latter contains both an external magnetic field besides the usual plasma parameter effects. Based on the balance between the nonlinearity and the dispersion terms, the regions for possible envelope solitons are investigated indicating that new regimes for modulational instability of envelope ion-acoustic waves could be obtained, which cannot exist in the unmagnetized case. This will allow us to establish additional new regimes, different from the usual unmagnetized plasma, for envelope ion-acoustic waves to propagate in multicomponent plasma that may be observed in space or astrophysics.
Higher-order time integration of Coulomb collisions in a plasma using Langevin equations
Dimits, A.M.; Cohen, B.I.; Caflisch, R.E.; Rosin, M.S.; Ricketson, L.F.
The extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler�Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [O(?t) vs. O(?t{sup 1/2})] in the strong convergence rate both for the speed |v| and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the �area-integral� terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multi-time-level schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional Monte-Carlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the Euler�Maruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. This method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration.
(U) Equation of State and Compaction Modeling for CeO2
Fredenburg, David A.; Chisolm, Eric D.
Recent efforts have focused on developing a solid-liquid and three-phase equation of state (EOS) for CeO2, while parallel experimental efforts have focused on obtaining high-fidelity Hugoniot measurements on CeO2 in the porous state. The current work examines the robustness of two CeO2 SESAME equations of state, a solid-liquid EOS, 96170, and a three-phase EOS, 96171, by validating the EOS against a suite of high-pressure shock compression experiments on initially porous CeO2. At lower pressures compaction is considered by incorporating a two-term exponential form of the P-compaction model, using three separate definitions for ?(P). Simulations are executed spanning the partially compacted and fully compacted EOS regimes over the pressure range 0.5 - 109 GPa. Comparison of calculated Hugoniot results with those obtained experimentally indicate good agreement for all definitions of ?(P) with both the solid-liquid and three-phase EOS in the low-pressure compaction regime. At higher pressures the three-phase EOS does a better job at predicting the measured Hugoniot response, though at the highest pressures EOS 96171 predicts a less compliant response than is observed experimentally. Measured material velocity profiles of the shock-wave after it has transmitted through the powder are also compared with those simulated using with solid-liquid and three-phase EOS. Profiles lend insight into limits of the current experimental design, as well as the threshold conditions for the shock-induced phase transition in CeO2.
A Bloch-Torrey Equation for Diffusion in a Deforming Media
Rohmer, Damien; Gullberg, Grant T.
Diffusion Tensor Magnetic Resonance Imaging (DTMRI)technique enables the measurement of diffusion parameters and therefore,informs on the structure of the biological tissue. This technique isapplied with success to the static organs such as brain. However, thediffusion measurement on the dynamically deformable organs such as thein-vivo heart is a complex problem that has however a great potential inthe measurement of cardiac health. In order to understand the behavior ofthe Magnetic Resonance (MR)signal in a deforming media, the Bloch-Torreyequation that leads the MR behavior is expressed in general curvilinearcoordinates. These coordinates enable to follow the heart geometry anddeformations through time. The equation is finally discretized andpresented in a numerical formulation using implicit methods, in order toget a stable scheme that can be applied to any smooth deformations.Diffusion process enables the link between the macroscopic behavior ofmolecules and themicroscopic structure in which they evolve. Themeasurement of diffusion in biological tissues is therefore of majorimportance in understanding the complex underlying structure that cannotbe studied directly. The Diffusion Tensor Magnetic ResonanceImaging(DTMRI) technique enables the measurement of diffusion parametersand therefore provides information on the structure of the biologicaltissue. This technique has been applied with success to static organssuch as the brain. However, diffusion measurement of dynamicallydeformable organs such as the in-vivo heart remains a complex problem,which holds great potential in determining cardiac health. In order tounderstand the behavior of the magnetic resonance (MR) signal in adeforming media, the Bloch-Torrey equation that defines the MR behavioris expressed in general curvilinear coordinates. These coordinates enableus to follow the heart geometry and deformations through time. Theequation is finally discretized and presented in a numerical formulationusing implicit methods in order to derive a stable scheme that can beapplied to any smooth deformations.
Exact solutions of (n+1)-dimensional Yang-Mills equations in curved space-time
Sanchez-Monroy, J.A.; Quimbay, C.J.
In the context of a semiclassical approach where vectorial gauge fields can be considered as classical fields, we obtain exact static solutions of the SU(N) Yang-Mills equations in an (n+1)-dimensional curved space-time, for the cases n=1,2,3. As an application of the results obtained for the case n=3, we consider the solutions for the anti-de Sitter and Schwarzschild metrics. We show that these solutions have a confining behavior and can be considered as a first step in the study of the corrections of the spectra of quarkonia in a curved background. Since the solutions that we find in this work are valid also for the group U(1), the case n=2 is a description of the (2+1) electrodynamics in the presence of a point charge. For this case, the solution has a confining behavior and can be considered as an application of the planar electrodynamics in a curved space-time. Finally we find that the solution for the case n=1 is invariant under a parity transformation and has the form of a linear confining solution. - Highlights: Black-Right-Pointing-Pointer We study exact static confining solutions of the SU(N) Yang-Mills equations in an (n+1)-dimensional curved space-time. Black-Right-Pointing-Pointer The solutions found are a first step in the study of the corrections on the spectra of quarkonia in a curved background. Black-Right-Pointing-Pointer A expression for the confinement potential in low dimensionality is found.
Callan-Symanzik equation and asymptotic freedom in the Marr-Shimamoto model
Scarfone, Leonard M.
The exactly soluble nonrelativistic Marr-Shimamoto model was introduced in 1964 as an example of the Lee model with a propagator and a nontrivial vertex function. An exactly soluble relativistic version of this model, known as the Zachariasen model, has been found to be asymptotically free in terms of coupling constant renormalization at an arbitrary spacelike momentum and on the basis of exact solutions of the Gell-Mann-Low equations. This is accomplished with conventional cut-off regularization by setting up the Yukawa and Fermi coupling constants at Euclidean momenta in terms of on mass-shell couplings and then taking the asymptotic limit. In view of this background, it may be expected that an investigation of the nonrelativistic Marr-Shimamoto theory may also exhibit asymptotic freedom in view of its manifest mathematical similarity to that of the Zachariasen model. To prove this point, the present paper prefers to examine asymptotic freedom in the nonrelativistic Marr-Shimamoto theory using the powerful concepts of the renormalization group and the Callan-Symanzik equation, in conjunction with the specificity of dimensional regularization and on-shell renormalization. This approach is based on calculations of the Callan-Symanzik coefficients and determinations of the effective coupling constants. It is shown that the Marr-Shimamoto theory is asymptotically free for dimensions D<3 and for values of D>3 occurring in periodic intervals over the range of 0
Noise propagation in hybrid models of nonlinear systems: The Ginzburg�Landau equation
Taverniers, S�ren; Alexander, Francis J.; Tartakovsky, Daniel M.
Every physical phenomenon can be described by multiple models with varying degrees of fidelity. The computational cost of higher fidelity models (e.g., molecular dynamics simulations) is invariably higher than that of their lower fidelity counterparts (e.g., a continuum model based on differential equations). While the former might not be suitable for large-scale simulations, the latter are not universally valid. Hybrid algorithms provide a compromise between the computational efficiency of a coarse-scale model and the representational accuracy of a fine-scale description. This is achieved by conducting a fine-scale computation in subdomains where it is absolutely required (e.g., due to a local breakdown of a continuum model) and coupling it with a coarse-scale computation in the rest of a computational domain. We analyze the effects of random fluctuations generated by the fine-scale component of a nonlinear hybrid on the hybrid's overall accuracy and stability. Two variants of the time-dependent Ginzburg�Landau equation (GLE) and their discrete representations provided by a nearest-neighbor Ising model serve as a computational testbed. Our analysis shows that coupling these descriptions in a one-dimensional simulation leads to erroneous results. Adding a random source term to the GLE provides accurate prediction of the mean behavior of the quantity of interest (magnetization). It also allows the two GLE variants to correctly capture the strength of the microscale fluctuations. Our work demonstrates the importance of fine-scale noise in hybrid simulations, and suggests the need for replacing an otherwise deterministic coarse-scale component of the hybrid with its stochastic counterpart.
Rare-event Simulation for Stochastic Korteweg-de Vries Equation
Xu, Gongjun; Lin, Guang; Liu, Jingchen
An asymptotic analysis of the tail probabilities for the dynamics of a soliton wave $U(x,t)$ under a stochastic time-dependent force is developed. The dynamics of the soliton wave $U(x,t)$ is described by the Korteweg-de Vries Equation with homogeneous Dirichlet boundary conditions under a stochastic time-dependent force, which is modeled as a time-dependent Gaussian noise with amplitude $\\epsilon$. The tail probability we considered is $w(b) :=P(\\sup_{t\\in [0,T]} U(x,t) > b ),$ as $b\\rightarrow \\infty,$ for some constant $T>0$ and a fixed $x$, which can be interpreted as tail probability of the amplitude of water wave on shallow surface of a fluid or long internal wave in a density-stratified ocean. Our goal is to characterize the asymptotic behaviors of $w(b)$ and to evaluate the tail probability of the event that the soliton wave exceeds a certain threshold value under a random force term. Such rare-event calculation of $w(b)$ is very useful for fast estimation of the risk of the potential damage that could caused by the water wave in a density-stratified ocean modeled by the stochastic KdV equation. In this work, the asymptotic approximation of the probability that the soliton wave exceeds a high-level $b$ is derived. In addition, we develop a provably efficient rare-event simulation algorithm to compute $w(b)$. The efficiency of the algorithm only requires mild conditions and therefore it is applicable to a general class of Gaussian processes and many diverse applications.
Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index
Lehtikangas, O.; Tarvainen, T.; Kim, A.D.; Arridge, S.R.
The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena on the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light.
Liquid film thickness inside the high pressure swirl injectors: Real scale measurement and evaluation of analytical equations
Moon, Seoksu; Bae, Choongsik; Abo-Serie, Essam
Liquid film thickness inside two swirl injectors for direct injection (DI) gasoline engines was measured at different injection pressure conditions ranging from 2.0 to 7.0 MPa and then previous analytical and empirical equations were examined from the experimental results. Based on the evaluation, a new equation for the liquid film thickness inside the swirl injectors was introduced. A direct photography using two real scale transparent nozzles and a pulsed light source was employed to measure the liquid film thickness inside the swirl injectors. The error in the liquid film thickness measurement, generated from different refractive indices among transparent nozzle, fuel and air, was estimated and corrected based on the geometric optics. Two injectors which have different nozzle diameter and nozzle length were applied to introduce a more general empirical equation for the liquid film thickness inside the pressure swirl injectors. The results showed that the liquid film thickness remains constant at the injection pressures for direct injection gasoline engines while the ratio of nozzle length to nozzle diameter (L/D) shows significant effect on the liquid film thickness. The previously introduced analytical and empirical equations for relatively low injection pressure swirl injectors overestimated the effect of injection pressure at the operating range of high pressure swirl injectors and, in addition, the effect of L/D ratio and swirler geometry was rarely considered. A new empirical equation was suggested based on the experimental results by taking into account the effects of fuel properties, nozzle diameter, nozzle length and swirler geometry. (author)
An efficient computational method for solving nonlinear stochastic It� integral equations: Application for stochastic problems in physics
Heydari, M.H.; Hooshmandasl, M.R.; Cattani, C.; Maalek Ghaini, F.M.
Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of It�-integration is proposed for solving nonlinear stochastic It� integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Error analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.
An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transport
Shadid, J.N.; Tuminaro, R.S.; Walker, H.F.
The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.
Equations of State of Anhydrous AlF3 and AlI3: Modeling of Extreme
Office of Scientific and Technical Information (OSTI)
Condition Halide Chemistry (Journal Article) | SciTech Connect Journal Article: Equations of State of Anhydrous AlF3 and AlI3: Modeling of Extreme Condition Halide Chemistry Citation Details In-Document Search Title: Equations of State of Anhydrous AlF3 and AlI3: Modeling of Extreme Condition Halide Chemistry Authors: Stavrou, E ; Zaug, J M ; Bastea, S ; Crowhurst, J C ; Goncharov, A F ; Radousky, H B ; Armstrong, M R ; Roberts, S K ; Plaue, J W Publication Date: 2015-02-18 OSTI Identifier:
Thermal equation of state and stability of (Mg0.06Fe0.94)O (Journal
Office of Scientific and Technical Information (OSTI)
Article) | SciTech Connect Thermal equation of state and stability of (Mg0.06Fe0.94)O Citation Details In-Document Search This content will become publicly available on November 8, 2017 Title: Thermal equation of state and stability of (Mg0.06Fe0.94)O Authors: Wicks, June K. ; Jackson, Jennifer M. ; Sturhahn, Wolfgang ; Zhuravlev, Kirill K. ; Tkachev, Sergey N. ; Prakapenka, Vitali B. Publication Date: 2015-12-01 OSTI Identifier: 1251833 Grant/Contract Number: FG02-94ER14466; AC02-06CH11357
An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere
McCorquodale, Peter; Ullrich, Paul A.; Johansen, Hans; Colella, Phillip
We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed-sphere. This approach combines a Runge--Kutta time discretization with a fourth-order accurate spatial discretization, and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy, but with many fewer operations.
Equation of state of an interacting Bose gas at finite temperature: A path-integral Monte Carlo study
Pilati, S.; Giorgini, S.; Sakkos, K.; Boronat, J.; Casulleras, J.
By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same s-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.
Thermal equation of state and stability of (Mg0.06Fe0.94)O (Journal
Office of Scientific and Technical Information (OSTI)
Article) | DOE PAGES Thermal equation of state and stability of (Mg0.06Fe0.94)O This content will become publicly available on November 8, 2017 Title: Thermal equation of state and stability of (Mg0.06Fe0.94)O Authors: Wicks, June K. ; Jackson, Jennifer M. ; Sturhahn, Wolfgang ; Zhuravlev, Kirill K. ; Tkachev, Sergey N. ; Prakapenka, Vitali B. Publication Date: 2015-12-01 OSTI Identifier: 1251833 Grant/Contract Number: FG02-94ER14466; AC02-06CH11357 Type: Publisher's Accepted Manuscript
Expansion solution of Laplace`s equation: Technique and application to hollow beam gun design
Jackson, R.H.; Taccetti, J.M.
This paper presents a flexible algorithm for the general calculation of expansion solutions to Laplace`s equation. The limiting factor in application of the technique is shown to be series truncation error and not errors in calculating numerical derivatives. Application of the algorithm to the accurate computation of arbitrary magnetic fields in cylindrical geometry from on-axis or coil data will be presented. For an ideal current loop, magnetic field accuracies of better than 0.01% of the exact elliptic integral solution can be obtained out to approximately 70--80% of the loop radius. Accuracy improves dramatically for radii closer to the axis. Results also is shown for thin current disks, thin solenoids and thick coils. Other aspects of the technique is illustrated by application to the design of a coil system for a hollow beam electron gun. With some reasonable assumptions about the overlay of the electron trajectories and the magnetic flux contours, it is possible to generate an estimate for the on-axis profile of the gun magnetic field. The expansion technique can then be applied to calculate the off-axis field and its impact on the trajectories without assuming any particular coil system. The initial estimate can then be refined and retested. Finally, an optimization technique is used to develop a coil system which closely reproduces the refined field. The results of carrying out this set of calculations on a 150 kV, 20 A hollow electron gun design for an FEL experiment is reported.
Numerical approximation of the Schr�dinger equation with the electromagnetic field by the Hagedorn wave packets
Zhou, Zhennan
In this paper, we approximate the semi-classical Schr�dinger equation in the presence of electromagnetic field by the Hagedorn wave packets approach. By operator splitting, the Hamiltonian is divided into the modified part and the residual part. The modified Hamiltonian, which is the main new idea of this paper, is chosen by the fact that Hagedorn wave packets are localized both in space and momentum so that a crucial correction term is added to the truncated Hamiltonian, and is treated by evolving the parameters associated with the Hagedorn wave packets. The residual part is treated by a Galerkin approximation. We prove that, with the modified Hamiltonian only, the Hagedorn wave packets dynamics give the asymptotic solution with error O(?{sup 1/2}), where ? is the scaled Planck constant. We also prove that, the Galerkin approximation for the residual Hamiltonian can reduce the approximation error to O(?{sup k/2}), where k depends on the number of Hagedorn wave packets added to the dynamics. This approach is easy to implement, and can be naturally extended to the multidimensional cases. Unlike the high order Gaussian beam method, in which the non-constant cut-off function is necessary and some extra error is introduced, the Hagedorn wave packets approach gives a practical way to improve accuracy even when ? is not very small.
High order finite difference methods with subcell resolution for advection equations with stiff source terms
Wang, Wei; Shu, Chi-Wang; Yee, H.C.; Sj�green, Bj�rn
A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers.
Equation of state of bcc-Mo by static volume compression to 410 GPa
Akahama, Yuichi; Hirao, Naohisa; Ohishi, Yasuo; Singh, Anil K.
Unit cell volumes of Mo and Pt have been measured simultaneously to ≈400 GPa by x-ray powder diffraction using a diamond anvil cell and synchrotron radiation source. The body-centered cubic (bcc) phase of Mo was found to be stable up to 410 GPa. The equation of state (EOS) of bcc-Mo was determined on the basis of Pt pressure scale. A fit of Vinet EOS to the volume compression data gave K{sub 0} = 262.3(4.6) GPa, K{sub 0}′ = 4.55(16) with one atmosphere atomic volume V{sub 0} = 31.155(24) A{sup 3}. The EOS was in good agreement with the previous ultrasonic data within pressure difference of 2.5%–3.3% in the multimegabar range, though the EOS of Mo proposed from a shock compression experiment gave lower pressure by 7.2%–11.3% than the present EOS. The agreement would suggest that the Pt pressure scale provides an accurate pressure value in an ultra-high pressure range.
An equation of state for partially ionized plasmas: The Coulomb contribution to the free energy
Kilcrease, D. P.; Colgan, J.; Hakel, P.; Fontes, C. J.; Sherrill, M. E.
We have previously developed an equation of state (EOS) model called ChemEOS (Hakel and Kilcrease, Atomic Processes in Plasmas, Eds., J. Cohen et al., AIP, 2004) for a plasma of interacting ions, atoms and electrons. It is based on a chemical picture of the plasma and is derived from an expression for the Helmholtz free energy of the interacting species. All other equilibrium thermodynamic quantities are then obtained by minimizing this free energy subject to constraints, thus leading to a thermodynamically consistent EOS. The contribution to this free energy from the Coulomb interactions among the particles is treated using the method of Chabrier and Potekhin (Phys. Rev. E 58, 4941 (1998)) which we have adapted for partially ionized plasmas. This treatment is further examined and is found to give rise to unphysical behavior for various elements at certain values of the density and temperature where the Coulomb coupling begins to become significant and the atoms are partially ionized. We examine the source of this unphysical behavior and suggest corrections that produce acceptable results. The sensitivity of the thermodynamic properties and frequency-dependent opacity of iron is examined with and without these corrections. Lastly, the corrected EOS is used to determine the fractional ion populations and level populations for a new generation of OPLIB low-Z opacity tables currently being prepared at Los Alamos National Laboratory with the ATOMIC code.
An efficient implementation of the Chebyshev Rational Approximation Method (CRAM) for solving the burnup equations
Pusa, M.; Leppaenen, J.
The Chebyshev Rational Approximation Method (CRAM) has been recently introduced by the authors for solving the burnup equations with excellent results. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices and it can be characterized as the best rational approximation on the negative real axis. The coefficients of the rational approximation are fixed and have been reported for various approximation orders. In addition to these coefficients, implementing the method only requires a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM approximation. The introduced direct method is based on sparse Gaussian elimination where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of the proposed Gaussian elimination method is discussed based on considering the numerical properties of burnup matrices. Suitable algorithms are presented for computing the symbolic factorization and numerical elimination in order to facilitate the implementation of CRAM and its adoption into routine use. The accuracy and efficiency of the described technique are demonstrated by computing the CRAM approximations for a large test case with over 1600 nuclides. (authors)
Simplified treatment of exact resonance elastic scattering model in deterministic slowing down equation
Ono, M.; Wada, K.; Kitada, T.
Simplified treatment of resonance elastic scattering model considering thermal motion of heavy nuclides and the energy dependence of the resonance cross section was implemented into NJOY [1]. In order to solve deterministic slowing down equation considering the effect of up-scattering without iterative calculations, scattering kernel for heavy nuclides is pre-calculated by the formula derived by Ouisloumen and Sanchez [2], and neutron spectrum in up-scattering term is expressed by NR approximation. To check the verification of the simplified treatment, the treatment is applied to U-238 for the energy range from 4 eV to 200 eV. Calculated multi-group capture cross section of U-238 is greater than that of conventional method and the increase of the capture cross sections is remarkable as the temperature becomes high. Therefore Doppler coefficient calculated in UO{sub 2} fuel pin is calculated more negative value than that on conventional method. The impact on Doppler coefficient is equivalent to the results of exact treatment of resonance elastic scattering reported in previous studies [2-7]. The agreement supports the validation of the simplified treatment and therefore this treatment is applied for other heavy nuclide to evaluate the Doppler coefficient in MOX fuel. The result shows that the impact of considering thermal agitation in resonance scattering in Doppler coefficient comes mainly from U-238 and that of other heavy nuclides such as Pu-239, 240 etc. is not comparable in MOX fuel. (authors)
Equation of state and contact of a strongly interacting Bose gas in the normal state
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Liu, Xia -Ji; Mulkerin, Brendan; He, Lianyi; Hu, Hui
Here, we theoretically investigate the equation of state and Tan's contact of a nondegenerate three-dimensional Bose gas near a broad Feshbach resonance, within the framework of large-N expansion. Our results agree with the path-integral Monte Carlo simulations in the weak-coupling limit and recover the second-order virial expansion predictions at strong interactions and high temperatures. At resonance, we find that the chemical potential and energy are significantly enhanced by the strong repulsion, while the entropy does not change significantly. With increasing temperature, the two-body contact initially increases and then decreases like T–1 at large temperature, and therefore exhibits a peak structuremore » at about 4Tc0, where Tc0 is the Bose-Einstein condensation temperature of an ideal, noninteracting Bose gas. These results may be experimentally examined with a nondegenerate unitary Bose gas, where the three-body recombination rate is substantially reduced. In particular, the nonmonotonic temperature dependence of the two-body contact could be inferred from the momentum distribution measurement.« less
An efficient permeability scaling-up technique applied to the discretized flow equations
Urgelli, D.; Ding, Yu
Grid-block permeability scaling-up for numerical reservoir simulations has been discussed for a long time in the literature. It is now recognized that a full permeability tensor is needed to get an accurate reservoir description at large scale. However, two major difficulties are encountered: (1) grid-block permeability cannot be properly defined because it depends on boundary conditions; (2) discretization of flow equations with a full permeability tensor is not straightforward and little work has been done on this subject. In this paper, we propose a new method, which allows us to get around both difficulties. As the two major problems are closely related, a global approach will preserve the accuracy. So, in the proposed method, the permeability up-scaling technique is integrated in the discretized numerical scheme for flow simulation. The permeability is scaled-up via the transmissibility term, in accordance with the fluid flow calculation in the numerical scheme. A finite-volume scheme is particularly studied, and the transmissibility scaling-up technique for this scheme is presented. Some numerical examples are tested for flow simulation. This new method is compared with some published numerical schemes for full permeability tensor discretization where the full permeability tensor is scaled-up through various techniques. Comparing the results with fine grid simulations shows that the new method is more accurate and more efficient.
Plasma-accelerated flyer-plates for equation of state studies
Fratanduono, D. E.; Smith, R. F.; Eggert, J. H.; Braun, D. G.; Collins, G. W.; Boehly, T. R.
We report on a new technique to accelerate flyer-plates to high velocities ({approx}5 km/s). In this work, a strong shock is created through direct laser ablation of a thin polyimide foil. Subsequent shock breakout of that foil results in the generation of a plasma characterized by a smoothly increasing density gradient and a strong forward momentum. Stagnation of this plasma onto an aluminum foil and the resultant momentum transfer accelerates a thin aluminum flyer-plate. The aluminum flyer-plate is then accelerated to a peak velocity of {approx}5 km/s before impact with a transparent lithium fluoride (LiF) window. Simulations of the stagnating plasma ramp compression and wave reverberations within the flyer-plate suggest that the temperature at the flyer-plate impact surface is elevated by less than 50 Degree-Sign C. Optical velocimetry is used to measure the flyer-plate velocity and impact conditions enabling the shocked refractive index of LiF to be determined. The results presented here are in agreement with conventional flyer-plate measurements validating the use of plasma-accelerated flyer-plates for equation of state and impact studies.
Entropy vs. energy waveform processing: A comparison based on the heat equation
Hughes, Michael S.; McCarthy, John E.; Bruillard, Paul J.; Marsh, Jon N.; Wickline, Samuel A.
Virtually all modern imaging devices collect electromagnetic or acoustic waves and use the energy carried by these waves to determine pixel values to create what is basically an "energy" picture. However, waves also carry "information", as quantified by some form of entropy, and this may also be used to produce an "information" image. Numerous published studies have demonstrated the advantages of entropy, or "information imaging", over conventional methods. The most sensitive information measure appears to be the joint entropy of the collected wave and a reference signal. The sensitivity of repeated experimental observations of a slowly-changing quantity may be defined as the mean variation (i.e., observed change) divided by mean variance (i.e., noise). Wiener integration permits computation of the required mean values and variances as solutions to the heat equation, permitting estimation of their relative magnitudes. There always exists a reference, such that joint entropy has larger variation and smaller variance than the corresponding quantities for signal energy, matching observations of several studies. Moreover, a general prescription for finding an "optimal" reference for the joint entropy emerges, which also has been validated in several studies.
Entropy vs. energy waveform processing: A comparison based on the heat equation
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Hughes, Michael S.; McCarthy, John E.; Bruillard, Paul J.; Marsh, Jon N.; Wickline, Samuel A.
Virtually all modern imaging devices collect electromagnetic or acoustic waves and use the energy carried by these waves to determine pixel values to create what is basically an "energy" picture. However, waves also carry "information", as quantified by some form of entropy, and this may also be used to produce an "information" image. Numerous published studies have demonstrated the advantages of entropy, or "information imaging", over conventional methods. The most sensitive information measure appears to be the joint entropy of the collected wave and a reference signal. The sensitivity of repeated experimental observations of a slowly-changing quantity may be definedmore » as the mean variation (i.e., observed change) divided by mean variance (i.e., noise). Wiener integration permits computation of the required mean values and variances as solutions to the heat equation, permitting estimation of their relative magnitudes. There always exists a reference, such that joint entropy has larger variation and smaller variance than the corresponding quantities for signal energy, matching observations of several studies. Moreover, a general prescription for finding an "optimal" reference for the joint entropy emerges, which also has been validated in several studies.« less
An equation of state for partially ionized plasmas: The Coulomb contribution to the free energy
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Kilcrease, D. P.; Colgan, J.; Hakel, P.; Fontes, C. J.; Sherrill, M. E.
We have previously developed an equation of state (EOS) model called ChemEOS (Hakel and Kilcrease, Atomic Processes in Plasmas, Eds., J. Cohen et al., AIP, 2004) for a plasma of interacting ions, atoms and electrons. It is based on a chemical picture of the plasma and is derived from an expression for the Helmholtz free energy of the interacting species. All other equilibrium thermodynamic quantities are then obtained by minimizing this free energy subject to constraints, thus leading to a thermodynamically consistent EOS. The contribution to this free energy from the Coulomb interactions among the particles is treated using themore » method of Chabrier and Potekhin (Phys. Rev. E 58, 4941 (1998)) which we have adapted for partially ionized plasmas. This treatment is further examined and is found to give rise to unphysical behavior for various elements at certain values of the density and temperature where the Coulomb coupling begins to become significant and the atoms are partially ionized. We examine the source of this unphysical behavior and suggest corrections that produce acceptable results. The sensitivity of the thermodynamic properties and frequency-dependent opacity of iron is examined with and without these corrections. Lastly, the corrected EOS is used to determine the fractional ion populations and level populations for a new generation of OPLIB low-Z opacity tables currently being prepared at Los Alamos National Laboratory with the ATOMIC code.« less
Verification of conventional equations of state for tantalum under quasi-isentropic compression
Binqiang, Luo; Guiji, Wang; Jianjun, Mo; Hongpin, Zhang; Fuli, Tan; Jianheng, Zhao; Cangli, Liu; Chengwei, Sun
Shock Hugoniot data have been widely used to calibrate analytic equations of state (EOSs) of condensed matter at high pressures. However, the suitability of particular analytic EOSs under off-Hugoniot states has not been sufficiently verified using experimental data. We have conducted quasi-isentropic compression experiments (ICEs) of tantalum using the compact pulsed power generator CQ-4, and explored the relation of longitudinal stress versus volume of tantalum under quasi-isentropic compression using backward integration and characteristic inverse methods. By subtracting the deviatoric stress and additional pressure caused by irreversible plastic dissipation, the isentropic pressure can be extracted from the longitudinal stress. Several theoretical isentropes are deduced from analytic EOSs and compared with ICE results to validate the suitability of these analytic EOSs in isentropic compression states. The comparisons show that the Gruneisen EOS with Gruneisen Gamma proportional to volume is accurate, regardless whether the Hugoniot or isentrope is used as the reference line. The Vinet EOS yields better accuracy in isentropic compression states. Theoretical isentropes derived from Tillotson, PUFF, and Birch-Murnaghan EOSs well agree with the experimental isentrope in the range of 0–100 GPa, but deviate gradually with pressure increasing further.
Techniques for Equation-of-State Measurements on a Three-Stage Light-Gas Gun
Understanding high pressure behavior materials is necessary in order to address the physical processes associated with hypervelocity impact events related to space science applications including orbital debris impact and impact lethality. Until recently the highest-pressure states in materials have been achieved from impact loading techniques from two-stage light gas guns with velocity limitations of approximately 81cm/s. In this paper, techniques that are being developed and implemented to obtain the needed shock loading parameters (Hugoniot states) for material characterization studies, namely shock velocity and particle velocity, will be described at impact velocities up to 11 kds. The determination of equation-of-state (EOS) and thermodynamic states of materials in the regimes of extreme high pressures is now attainable utilizing the three-stage launcher. What is new in this report is that these techniques are being implemented for use at engagement velocities never before attained utilizing two-stage light-gas gun technology. The design and test methodologies used to determine Hugoniot states are described in this paper.
Equation of State Model Quality Study for Ti and Ti64.
Wills, Ann Elisabet; Sanchez, Jason James
Titanium and the titanium alloy Ti64 (6% aluminum, 4% vanadium and the balance ti- tanium) are materials used in many technologically important applications. To be able to computationally investigate and design these applications, accurate Equations of State (EOS) are needed and in many cases also additional constitutive relations. This report describes what data is available for constructing EOS for these two materials, and also describes some references giving data for stress-strain constitutive models. We also give some suggestions for projects to achieve improved EOS and constitutive models. In an appendix, we present a study of the 'cloud formation' issue observed in the ALEGRA code. This issue was one of the motivating factors for this literature search of available data for constructing improved EOS for Ti and Ti64. However, the study shows that the cloud formation issue is only marginally connected to the quality of the EOS, and, in fact, is a physical behavior of the system in question. We give some suggestions for settings in, and improvements of, the ALEGRA code to address this computational di culty.
Detecting features in the dark energy equation of state: a wavelet approach
Hojjati, Alireza; Pogosian, Levon; Zhao, Gong-Bo E-mail: firstname.lastname@example.com
We study the utility of wavelets for detecting the redshift evolution of the dark energy equation of state w(z) from the combination of supernovae (SNe), CMB and BAO data. We show that local features in w, such as bumps, can be detected efficiently using wavelets. To demonstrate, we first generate a mock supernovae data sample for a SNAP-like survey with a bump feature in w(z) hidden in, then successfully discover it by performing a blind wavelet analysis. We also apply our method to analyze the recently released ''Constitution'' SNe data, combined with WMAP and BAO from SDSS, and find weak hints of dark energy dynamics. Namely, we find that models with w(z) < −1 for 0.2 < z < 0.5, and w(z) > −1 for 0.5 < z < 1, are mildly favored at 95% confidence level. This is in good agreement with several recent studies using other methods, such as redshift binning with principal component analysis (PCA) (e.g. Zhao and Zhang, arXiv: 0908.1568)
Parabolized Stability Equations analysis of nonlinear interactions with forced eigenmodes to control subsonic jet instabilities
Itasse, Maxime Brazier, Jean-Philippe Léon, Olivier Casalis, Grégoire
Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequency matches the desired "target" mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the "killer" modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.
Equations of state of ice VI and ice VII at high pressure and high temperature
Bezacier, Lucile; Hanfland, Michael; Journaux, Baptiste; Perrillat, Jean-Philippe; Cardon, Herv�; Daniel, Isabelle
High-pressure H{sub 2}O polymorphs among which ice VI and ice VII are abundant in the interiors of large icy satellites and exo-planets. Knowledge of the elastic properties of these pure H{sub 2}O ices at high-temperature and high-pressure is thus crucial to decipher the internal structure of icy bodies. In this study we assess for the first time the pressure-volume-temperature (PVT) relations of both polycrystalline pure ice VI and ice VII at high pressures and temperatures from 1 to 9 GPa and 300 to 450 K, respectively, by using in situ synchrotron X-ray diffraction. The PVT data are adjusted to a second-order Birch-Murnaghan equation of state and give V{sub 0} = 14.17(2) cm{sup 3}?mol{sup ?1}, K{sub 0} = 14.05(23) GPa, and ?{sub 0} = 14.6(14) � 10{sup ?5} K{sup ?1} for ice VI and V{sub 0} = 12.49(1) cm{sup 3}?mol{sup ?1}, K{sub 0} = 20.15(16) GPa, and ?{sub 0} = 11.6(5) � 10{sup ?5} K{sup ?1} for ice VII.
Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
Tanimura, Yoshitaka
For a system strongly coupled to a heat bath, the quantum coherence of the system and the heat bath plays an important role in the system dynamics. This is particularly true in the case of non-Markovian noise. We rigorously investigate the influence of system-bath coherence by deriving the reduced hierarchal equations of motion (HEOM), not only in real time, but also in imaginary time, which represents an inverse temperature. It is shown that the HEOM in real time obtained when we include the system-bath coherence of the initial thermal equilibrium state possess the same form as those obtained from a factorized initial state. We find that the difference in behavior of systems treated in these two manners results from the difference in initial conditions of the HEOM elements, which are defined in path integral form. We also derive HEOM along the imaginary time path to obtain the thermal equilibrium state of a system strongly coupled to a non-Markovian bath. Then, we show that the steady state hierarchy elements calculated from the real-time HEOM can be expressed in terms of the hierarchy elements calculated from the imaginary-time HEOM. Moreover, we find that the imaginary-time HEOM allow us to evaluate a number of thermodynamic variables, including the free energy, entropy, internal energy, heat capacity, and susceptibility. The expectation values of the system energy and system-bath interaction energy in the thermal equilibrium state are also evaluated.
Generalized Dix equation and analytic treatment of normal-movement velocity for anisotropic media
Grechka, V.; Tsvankin, I.; Cohen, J.K.
Despite the complexity of wave propagation in anisotropic media, reflection moveout on conventional common-midpoint (CMP) spreads is usually well described by the normal-moveout (NMO) velocity defined in the zero-offset limit. In their recent work, Grechka and Tsvankin showed that the azimuthal variation of NMO velocity around a fixed CMP location generally has an elliptical form (i.e., plotting the NMO velocity in each azimuthal direction produces an ellipse) and is determined by the spatial derivatives of the slowness vector evaluated at the CMP location. This formalism is used here to develop exact solutions for the NMO velocity in anisotropic media of arbitrary symmetry. The high accuracy of the NMO expressions is illustrated by comparison with ray-traced reflection traveltimes in piecewise-homogeneous, azimuthally anisotropic models. The authors also apply the generalized Dix equation to field data collected over a fractured reservoir and show that P-wave moveout can be used to find the depth-dependent fracture orientation and to evaluate the magnitude of azimuthal anisotropy.
Numerical solution of the time dependent Ginzburg-Landau equations for mixed (d + s)-wave superconductors
Gon�alves, W. C.; Sardella, E.; UNESP-Universidade Estadual Paulista, IPMet-Instituto de Pesquisas Meteorol�gicas, CEP 17048-699 Bauru, SP ; Becerra, V. F.; Milo�evi?, M. V.; Peeters, F. M.; Departamento de F�sica, Universidade Federal do Cear�, 60455-900 Fortaleza, Cear�
The time-dependent Ginzburg-Landau formalism for (d + s)-wave superconductors and their representation using auxiliary fields is investigated. By using the link variable method, we then develop suitable discretization of these equations. Numerical simulations are carried out for a mesoscopic superconductor in a homogeneous perpendicular magnetic field which revealed peculiar vortex states.
Solutions of the Schr�dinger equation with inversely quadratic effective plus Mie-type potential using Nikiforov-Uvarov method
Ita, B. I.; Anake, T. A.
The Schr�dinger equation with the interaction of inversely quadratic effective and Mie-type potential has been solved for any angular momentum quantum number l using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms of the Laguerre polynomials. Several cases of the potential are also considered and their eigen values obtained.
A boundary-value problem in weighted H�lder spaces for elliptic equations which degenerate at the boundary of the domain
Bazalii, B V; Degtyarev, S P
An elliptic boundary-value problem for second-order equations with nonnegative characteristic form is investigated in the situation when there is a weak degeneracy on the boundary of the domain. A priori estimates are obtained for solutions and the problem is proved to be solvable in some weighted H�lder spaces. Bibliography: 18 titles.
Two-dimensional equations of the surface harmonics method for solving problems of spatial neutron kinetics in square-lattice reactors
Boyarinov, V. F. Kondrushin, A. E. Fomichenko, P. A.
Two-dimensional time-dependent finite-difference equations of the surface harmonics method (SHM) for the description of the neutron transport are derived for square-lattice reactors. These equations are implemented in the SUHAM-TD code. Verification of the derived equations and the developed code are performed by the example of known test problems, and the potential and efficiency of the SHM as applied to the solution of the time-dependent neutron transport equation in the diffusion approximation in two-dimensional geometry are demonstrated. These results show the substantial advantage of SHM over direct finite-difference modeling in computational costs.
High Temperature, high pressure equation of state density correlations and viscosity correlations
Tapriyal, D.; Enick, R.; McHugh, M.; Gamwo, I.; Morreale, B.
Global increase in oil demand and depleting reserves has derived a need to find new oil resources. To find these untapped reservoirs, oil companies are exploring various remote and harsh locations such as deep waters in Gulf of Mexico, remote arctic regions, unexplored deep deserts, etc. Further, the depth of new oil/gas wells being drilled has increased considerably to tap these new resources. With the increase in the well depth, the bottomhole temperature and pressure are also increasing to extreme values (i.e. up to 500 F and 35,000 psi). The density and viscosity of natural gas and crude oil at reservoir conditions are critical fundamental properties required for accurate assessment of the amount of recoverable petroleum within a reservoir and the modeling of the flow of these fluids within the porous media. These properties are also used to design appropriate drilling and production equipment such as blow out preventers, risers, etc. With the present state of art, there is no accurate database for these fluid properties at extreme conditions. As we have begun to expand this experimental database it has become apparent that there are neither equations of state for density or transport models for viscosity that can be used to predict these fundamental properties of multi-component hydrocarbon mixtures over a wide range of temperature and pressure. Presently, oil companies are using correlations based on lower temperature and pressure databases that exhibit an unsatisfactory predictive capability at extreme conditions (e.g. as great as {+-} 50%). From the perspective of these oil companies that are committed to safely producing these resources, accurately predicting flow rates, and assuring the integrity of the flow, the absence of an extensive experimental database at extreme conditions and models capable of predicting these properties over an extremely wide range of temperature and pressure (including extreme conditions) makes their task even more daunting.
Equation of state and transport property measurements of warm dense matter.
Knudson, Marcus D.; Desjarlais, Michael Paul
Location of the liquid-vapor critical point (c.p.) is one of the key features of equation of state models used in simulating high energy density physics and pulsed power experiments. For example, material behavior in the location of the vapor dome is critical in determining how and when coronal plasmas form in expanding wires. Transport properties, such as conductivity and opacity, can vary an order of magnitude depending on whether the state of the material is inside or outside of the vapor dome. Due to the difficulty in experimentally producing states near the vapor dome, for all but a few materials, such as Cesium and Mercury, the uncertainty in the location of the c.p. is of order 100%. These states of interest can be produced on Z through high-velocity shock and release experiments. For example, it is estimated that release adiabats from {approx}1000 GPa in aluminum would skirt the vapor dome allowing estimates of the c.p. to be made. This is within the reach of Z experiments (flyer plate velocity of {approx}30 km/s). Recent high-fidelity EOS models and hydrocode simulations suggest that the dynamic two-phase flow behavior observed in initial scoping experiments can be reproduced, providing a link between theory and experiment. Experimental identification of the c.p. in aluminum would represent the first measurement of its kind in a dynamic experiment. Furthermore, once the c.p. has been experimentally determined it should be possible to probe the electrical conductivity, opacity, reflectivity, etc. of the material near the vapor dome, using a variety of diagnostics. We propose a combined experimental and theoretical investigation with the initial emphasis on aluminum.
SESAME 96170, a solid-liquid equation of state for CeO2
Chisolm, Eric D.
I describe an equation of state (EOS) for the low-pressure solid phase and liquid phase of cerium (IV) oxide, CeO2. The models and parameters used to calculate the EOS are presented in detail, and I compare with data for the full-density crystal. Hugoniot data are available only for high-porosity powders, and I discuss difficulties in comparing with such data. I have constructed SESAME 96170, an EOS for cerium (IV) oxide that includes the ambient solid and liquid phases. The EOS extends over the full standard SESAME range, but should not be used at low temperatures and high densities because of the lack of a high-pressure solid phase. I have described the models used to compute the three terms of the EOS (cold curve, nuclear, and thermal electronic), and I have given the parameters used in the models. They were determined by comparison with experimental data at P = 1 atm, including the constant-pressure specific heat, coefficient of thermal expansion, and melting and boiling points. The EOS compares well with data in its intended range of validity, but the presence of high-frequency optical modes in its phonon spectrum limits the agreement of our models with thermal data. The next step is to construct a multiphase EOS that includes the low- and high-pressure solid phases and the liquid. The DAC data from Duclos will most strongly constrain the parameters of the high-pressure solid. A remaining issue is the comparison of the crystal-density EOS with experimental Hugoniot data, which are taken at much lower initial data because the samples are porous powders. A satisfactory means of modeling porosity, allowing comparison of theory and experiment, has not yet been produced.
First-principles equation-of-state table of deuterium for inertial confinement fusion applications
Hu, S. X.; Goncharov, V. N.; Skupsky, S.; Militzer, B.
Understanding and designing inertial confinement fusion (ICF) implosions through radiation-hydrodynamics simulations relies on the accurate knowledge of the equation of state (EOS) of the deuterium and tritium fuels. To minimize the drive energy for ignition, the imploding shell of DT fuel must be kept as cold as possible. Such low-adiabat ICF implosions can access to coupled and degenerate plasma conditions, in which the analytical EOS models become inaccurate due to many-body effects. Using the path-integral Monte Carlo (PIMC) simulations we have derived a first-principles EOS (FPEOS) table of deuterium that covers typical ICF fuel conditions at densities ranging from 0.002 to 1596 g/cm{sup 3} and temperatures of 1.35 eV to 5.5 keV. We report the internal energy and the pressure and discuss the structure of the plasma in terms of pair-correlation functions. When compared with the widely used SESAME table and the revised Kerley03 table, discrepancies in the internal energy and in the pressure are identified for moderately coupled and degenerate plasma conditions. In contrast to the SESAME table, the revised Kerley03 table is in better agreement with our FPEOS results over a wide range of densities and temperatures. Although subtle differences still exist for lower temperatures (T < 10 eV) and moderate densities (1 to 10 g/cm{sup 3}), hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table and the Kerley03 table have resulted in similar results for the peak density, areal density ({rho}R), and neutron yield, which differ significantly from the SESAME simulations.
Conditions for critical effects in the mass action kinetics equations for water radiolysis
Wittman, Richard S.; Buck, Edgar C.; Mausolf, Edward J.; McNamara, Bruce K.; Smith, Frances N.; Soderquist, Chuck Z.
We report on a subtle global feature of the mass action kinetics equations for water radiolysis that results in predictions of a critical behavior in H2O2 and associated radical concentrations. While radiolysis kinetics has been studied extensively in the past, it is only in recent years that high speed computing has allowed the rapid exploration of the solution over widely varying dose and compositional conditions. We explore the radiolytic production of H2O2 under various externally fixed conditions of molecular H2 and O2 that have been regarded as problematic in the literature � specifically, �jumps� in predicted concentrations, and inconsistencies between predictions and experiments have been reported for alpha radiolysis. We computationally map-out a critical concentration behavior for alpha radiolysis kinetics using a comprehensive set of reactions. We then show that all features of interest are accurately reproduced with 15 reactions. An analytical solution for steady-state concentrations of the 15 reactions reveals regions in [H2] and [O2] where the H2O2 concentration is not unique � both stable and unstable concentrations exist. The boundary of this region can be characterized analytically as a function of G-values and rate constants independent of dose rate. Physically, the boundary can be understood as separating a region where a steady-state H2O2 concentration exists, from one where it does not exist without a direct decomposition reaction. We show that this behavior is consistent with reported alpha radiolysis data and that no such behavior should occur for gamma radiolysis. We suggest experiments that could verify or discredit a critical concentration behavior for alpha radiolysis and could place more restrictive ranges on G-values from derived relationships between them.
Conditions for critical effects in the mass action kinetics equations for water radiolysis
Wittman, Richard S.; Buck, Edgar C.; Mausolf, Edward J.; McNamara, Bruce K.; Smith, Frances N.; Soderquist, Chuck Z.
We report on a subtle global feature of the mass action kinetics equations for water radiolysis that results in predictions of a critical behavior in H2O2 and associated radical concentrations. While radiolysis kinetics has been studied extensively in the past, it is only in recent years that high speed computing has allowed the rapid exploration of the solution over widely varying dose and compositional conditions. We explore the radiolytic production of H2O2 under various externally fixed conditions of molecular H2 and O2 that have been regarded as problematic in the literature � specifically, �jumps� in predicted concentrations, and inconsistencies between predictions and experiments have been reported for alpha radiolysis. We computationally map-out a critical concentration behavior for alpha radiolysis kinetics using a comprehensive set of reactions. We then show that all features of interest are accurately reproduced with 15 reactions. An analytical solution for steady-state concentrations of the 15 reactions reveals regions in [H2] and [O2] where the H2O2 concentration is not unique � both stable and unstable concentrations exist. The boundary of this region can be characterized analytically as a function of G-values and rate constants independent of dose rate. Physically, the boundary can be understood as separating a region where a steady-state H2O2 concentration exists, from one where it does not exist without a direct decomposition reaction. We show that this behavior is consistent with reported alpha radiolysis data and that no such behavior should occur for gamma radiolysis. We suggest experiments that could verify or discredit a critical concentration behavior for alpha radiolysis and could place more restrictive ranges on G-values from derived relationships between them.
The Discrete Equation Method (DEM) for Fully Compressible, Two-Phase Flows in Ducts of Spatially Varying Cross-Section
R. A. Berry; R. Saurel; O. LeMetayer
For the simulation of light water nuclear reactor coolant flows, general two-phase models (valid for all volume fractions) have been generally used which, while allowing for velocity disequilibrium, normally force pressure equilibrium between the phases (see, for example, the numerous models of this type described in H. St�dtke, Gasdynamic Aspects of Two-Phase Flow, Wiley-VCH, 2006). These equations are not hyperbolic, their physical wave dynamics are incorrect, and their solution algorithms rely on dubious truncation error induced artificial viscosity to render them numerically well posed over a portion of the computational spectrum. The inherent problems of the traditional approach to multiphase modeling, which begins with an averaged system of (ill-posed) partial differential equations (PDEs) which are then discretized to form a numerical scheme, are avoided by employing a new homogenization method known as the Discrete Equation Method (DEM) (R. Abgrall and R. Saurel, Discrete Equations for Physical and Numerical Compressible Multiphase Mixtures, J. Comp. Phys. 186, 361-396, 2003). This method results in well-posed hyperbolic systems, this property being important for transient flows. This also allows a clear treatment of non-conservative terms (terms involving interfacial variables and volume fraction gradients) permitting the solution of interface problems without conservation errors, this feature being important for the direct numerical simulation of two-phase flows. Unlike conventional methods, the averaged system of PDEs for the mixture are not used, and the DEM method directly obtains a well-posed discrete equation system from the single-phase conservation laws, producing a numerical scheme which accurately computes fluxes for arbitrary number of phases and solves non-conservative products. The method effectively uses a sequence of single phase Riemann problem solutions. Phase interactions are accounted for by Riemann solvers at each interface. Non-conservative terms are correctly approximated. Some of the closure relations missing from the traditional approach are automatically obtained. Lastly, the continuous equation system resulting from the discrete equations can be identified by taking the continuous limit with weak-wave assumptions. In this work, this approach is tested by constructing a DEM model for the flow of two compressible phases in 1-D ducts of spatially varying cross-section with explicit time integration. An analytical equation of state is included for both water vapor and liquid phases, and a realistic interphase mass transfer model is developed based on interphase heat transfer. A robust compliment of boundary conditions are developed and discussed. Though originally conceived as a first step toward implict time integration of the DEM method (to relieve time step size restrictions due to stiffness and to achieve tighter coupling of equations) in multidimensions, this model offers some unique capabilities for incorporation into next generation light water reactor safety analysis codes. We demonstrate, on a converging-diverging two-phase nozzle, that this well-posed, 2-pressure, 2-velocity DEM model can be integrated to a realistic and meaningful steady-state with both phases treated as compressible.
A Spatial Discretization Scheme for Solving the Transport Equation on Unstructured Grids of Polyhedra
Thompson, K.G.
In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a coarsely discretized problem that contains sharp boundary layers. We also examine eigenvalue and fixed source problems with mixed-shape meshes, anisotropic scattering and multi-group cross sections. Finally, we simulate the MOX fuel assembly in the Advance Test Reactor.
Conjugate heat and mass transfer in the lattice Boltzmann equation method
Li, LK; Chen, C; Mei, RW; Klausner, JF
An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer in porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved interfaces, the present treatment yields second-order accurate interior and interfacial temperatures (concentrations) and first-order accurate interfacial heat (mass) flux. An increase of order of convergence by one degree is obtained for each of these three quantities compared with the half-lattice division scheme. The surface-averaged Sherwood numbers computed in test (iv) agree well with published results.
Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: Application to silicon dioxide
Sjostrom, Travis; Crockett, Scott
The liquid regime equation of state of silicon dioxide SiO2 is calculated via quantum molecular dynamics in the density range of 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the α-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), and above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data are found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a new liquid regime equation of state table for SiO2.
(3 + 1)-dimensional cylindrical Korteweg-de Vries equation for nonextensive dust acoustic waves: Symbolic computation and exact solutions
Guo Shimin; Wang Hongli; Mei Liquan
By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.
Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: Application to silicon dioxide
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Sjostrom, Travis; Crockett, Scott
The liquid regime equation of state of silicon dioxide SiO2 is calculated via quantum molecular dynamics in the density range of 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the α-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), and above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data are found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a newmore » liquid regime equation of state table for SiO2.« less
Microsoft Word - NETL-TRS-5-2014_High-Temperature, High-Pressure Equation of State.20141003.docx
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
High-Temperature, High-Pressure Equation of State: Solidification of Hydrocarbons and Viscosity Measurement of Krytox Oil Using Rolling-Ball Viscometer 3 October 2014 Office of Fossil Energy NETL-TRS-5-2014 Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility
Solutions of the Schr�dinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method
Ita, B. I.
By using the Nikiforov-Uvarov (NU) method, the Schr�dinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.
Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect
Li, Zhihui; Ma, Qiang; Wu, Junlin; Jiang, Xinyu; Zhang, Hanxin
Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.
Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations
Kelly, Aaron; Markland, Thomas E.; Brackbill, Nora
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation
Goffin, Mark A.; Buchan, Andrew G.; Dargaville, Steven; Pain, Christopher C.; Smith, Paul N.; Smedley-Stevenson, Richard P.
A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specified functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation. -- Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.
Modeling of nonlinear vibrational relaxation of large molecules in shock waves with a nonlinear, temperature-varying master equation.
Davis, M. J.; Kiefer, J. H.; Chemistry; Univ. of Illinois at Chicago
We model recent experiments on the vibrational relaxation of oxirane in a shock tube. A master equation is developed which includes self-collisions of the oxirane, leading to a nonlinear master equation. This master equation is also applied to a more limited study of vibrational relaxation for cyclopropane in a shock tube. The time variation of the temperature dependence of the bath is also included in the calculations. Good agreement between the modeling and experiments are obtained through a fit to the energy transfer parameters. These fits demonstrate that self-collisions are dominant in promoting the relaxation even for mixtures of Kr and oxirane where the oxirane is 2% and 4% dilute. This dominance comes from two sources: (1) much larger energy transfer per collision for oxirane-oxirane collisions and (2) resonant energy transfer effects. For cyclopropane, some of the good fits show smaller energy transfer characteristics for self-collisions than buffer gas collisions. Even in these cases self-collisions are an important part of the energy transfer process through resonant energy transfer effects.
Backscattering and absorption coefficients for electrons: Solutions of invariant embedding transport equations using a method of convergence
Figueroa, C.; Brizuela, H.; Heluani, S. P.
The backscattering coefficient is a magnitude whose measurement is fundamental for the characterization of materials with techniques that make use of particle beams and particularly when performing microanalysis. In this work, we report the results of an analytic method to calculate the backscattering and absorption coefficients of electrons in similar conditions to those of electron probe microanalysis. Starting on a five level states ladder model in 3D, we deduced a set of integro-differential coupled equations of the coefficients with a method know as invariant embedding. By means of a procedure proposed by authors, called method of convergence, two types of approximate solutions for the set of equations, namely complete and simple solutions, can be obtained. Although the simple solutions were initially proposed as auxiliary forms to solve higher rank equations, they turned out to be also useful for the estimation of the aforementioned coefficients. In previous reports, we have presented results obtained with the complete solutions. In this paper, we present results obtained with the simple solutions of the coefficients, which exhibit a good degree of fit with the experimental data. Both the model and the calculation method presented here can be generalized to other techniques that make use of different sorts of particle beams.
A comparison of conjugate gradient, SIP, and other iterative methods for the solution of Poisson's equation with irregular boundary conditions
Bergmann, D.J.
Several well known iterative methods for solving Poisson's equation, including Strongly Implicit Procedure and several preconditioned conjugate gradient methods are first applied to a problem with simple boundary conditions and a known solution. Then a problem with more complicated boundary conditions, similar to those encountered when modeling AVLIS plasmas, is solved. Differences in the solutions of the various methods are examined through the use of Fourier analysis. It was found that combinations of different iterative schemes will in some cases be the most efficient method of solution. 22 refs., 29 figs.
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
Ciraolo, Giulio Gargano, Francesco Sciacca, Vincenzo
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.
Time-fractional Gardner equation for ion-acoustic waves in negative-ion-beam plasma with negative ions and nonthermal nonextensive electrons
Guo, Shimin Mei, Liquan; Zhang, Zhengqiang
Nonlinear propagation of ion-acoustic waves is investigated in a one-dimensional, unmagnetized plasma consisting of positive ions, negative ions, and nonthermal electrons featuring Tsallis distribution that is penetrated by a negative-ion-beam. The classical Gardner equation is derived to describe nonlinear behavior of ion-acoustic waves in the considered plasma system via reductive perturbation technique. We convert the classical Gardner equation into the time-fractional Gardner equation by Agrawal's method, where the time-fractional term is under the sense of Riesz fractional derivative. Employing variational iteration method, we construct solitary wave solutions of the time-fractional Gardner equation with initial condition which depends on the nonlinear and dispersion coefficients. The effect of the plasma parameters on the compressive and rarefactive ion-acoustic solitary waves is also discussed in detail.
Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes
Goffin, Mark A.; Baker, Christopher M.J.; Buchan, Andrew G.; Pain, Christopher C.; Eaton, Matthew D.; Smith, Paul N.
This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k{sub eff}, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k{sub eff} with directional dependence. General error estimators are derived for any given functional of the flux and applied to k{sub eff} to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k{sub eff} goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.
Interfacing relativistic and nonrelativistic methods. I. Normalized elimination of the small component in the modified Dirac equation
Dyall, K.G.
The introduction of relativistic terms into the nonrelativistic all-electron Schr{umlt o}dinger equation is achieved by the method of normalized elimination of the small component (ESC) within the matrix representation of the modified Dirac equation. In contrast to the usual method of ESC, the method presented retains the correct relativistic normalization, and permits the construction of a single matrix relating the large and small component coefficient matrices for an entire set of positive energy one-particle states, thus enabling the whole set to be obtained with a single diagonalization. This matrix is used to define a modified set of one- and two-electron integrals which have the same appearance as the nonrelativistic integrals, and to which they reduce in the limit {alpha}{r_arrow}0. The normalized method corresponds to a projection of the Dirac{endash}Fock matrix onto the positive energy states. Inclusion of the normalization reduces the discrepancy between the eigenvalues of the ESC approach and the Dirac eigenvalues for a model problem from order {alpha}{sup 2} to order {alpha}{sup 4}, providing a closer approximation to the original, uneliminated solutions. The transition between the nonrelativistic and relativistic limits is achieved by simply scaling the fine structure constant {alpha}. {copyright} {ital 1997 American Institute of Physics.}
The MGGB equation-of-state for multifield applications: a numerical recipe for analytic expression of sesame EOS data
Kashiwa, B. A.
Abstract A thermodynamically consistent and fully general equation�of� state (EOS) for multifield applications is described. EOS functions are derived from a Helmholtz free energy expressed as the sum of thermal (fluctuational) and collisional (condensed�phase) contributions; thus the free energy is of the Mie�Gr�uneisen1 form. The phase�coexistence region is defined using a parameterized saturation curve by extending the form introduced by Guggenheim,2 which scales the curve relative to conditions at the critical point. We use the zero�temperature condensed�phase contribution developed by Barnes,3 which extends the Thomas�Fermi�Dirac equation to zero pressure. Thus, the functional form of the EOS could be called MGGB (for Mie� Gr�uneisen�Guggenheim�Barnes). Substance�specific parameters are obtained by fitting the low�density energy to data from the Sesame4 library; fitting the zero�temperature pressure to the Sesame cold curve; and fitting the saturation curve and latent heat to laboratory data,5 if available. When suitable coexistence data, or Sesame data, are not available, then we apply the Principle of Corresponding States.2 Thus MGGB can be thought of as a numerical recipe for rendering the tabular Sesame EOS data in an analytic form that includes a proper coexistence region, and which permits the accurate calculation of derivatives associated with compressibility, expansivity, Joule coefficient, and specific heat, all of which are required for multifield applications. 1
A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves
Pelanti, Marica; Shyue, Keh-Ming
We model liquid�gas flows with cavitation by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel�Petitpas�Berry (Saurel et al., 2009) [9]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical six-equation system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure at equilibrium with the correct mixture equation of state. Temperature and Gibbs free energy exchange terms are included in the equations as relaxation terms to model heat and mass transfer and hence liquid�vapor transition. The algorithm uses a high-resolution wave propagation method for the numerical approximation of the homogeneous hyperbolic portion of the model. In two dimensions a fully-discretized scheme based on a hybrid HLLC/Roe Riemann solver is employed. Thermo-chemical terms are handled numerically via a stiff relaxation solver that forces thermodynamic equilibrium at liquid�vapor interfaces under metastable conditions. We present numerical results of sample tests in one and two space dimensions that show the ability of the proposed model to describe cavitation mechanisms and evaporation wave dynamics.
Phase retrieval with the transport-of-intensity equation in an arbitrarily-shaped aperture by iterative discrete cosine transforms
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Huang, Lei; Zuo, Chao; Idir, Mourad; Qu, Weijuan; Asundi, Anand
A novel transport-of-intensity equation (TIE) based phase retrieval method is proposed with putting an arbitrarily-shaped aperture into the optical wavefield. In this arbitrarily-shaped aperture, the TIE can be solved under non-uniform illuminations and even non-homogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and non-uniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phasemore » distribution under non-uniform illumination and non-homogeneous boundary conditions within an arbitrarily-shaped aperture, which enables the technique of TIE with hard aperture become a more flexible phase retrieval tool in practical measurements.« less
Improving the efficiency of hierarchical equations of motion approach and application to coherent dynamics in Aharonov–Bohm interferometers
Hou, Dong; Xu, RuiXue; Zheng, Xiao; Wang, Shikuan; Wang, Rulin; Ye, LvZhou; Yan, YiJing
Several recent advancements for the hierarchical equations of motion (HEOM) approach are reported. First, we propose an a priori estimate for the optimal number of basis functions for the reservoir memory decomposition. Second, we make use of the sparsity of auxiliary density operators (ADOs) and propose two ansatzs to screen out all the intrinsic zero ADO elements. Third, we propose a new truncation scheme by utilizing the time derivatives of higher-tier ADOs. These novel techniques greatly reduce the memory cost of the HEOM approach, and thus enhance its efficiency and applicability. The improved HEOM approach is applied to simulate the coherent dynamics of Aharonov–Bohm double quantum dot interferometers. Quantitatively accurate dynamics is obtained for both noninteracting and interacting quantum dots. The crucial role of the quantum phase for the magnitude of quantum coherence and quantum entanglement is revealed.
Photoacoustically Measured Speeds of Sound and the Equation of State of HBO2: On Understanding Detonation with Boron Fuel
Zaug, J M; Bastea, S; Crowhurst, J; Armstrong, M; Fried, L; Teslich, N
Elucidation of geodynamic, geochemical, and shock induced processes is limited by challenges to accurately determine molecular fluid equations of state (EOS). High pressure liquid state reactions of carbon species underlie physiochemical mechanisms such as differentiation of planetary interiors, deep carbon sequestration, propellant deflagration, and shock chemistry. In this proceedings paper we introduce a versatile photoacoustic technique developed to measure accurate and precise speeds of sound (SoS) of high pressure molecular fluids and fluid mixtures. SoS of an intermediate boron oxide, HBO{sub 2} are measured up to 0.5 GPa along the 277 C isotherm. A polarized exponential-6 interatomic potential form, parameterized using our SoS data, enables EOS determinations and corresponding semi-empirical evaluations of >2000 C thermodynamic states including energy release from bororganic formulations. Our thermochemical model propitiously predicts boronated hydrocarbon shock Hugoniot results.
Vapor-liquid equilibria for an R134a/lubricant mixture: Measurements and equation-of-state modeling
Huber, M.L.; Holcomb, C.D.; Outcalt, S.L.; Elliott, J.R.
The authors measured bubble point pressures and coexisting liquid densities for two mixtures of R-134a and a polyolester (POE) lubricant. The mass fraction of the lubricant was approximately 9% and 12%, and the temperature ranged from 280 K to 355 K. The authors used the Elliott, Suresh, and Donohue (ESD) equation of state to model the bubble point pressure data. The bubble point pressures were represented with an average absolute deviation of 2.5%. A binary interaction parameter reduced the deviation to 1.4%. The authors also applied the ESD model to other R-134a/POE lubricant data in the literature. As the concentration of the lubricant increased, the performance of the model deteriorated markedly. However, the use of a single binary interaction parameter reduced the deviations significantly.
Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime
Ticknor, Christopher; Collins, Lee A.; Kress, Joel D.
We present simulations of a four component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5�200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. In addition, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.
Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Ticknor, Christopher; Collins, Lee A.; Kress, Joel D.
We present simulations of a four component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5–200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. In addition, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based onmore » the Coulomb coupling parameter and one-component plasmas.« less
Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part II: Application to Partial Differential Equations
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Pawlowski, Roger P.; Phipps, Eric T.; Salinger, Andrew G.; Owen, Steven J.; Siefert, Christopher M.; Staten, Matthew L.
A template-based generic programming approach was presented in Part I of this series of papers [Sci. Program. 20 (2012), 197–219] that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertaintymore » quantification results for a 3D PDE application.« less
Stability of the standard Crank-Nicolson-Galerkin scheme applied to the diffusion-convection equation: Some new insights
Perrochet, P.; Berod, D. )
A stability analysis of the classical Crank-Nicolson-Galerkin (CNG) scheme applied to the one-dimensional solute transport equation is proposed on the basis of two fairly different approaches. Using a space-time eigenvalue analysis, it is shown, at least for subsurface hydrology applications, that the CNG scheme is theoretically stable under the condition PeCr [le] 2, where Pe and Cr are the mesh Peclet and Courant numbers. Then, to assess the computational stability of the scheme, the amplification matrix is constructed, and its norm is displayed in the (Pe, Cr) space. The results indicate that the norm of the amplification matrix is never smaller than unity and exhibits a hyperbolic nature analogous to the above theoretical condition. 21 refs., 2 figs.
Properties of a soft-core model of methanol: An integral equation theory and computer simulation study
Hu�, Matej; Urbic, Tomaz; Muna�, Gianmarco
Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations. The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.
Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Zhao, Renjie; Evans, James W.; Oliveira, Tiago J.
Here, a discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating kinks along the step edges. Model energetics and kinetics appropriately account for binding of adatoms at steps and kinks, distinct terrace and edge diffusion rates, and possible additional barriers for attachment to steps. Analysis of adatom attachment fluxes as well as limiting values of adatom densities at step edges for nonuniform deposition scenarios allows determination of both permeability and kinetic coefficients. Behavior of these quantities is assessedmore » as a function of key system parameters including kink density, step attachment barriers, and the step edge diffusion rate.« less
The Light-Front Schrödinger Equation and Determination of the Perturbative QCD Scale from Color Confinement
Brodsky, Stanley J.; de Teramond, Guy F.; Deur, Alexandre P.; Dosch, Hans G.
The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also show how the mass scale κ underlying confinement and hadron masses determines the scale ΛMS¯¯¯¯ controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The result is an effective coupling defined at all momenta. The predicted value ΛMS¯¯¯¯=0.328±0.034 GeV is in agreement with the world average 0.339±0.010 GeV. The analysis applies to any renormalization scheme.
Equation of state of a weakly interacting two-dimensional Bose gas studied at zero temperature by means of quantum Monte Carlo methods
Astrakharchik, G. E.; Boronat, J.; Casulleras, J.; Kurbakov, I. L.; Lozovik, Yu. E.
The equation of state of a weakly interacting two-dimensional Bose gas is studied at zero temperature by means of quantum Monte Carlo methods. Going down to as low densities as na{sup 2}{proportional_to}10{sup -100} permits us to obtain agreement on beyond mean-field level between predictions of perturbative methods and direct many-body numerical simulation, thus providing an answer to the fundamental question of the equation of state of a two-dimensional dilute Bose gas in the universal regime (i.e., entirely described by the gas parameter na{sup 2}). We also show that the measure of the frequency of a breathing collective oscillation in a trap at very low densities can be used to test the universal equation of state of a two-dimensional Bose gas.
Fixed conditions for achieving the real-valued partition function of one-dimensional Gross-Pitaevskii equation coupled with time-dependent potential
Prayitno, T. B.
We have imposed the conditions in order to preserve the real-valued partition function in the case of onedimensional Gross-Pitaevskii equation coupled by time-dependent potential. In this case we have solved the Gross-Pitaevskii equation by means of the time-dependent perturbation theory by extending the previous work of Kivshar et al. [Phys. Lett A 278, 225–230 (2001)]. To use the method, we have treated the equation as the macroscopic quantum oscillator and found that the expression of the partition function explicitly has complex values. In fact, we have to choose not only the appropriate functions but also the suitable several values of the potential to keep the real-valued partition function.
Remarks on the derivation of the governing equations for the dynamics of a nonlinear beam to a non ideal shaft coupling
Fenili, Andr�; Lopes Rebello da Fonseca Brasil, Reyolando Manoel
We derive nonlinear governing equations without assuming that the beam is inextensible. The derivation couples the equations that govern a weak electric motor, which is used to rotate the base of the beam, to those that govern the motion of the beam. The system is considered non-ideal in the sense that the response of the motor to an applied voltage and the motion of the beam must be obtained interactively. The moment that the motor exerts on the base of the beam cannot be determined without solving for the motion of the beam.
Seismological comparisons of solar models with element diffusion using the MHD, OPAL, and SIREFF equations of state
Guzik, J.A.; Swenson, F.J.
We compare the thermodynamic and helioseismic properties of solar models evolved using three different equation of state (EOS) treatments: the Mihalas, D{umlt a}ppen & Hummer EOS tables (MHD); the latest Rogers, Swenson, & Iglesias EOS tables (OPAL), and a new analytical EOS (SIREFF) developed by Swenson {ital et al.} All of the models include diffusive settling of helium and heavier elements. The models use updated OPAL opacity tables based on the 1993 Grevesse & Noels solar element mixture, incorporating 21 elements instead of the 14 elements used for earlier tables. The properties of solar models that are evolved with the SIREFF EOS agree closely with those of models evolved using the OPAL or MHD tables. However, unlike the MHD or OPAL EOS tables, the SIREFF in-line EOS can readily account for variations in overall Z abundance and the element mixture resulting from nuclear processing and diffusive element settling. Accounting for Z abundance variations in the EOS has a small, but non-negligible, effect on model properties (e.g., pressure or squared sound speed), as much as 0.2{percent} at the solar center and in the convection zone. The OPAL and SIREFF equations of state include electron exchange, which produces models requiring a slightly higher initial helium abundance, and increases the convection zone depth compared to models using the MHD EOS. However, the updated OPAL opacities are as much as 5{percent} lower near the convection zone base, resulting in a small decrease in convection zone depth. The calculated low-degree nonadiabatic frequencies for all of the models agree with the observed frequencies to within a few microhertz (0.1{percent}). The SIREFF analytical calibrations are intended to work over a wide range of interior conditions found in stellar models of mass greater than 0.25M{sub {circle_dot}} and evolutionary states from pre-main-sequence through the asymptotic giant branch (AGB). It is significant that the SIREFF EOS produces solar models that both measure up to the stringent requirements imposed by solar oscillation observations and inferences, and are more versatile than EOS tables. {copyright} {ital 1997} {ital The American Astronomical Society}
A deterministic solution of the first order linear Boltzmann transport equation in the presence of external magnetic fields
St Aubin, J. Keyvanloo, A.; Fallone, B. G.; Vassiliev, O.
Purpose: Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today�s treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann transport equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields. Methods: The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf-macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 � 10 cm{sup 2} field as well as a smaller 2 � 2 cm{sup 2} field. Results: Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm�s high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization. Conclusions: The feasibility of including magnetic field effects in a deterministic solution to the first order linear Boltzmann transport equation is shown. The results show a high degree of accuracy when compared against Monte Carlo calculations in all magnetic field strengths and orientations tested.
A finite elements method to solve the Bloch–Torrey equation applied to diffusion magnetic resonance imaging
Nguyen, Dang Van; Li, Jing-Rebecca; Grebenkov, Denis; Le Bihan, Denis
The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch–Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch–Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge–Kutta–Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.
Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence
Subotnik, Joseph E. Ouyang, Wenjun; Landry, Brian R.
In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied � some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly.
Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Pan, Wenxiao; Daily, Michael; Baker, Nathan A.
Background: The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors. Methods: We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with "imperfect" reaction rates. Results: The numerical method is first verified in simple systems and thenmore » applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Conclusions: Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.« less
Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics
Pan, Wenxiao; Daily, Michael D.; Baker, Nathan A.
We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.
A new equation of state with light nuclei and their weak interactions in core-collapse supernova simulations
Furusawa, Shun; Yamada, Shoichi [Waseda University, 3-4-1, Okubo, Shinjuku, Tokyo 169-8555 (Japan); Nagakura, Hiroki [Yukawa Institute for Theoretical Physics, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto, 606-8502 (Japan); Sumiyoshi, Kohsuke [Numazu College of Technology, Ooka 3600, Numazu, Shizuoka 410-8501 (Japan); Suzuki, Hideyuki [Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda, Chiba 278-8510 (Japan)
We perform numerical experiments to investigate the influence of inelastic neutrino reactions with light nuclei on the standing accretion shock instability. The time evolutions of shock waves are calculated with a simple light-bulb approximation for the neutrino transport and a multi-nuclei equation of state. The neutrino absorptions and inelastic interactions with deuterons, tritons, helions and alpha particles are taken into account in the hydrodynamical simulations in addition to the ordinary charged-current interactions with nucleons. Axial symmetry is assumed but no equatorial symmetry is imposed. We show that the heating rates of deuterons reach as high as ? 10% of those of nucleons around the bottom of the gain region. On the other hands, alpha particles heat the matter near the shock wave, which is important when the shock wave expands and density and temperature of matter become low. It is also found that the models with heating by light nuclei have different evolutions from those without it in non-linear evolution phase. The matter in the gain region has various densities and temperatures and there appear regions that are locally rich in deuterons and alpha particles. These results indicate that the inelastic reactions of light nuclei, especially deuterons, should be incorporated in the simulations of core-collapse supernovae.
Effects of Landau quantization on the equations of state in intense laser plasma interactions with strong magnetic fields
Eliezer, Shalom; Norreys, Peter; Mendonca, Jose T.; Lancaster, Kate
Recently, magnetic fields of 0.7({+-}0.1) gigaGauss (GG) have been observed in the laboratory in laser plasma interactions. From scaling arguments, it appears that a few gigaGauss magnetic fields may be within reach of existing petawatt lasers. In this paper, the equations of state (EOS) are calculated in the presence of these very large magnetic fields. The appropriate domain for electron degeneracy and for Landau quantization is calculated for the density-temperature domain relevant to laser plasma interactions. The conditions for a strong Landau quantization, for a magnetic field in the domain of 1-10 GG, are obtained. The role of this paper is to formulate the EOS in terms of those that can potentially be realized in laboratory plasmas. By doing so, it is intended to alert the experimental laser-plasma physics community to the potential of realizing Landau quantization in the laboratory for the first time since the theory was first formulated.
Liouville master equation for multielectron dynamics: Neutralization of highly charged ions near a LiF surface
Wirtz, Ludger; Reinhold, Carlos O.; Lemell, Christoph
We present a simulation of the neutralization of highly charged ions in front of a lithium fluoride surface including the close-collision regime above the surface. The present approach employs a Monte Carlo solution of the Liouville master equation for the joint probability density of the ionic motion and the electronic population of the projectile and the target surface. It includes single as well as double particle-hole (de)excitation processes and incorporates electron correlation effects through the conditional dynamics of population strings. The input in terms of elementary one- and two-electron transfer rates is determined from classical trajectory Monte Carlo calculations as well as quantum-mechanical Auger calculations. For slow projectiles and normal incidence, the ionic motion depends sensitively on the interplay between image acceleration towards the surface and repulsion by an ensemble of positive hole charges in the surface ('trampoline effect'). For Ne{sup 10+} we find that image acceleration is dominant and no collective backscattering high above the surface takes place. For grazing incidence, our simulation delineates the pathways to complete neutralization. In accordance with recent experimental observations, most ions are reflected as neutral or even as singly charged negative particles, irrespective of the charge state of the incoming ions.
A Lagrangian-Eulerian method with zoomable hidden fine-mesh approach to solving advection-dispersion equations
Yeh, G.T. )
A Lagrangian-Eulerian method with zoomable hidden fine-mesh approach (LEZOOM), that can be adapted with either finite element or finite difference methods, is used to solve the advection-dispersion equation. The approach is based on automatic adaptation of zooming a hidden fine mesh in regions where the sharp front is located. Application of LEZOOM to four bench mark problems indicates that it can handle the advection-dispersion/diffusion problems with mesh Peclet numbers ranged from 0 to {infinity} and with mesh Courant numbers well in excess of 1. Difficulties that can be resolved with LEZOOM include numerical dispersion, oscillations, the clipping of peaks, and the effect of grid orientation. Nonuniform grid as well as spatial temporally variable flow pose no problems with LEZOOM. Both initial and boundary value problems can be solved accurately with LEZOOM. It is shown that although the mixed Lagrangian-Eulerian (LE) approach (LEZOOM without zooming) also produces excessive numerical dispersion as the upstream finite element (UFE) method, the LE approach is superior to the UFE method.
Equation-of-motion coupled-cluster method for doubly ionized states with spin-orbit coupling
Wang, Zhifan; Hu, Shu; Guo, Jingwei; Wang, Fan
In this work, we report implementation of the equation-of-motion coupled-cluster method for doubly ionized states (EOM-DIP-CC) with spin-orbit coupling (SOC) using a closed-shell reference. Double ionization potentials (DIPs) are calculated in the space spanned by 2h and 3h1p determinants with the EOM-DIP-CC approach at the CC singles and doubles level (CCSD). Time-reversal symmetry together with spatial symmetry is exploited to reduce computational effort. To circumvent the problem of unstable dianion references when diffuse basis functions are included, nuclear charges are scaled. Effect of this stabilization potential on DIPs is estimated based on results from calculations using a small basis set without diffuse basis functions. DIPs and excitation energies of some low-lying states for a series of open-shell atoms and molecules containing heavy elements with two unpaired electrons have been calculated with the EOM-DIP-CCSD approach. Results show that this approach is able to afford a reliable description on SOC splitting. Furthermore, the EOM-DIP-CCSD approach is shown to provide reasonable excitation energies for systems with a dianion reference when diffuse basis functions are not employed.
Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics
Pan, Wenxiao; Daily, Michael; Baker, Nathan A.
Background: The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors. Methods: We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with �imperfect� reaction rates. Results: The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Conclusions: Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.
The shallow water equations as a hybrid flow model for the numerical and experimental analysis of hydro power stations
Ostermann, Lars; Seidel, Christian
The numerical analysis of hydro power stations is an important method of the hydraulic design and is used for the development and optimisation of hydro power stations in addition to the experiments with the physical submodel of a full model in the hydraulic laboratory. For the numerical analysis, 2D and 3D models are appropriate and commonly used.The 2D models refer mainly to the shallow water equations (SWE), since for this flow model a large experience on a wide field of applications for the flow analysis of numerous problems in hydraulic engineering already exists. Often, the flow model is verified by in situ measurements. In order to consider 3D flow phenomena close to singularities like weirs, hydro power stations etc. the development of a hybrid fluid model is advantageous to improve the quality and significance of the global model. Here, an extended hybrid flow model based on the principle of the SWE is presented. The hybrid flow model directly links the numerical model with the experimental data, which may originate from physical full models, physical submodels and in-situ measurements. Hence a wide field of application of the hybrid model emerges including the improvement of numerical models and the strong coupling of numerical and experimental analysis.
Final Report - High-Order Spectral Volume Method for the Navier-Stokes Equations On Unstructured Tetrahedral Grids
Wang, Z J
The overriding objective for this project is to develop an efficient and accurate method for capturing strong discontinuities and fine smooth flow structures of disparate length scales with unstructured grids, and demonstrate its potentials for problems relevant to DOE. More specifically, we plan to achieve the following objectives: 1. Extend the SV method to three dimensions, and develop a fourth-order accurate SV scheme for tetrahedral grids. Optimize the SV partition by minimizing a form of the Lebesgue constant. Verify the order of accuracy using the scalar conservation laws with an analytical solution; 2. Extend the SV method to Navier-Stokes equations for the simulation of viscous flow problems. Two promising approaches to compute the viscous fluxes will be tested and analyzed; 3. Parallelize the 3D viscous SV flow solver using domain decomposition and message passing. Optimize the cache performance of the flow solver by designing data structures minimizing data access times; 4. Demonstrate the SV method with a wide range of flow problems including both discontinuities and complex smooth structures. The objectives remain the same as those outlines in the original proposal. We anticipate no technical obstacles in meeting these objectives.
Factorized three-body S-matrix restrained by the Yang�Baxter equation and quantum entanglements
Yu, Li-Wei; Zhao, Qing; Ge, Mo-Lin
This paper investigates the physical effects of the Yang�Baxter equation (YBE) to quantum entanglements through the 3-body S-matrix in entangling parameter space. The explicit form of 3-body S-matrix ?{sub 123}(?,?) based on the 2-body S-matrices is given due to the factorization condition of YBE. The corresponding chain Hamiltonian has been obtained and diagonalized, also the Berry phase for 3-body system is given. It turns out that by choosing different spectral parameters the ?(?,?)-matrix gives GHZ and W states respectively. The extended 1-D Kitaev toy model has been derived. Examples of the role of the model in entanglement transfer are discussed. - Highlights: � We give the relation between 3-body S-matrix and 3-qubit entanglement. � The relation between 3-qubit and 2-qubit entanglements is investigated via YBE. � 1D Kitaev toy model is derived by the Type-II solution of YBE. � The condition of YBE kills the �Zero boundary mode� in our chain model.
Validation of Simplified Load Equations through Loads Measurement and Modeling of a Small Horizontal-Axis Wind Turbine Tower; NREL (National Renewable Energy Laboratory)
Dana, S.; Damiani, R.; vanDam, J.
As part of an ongoing effort to improve the modeling and prediction of small wind turbine dynamics, NREL tested a small horizontal axis wind turbine in the field at the National Wind Technology Center (NWTC). The test turbine was a 2.1-kW downwind machine mounted on an 18-meter multi-section fiberglass composite tower. The tower was instrumented and monitored for approximately 6 months. The collected data were analyzed to assess the turbine and tower loads and further validate the simplified loads equations from the International Electrotechnical Commission (IEC) 61400-2 design standards. Field-measured loads were also compared to the output of an aeroelastic model of the turbine. Ultimate loads at the tower base were assessed using both the simplified design equations and the aeroelastic model output. The simplified design equations in IEC 61400-2 do not accurately model fatigue loads. In this project, we compared fatigue loads as measured in the field, as predicted by the aeroelastic model, and as calculated using the simplified design equations.
Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform
Ganguly, A. E-mail: email@example.com; Das, A.
We consider one-dimensional stationary position-dependent effective mass quantum model and derive a generalized Korteweg-de Vries (KdV) equation in (1+1) dimension through Lax pair formulation, one being the effective mass Schr�dinger operator and the other being the time-evolution of wave functions. We obtain an infinite number of conserved quantities for the generated nonlinear equation and explicitly show that the new generalized KdV equation is an integrable system. Inverse scattering transform method is applied to obtain general solution of the nonlinear equation, and then N-soliton solution is derived for reflectionless potentials. Finally, a special choice has been made for the variable mass function to get mass-deformed soliton solution. The influence of position and time-dependence of mass and also of the different representations of kinetic energy operator on the nature of such solitons is investigated in detail. The remarkable features of such solitons are demonstrated in several interesting figures and are contrasted with the conventional KdV-soliton associated with constant-mass quantum model.
Derivation of a Multiparameter Gamma Model for Analyzing the Residence-Time Distribution Function for Nonideal Flow Systems as an Alternative to the Advection-Dispersion Equation
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Embry, Irucka; Roland, Victor; Agbaje, Oluropo; Watson, Valetta; Martin, Marquan; Painter, Roger; Byl, Tom; Sharpe, Lonnie
A new residence-time distribution (RTD) function has been developed and applied to quantitative dye studies as an alternative to the traditional advection-dispersion equation (AdDE). The new method is based on a jointly combined four-parameter gamma probability density function (PDF). The gamma residence-time distribution (RTD) function and its first and second moments are derived from the individual two-parameter gamma distributions of randomly distributed variables, tracer travel distance, and linear velocity, which are based on their relationship with time. The gamma RTD function was used on a steady-state, nonideal system modeled as a plug-flow reactor (PFR) in the laboratory to validate themore » effectiveness of the model. The normalized forms of the gamma RTD and the advection-dispersion equation RTD were compared with the normalized tracer RTD. The normalized gamma RTD had a lower mean-absolute deviation (MAD) (0.16) than the normalized form of the advection-dispersion equation (0.26) when compared to the normalized tracer RTD. The gamma RTD function is tied back to the actual physical site due to its randomly distributed variables. The results validate using the gamma RTD as a suitable alternative to the advection-dispersion equation for quantitative tracer studies of non-ideal flow systems.« less
Banik, Sarmistha [BITS Pilani, Hyderabad Campus, Hyderabad-500078 (India); Hempel, Matthias [Departement Physik, Universit�t Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Bandyopadhyay, Debades [Astroparticle Physics and Cosmology Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata-700064 (India)
We develop new hyperon equation of state (EoS) tables for core-collapse supernova simulations and neutron stars. These EoS tables are based on a density-dependent relativistic hadron field theory where baryon-baryon interaction is mediated by mesons, using the parameter set DD2 for nucleons. Furthermore, light and heavy nuclei along with interacting nucleons are treated in the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich which includes excluded volume effects. Of all possible hyperons, we consider only the contribution of ?s. We have developed two variants of hyperonic EoS tables: in the np?? case the repulsive hyperon-hyperon interaction mediated by the strange ? meson is taken into account, and in the np? case it is not. The EoS tables for the two cases encompass a wide range of densities (10{sup �12} to ?1 fm{sup �3}), temperatures (0.1 to 158.48 MeV), and proton fractions (0.01 to 0.60). The effects of ? hyperons on thermodynamic quantities such as free energy per baryon, pressure, or entropy per baryon are investigated and found to be significant at higher densities. The cold, ?-equilibrated EoS (with the crust included self-consistently) results in a 2.1 M {sub ?} maximum mass neutron star for the np?? case, whereas that for the np? case is 1.95 M {sub ?}. The np?? EoS represents the first supernova EoS table involving hyperons that is directly compatible with the recently measured 2 M {sub ?} neutron stars.
Predicting the influence of long-range molecular interactions on macroscopic-scale diffusion by homogenization of the Smoluchowski equation
Kekenes-Huskey, P. M.; Gillette, A. K.; McCammon, J. A.; Department of Chemistry, Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093-0636
The macroscopic diffusion constant for a charged diffuser is in part dependent on (1) the volume excluded by solute �obstacles� and (2) long-range interactions between those obstacles and the diffuser. Increasing excluded volume reduces transport of the diffuser, while long-range interactions can either increase or decrease diffusivity, depending on the nature of the potential. We previously demonstrated [P. M. Kekenes-Huskey et al., Biophys. J. 105, 2130 (2013)] using homogenization theory that the configuration of molecular-scale obstacles can both hinder diffusion and induce diffusional anisotropy for small ions. As the density of molecular obstacles increases, van der Waals (vdW) and electrostatic interactions between obstacle and a diffuser become significant and can strongly influence the latter's diffusivity, which was neglected in our original model. Here, we extend this methodology to include a fixed (time-independent) potential of mean force, through homogenization of the Smoluchowski equation. We consider the diffusion of ions in crowded, hydrophilic environments at physiological ionic strengths and find that electrostatic and vdW interactions can enhance or depress effective diffusion rates for attractive or repulsive forces, respectively. Additionally, we show that the observed diffusion rate may be reduced independent of non-specific electrostatic and vdW interactions by treating obstacles that exhibit specific binding interactions as �buffers� that absorb free diffusers. Finally, we demonstrate that effective diffusion rates are sensitive to distribution of surface charge on a globular protein, Troponin C, suggesting that the use of molecular structures with atomistic-scale resolution can account for electrostatic influences on substrate transport. This approach offers new insight into the influence of molecular-scale, long-range interactions on transport of charged species, particularly for diffusion-influenced signaling events occurring in crowded cellular environments.
A computational method for solving stochastic It��Volterra integral equations based on stochastic operational matrix for generalized hat basis functions
Heydari, M.H.; Hooshmandasl, M.R.; Maalek Ghaini, F.M.; Cattani, C.
In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic It��Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0,T] is obtained. By using these basis functions and their stochastic operational matrix, such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by forward substitution. Also, the rate of convergence of the proposed method is considered and it has been shown that it is O(1/(n{sup 2}) ). Further, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method.
Effect of trapped electron on the dust ion acoustic waves in dusty plasma using time fractional modified Korteweg-de Vries equation
Nazari-Golshan, A.; Nourazar, S. S.; Department of Mechanical Engineering, Amirkabir University of Technology, Tehran
The time fractional modified Korteweg-de Vries (TFMKdV) equation is solved to study the nonlinear propagation of small but finite amplitude dust ion-acoustic (DIA) solitary waves in un-magnetized dusty plasma with trapped electrons. The plasma is composed of a cold ion fluid, stationary dust grains, and hot electrons obeying a trapped electron distribution. The TFMKdV equation is derived by using the semi-inverse and Agrawal's methods and then solved by the Laplace Adomian decomposition method. Our results show that the amplitude of the DIA solitary waves increases with the increase of time fractional order ?, the wave velocity v{sub 0}, and the population of the background free electrons ?. However, it is vice-versa for the deviation from isothermality parameter b, which is in agreement with the result obtained previously.
The diffusion approximation versus the telegraph equation for modeling solar energetic particle transport with adiabatic focusing. I. Isotropic pitch-angle scattering
Effenberger, Frederic; Litvinenko, Yuri E.
The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wave-like aspects of the cosmic-ray transport.
Hybrid radiosity-SP{sub 3} equation based bioluminescence tomography reconstruction for turbid medium with low- and non-scattering regions
Chen, Xueli E-mail: email@example.com; Zhang, Qitan; Yang, Defu; Liang, Jimin E-mail: email@example.com
To provide an ideal solution for a specific problem of gastric cancer detection in which low-scattering regions simultaneously existed with both the non- and high-scattering regions, a novel hybrid radiosity-SP{sub 3} equation based reconstruction algorithm for bioluminescence tomography was proposed in this paper. In the algorithm, the third-order simplified spherical harmonics approximation (SP{sub 3}) was combined with the radiosity equation to describe the bioluminescent light propagation in tissues, which provided acceptable accuracy for the turbid medium with both low- and non-scattering regions. The performance of the algorithm was evaluated with digital mouse based simulations and a gastric cancer-bearing mouse based in situ experiment. Primary results demonstrated the feasibility and superiority of the proposed algorithm for the turbid medium with low- and non-scattering regions.
The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface
Chabchoub, A.; Kibler, B.; Finot, C.; Millot, G.; Onorato, M.; Dudley, J.M.; Babanin, A.V.
The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.
On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces
Noguera, Norman; Rózga, Krzysztof
In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.
Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations
Priimak, Dmitri
We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.
On an explicit form of the Green function of the third boundary value problem for the Poisson equation in a circle
Sadybekov, Makhmud A.; Torebek, Berikbol T.; Turmetov, Batirkhan Kh.
The paper is devoted to the investigation of questions about constructing the explicit form of the Green�s function of the Robin problem. For constructing this function we use the representation of the fundamental solution of the Laplace equation in the form of a series. An integral representation of the Green function is obtained and for some values of the parameters, the problem is presented in elementary functions.
Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV
Garcia-Martin, R.; Pelaez, J. R.; Ruiz de Elvira, J.; Kaminski, R.; Yndurain, F. J.
We improve our description of {pi}{pi} scattering data by imposing additional requirements on our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of forward dispersion relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy K{sub l4} decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost all disagreement with previous chiral perturbation theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.
Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods
Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang
In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same.
Equation of state of dense plasmas: Orbital-free molecular dynamics as the limit of quantum molecular dynamics for high-Z elements
Danel, J.-F.; Blottiau, P.; Kazandjian, L.; Piron, R.; Torrent, M.
The applicability of quantum molecular dynamics to the calculation of the equation of state of a dense plasma is limited at high temperature by computational cost. Orbital-free molecular dynamics, based on a semiclassical approximation and possibly on a gradient correction, is a simulation method available at high temperature. For a high-Z element such as lutetium, we examine how orbital-free molecular dynamics applied to the equation of state of a dense plasma can be regarded as the limit of quantum molecular dynamics at high temperature. For the normal mass density and twice the normal mass density, we show that the pressures calculated with the quantum approach converge monotonically towards those calculated with the orbital-free approach; we observe a faster convergence when the orbital-free approach includes the gradient correction. We propose a method to obtain an equation of state reproducing quantum molecular dynamics results up to high temperatures where this approach cannot be directly implemented. With the results already obtained for low-Z plasmas, the present study opens the way for reproducing the quantum molecular dynamics pressure for all elements up to high temperatures.
Fluctuation statistics of mesoscopic Bose-Einstein condensates: Reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma
Jordan, Andrew N.; Ooi, C. H. Raymond; Svidzinsky, Anatoly A.
The atom fluctuation statistics of an ideal, mesoscopic, Bose-Einstein condensate are investigated from several different perspectives. By generalizing the grand canonical analysis (applied to the canonical ensemble problem), we obtain a self-consistent equation for the mean condensate particle number that coincides with the microscopic result calculated from the laser master equation approach. For the case of a harmonic trap, we obtain an analytic expression for the condensate particle number that is very accurate at all temperatures, when compared with numerical canonical ensemble results. Applying a similar generalized grand canonical treatment to the variance, we obtain an accurate result only below the critical temperature. Analytic results are found for all higher moments of the fluctuation distribution by employing the stochastic path integral formalism, with excellent accuracy. We further discuss a hybrid treatment, which combines the master equation and stochastic path integral analysis with results obtained based on the canonical ensemble quasiparticle formalism [Kocharovsky et al., Phys. Rev. A 61, 053606 (2000)], producing essentially perfect agreement with numerical simulation at all temperatures.
The CPA Equation of State and an Activity Coefficient Model for Accurate Molar Enthalpy Calculations of Mixtures with Carbon Dioxide and Water/Brine
Myint, P. C.; Hao, Y.; Firoozabadi, A.
Thermodynamic property calculations of mixtures containing carbon dioxide (CO2) and water, including brines, are essential in theoretical models of many natural and industrial processes. The properties of greatest practical interest are density, solubility, and enthalpy. Many models for density and solubility calculations have been presented in the literature, but there exists only one study, by Spycher and Pruess, that has compared theoretical molar enthalpy predictions with experimental data [1]. In this report, we recommend two different models for enthalpy calculations: the CPA equation of state by Li and Firoozabadi [2], and the CO2 activity coefficient model by Duan and Sun [3]. We show that the CPA equation of state, which has been demonstrated to provide good agreement with density and solubility data, also accurately calculates molar enthalpies of pure CO2, pure water, and both CO2-rich and aqueous (H2O-rich) mixtures of the two species. It is applicable to a wider range of conditions than the Spycher and Pruess model. In aqueous sodium chloride (NaCl) mixtures, we show that Duan and Sun�s model yields accurate results for the partial molar enthalpy of CO2. It can be combined with another model for the brine enthalpy to calculate the molar enthalpy of H2O-CO2-NaCl mixtures. We conclude by explaining how the CPA equation of state may be modified to further improve agreement with experiments. This generalized CPA is the basis of our future work on this topic.
Plasma column displacement measurements by modified Rogowski sine-coil and Biot-Savart/magnetic flux equation solution on IR-T1 tokamak
Razavi, M.; Mollai, M.; Khorshid, P.; Nedzelskiy, I.; Ghoranneviss, M.
The modified Rogowski sine-coil (MRSC) has been designed and implemented for the plasma column horizontal displacement measurements on small IR-T1 tokamak. MRSC operation has been examined on test assembly and tokamak. Obtained results show high sensitivity to the plasma column horizontal displacement and negligible sensitivity to the vertical displacement; linearity in wide, {+-}0.1 m, range of the displacements; and excellent, 1.5%, agreement with the results of numerical solution of Biot-Savart and magnetic flux equations.
Solving Faddeev equations for a bound state and a continuous spectrum of a three-nucleon system by the method of K-harmonic expansions
Kovalchuk, V. I.; Kozlovsky, I. V.; Tartakovsky, V. K.
A method for solving Faddeev equations in configuration space for a bound state and a continuous spectrum of the system of three nucleons was developed on the basis of expansions in K harmonics. Coulomb interaction and particle spins were not taken into account in this study. The method in question was used to describe the triton bound state and differential cross sections for neutron-deuteron scattering at subthreshold incident-neutron energies. The Volkov, Malfliet-Tjon, and Eikemeier-Hackenbroich local nucleon-nucleon potentials were employed in the present calculations.
Higher order nonlinear equations for the dust-acoustic waves in a dusty plasma with two temperature-ions and nonextensive electrons
Emamuddin, M.; Yasmin, S.; Mamun, A. A.
The nonlinear propagation of dust-acoustic waves in a dusty plasma whose constituents are negatively charged dust, Maxwellian ions with two distinct temperatures, and electrons following q-nonextensive distribution, is investigated by deriving a number of nonlinear equations, namely, the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV), and the Gardner equations. The basic characteristics of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two temperature ions and electron nonextensivity on the basic features of DA K-dV, mK-dV, and Gardner solitons are also examined. It has been observed that the DA Gardner solitons exhibit negative (positive) solitons for q
q{sub c}) (where q{sub c} is the critical value of the nonextensive parameter q). The implications of our results in understanding the localized nonlinear electrostatic perturbations existing in stellar polytropes, quark-gluon plasma, protoneutron stars, etc. (where ions with different temperatures and nonextensive electrons exist) are also briefly addressed.
Nonlinear structures of the Korteweg-de Vries and modified Korteweg-de Vries equations in non-Maxwellian electron-positron-ion plasma: Solitons collision and rogue waves
El-Tantawy, S. A.; Moslem, W. M.
Solitons (small-amplitude long-lived waves) collision and rogue waves (large-amplitude short-lived waves) in non-Maxwellian electron-positron-ion plasma have been investigated. For the solitons collision, the extended Poincar�-Lighthill-Kuo perturbation method is used to derive the coupled Korteweg-de Vries (KdV) equations with the quadratic nonlinearities and their corresponding phase shifts. The calculations reveal that both positive and negative polarity solitons can propagate in the present model. At critical value of plasma parameters, the coefficients of the quadratic nonlinearities disappear. Therefore, the coupled modified KdV (mKdV) equations with cubic nonlinearities and their corresponding phase shifts have been derived. The effects of the electron-to-positron temperature ratio, the ion-to-electron temperature ratio, the positron-to-ion concentration, and the nonextensive parameter on the colliding solitons profiles and their corresponding phase shifts are examined. Moreover, generation of ion-acoustic rogue waves from small-amplitude initial perturbations in plasmas is studied in the framework of the mKdV equation. The properties of the ion-acoustic rogue waves are examined within a nonlinear Schr�dinger equation (NLSE) that has been derived from the mKdV equation. The dependence of the rogue wave profile on the relevant physical parameters has been investigated. Furthermore, it is found that the NLSE that has been derived from the KdV equation cannot support the propagation of rogue waves.
Solutions of the bound-state Faddeev-Yakubovsky equations in three dimensions by using NN and 3N potential models
Hadizadeh, M. R.; Tomio, Lauro; Bayegan, S.
A recently developed three-dimensional approach (without partial-wave decomposition) is considered to investigate solutions of Faddeev-Yakubovsky integral equations in momentum space for three- and four-body bound states, with the inclusion of three-body forces. In the calculations of the binding energies, spin-dependent nucleon-nucleon (NN) potential models [soft-core potential S3, Malfliet-Tjon (MT) I-III, Yamaguchi-type potentials (YS), and P{sub 5.5}-model of Gibson-Lehman (P{sub 55}GL)] are considered along with the scalar two-meson exchange three-body potential. The presently reported results agree well with the ones obtained by other techniques, demonstrating the advantage of an approach in which the formalism is much more simplified and easy to manage for direct computation.
Long-time solution of the time-dependent Schroedinger equation for an atom in an electromagnetic field using complex coordinate contours
Tao, Liang; Vanroose, Wim; Reps, Brian; Rescigno, Thomas N.; McCurdy, C. William
We demonstrate that exterior complex scaling (ECS) can be used to impose outgoing wave boundary conditions exactly on solutions of the time-dependent Schrodinger equation for atoms in intense electromagnetic pulses using finite grid methods. The procedure is formally exact when applied in the appropriate gauge and is demonstrated in a calculation of high harmonic generation in which multiphoton resonances are seen for long pulse durations. However, we also demonstrate that while the application of ECS in this way is formally exact, numerical error can appear for long time propagations that can only be controlled by extending the finite grid. A mathematical analysis of the origins of that numerical error, illustrated with an analytically solvable model, is also given.
Long-time solution of the time-dependent Schroedinger equation for an atom in an electromagnetic field using complex coordinate contours
Tao Liang; Rescigno, T. N.; Vanroose, W.; Reps, B.; McCurdy, C. W.
We demonstrate that exterior complex scaling (ECS) can be used to impose outgoing wave boundary conditions exactly on solutions of the time-dependent Schroedinger equation for atoms in intense electromagnetic pulses using finite grid methods. The procedure is formally exact when applied in the appropriate gauge and is demonstrated in a calculation of high-harmonic generation in which multiphoton resonances are seen for long pulse durations. However, we also demonstrate that while the application of ECS in this way is formally exact, numerical error can appear for long-time propagations that can only be controlled by extending the finite grid. A mathematical analysis of the origins of that numerical error, illustrated with an analytically solvable model, is also given.
Kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations
Davidson, R.C.; Chen, C.
A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B{sup sol}({rvec x}) is developed. The analysis is carried out for a thin beam with characteristic beam radius r{sub b} {much_lt} S, and directed axial momentum {gamma}{sub b}m{beta}{sub b}c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f{sub b}({rvec x},{rvec p},t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B{sub z}(z) = B{sub 0} = const. and for the case of a periodic solenoidal focusing field B{sub z}(z + S) = B{sub z}(z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field {rvec B}{sup sol}({rvec x}) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.
Dose equations for shift-variant CT acquisition modes using variable pitch, tube current, and aperture, and the meaning of their associated CTDI{sub vol}
Dixon, Robert L.; Boone, John M.; Kraft, Robert A.
Purpose: With the increasing clinical use of shift-variant CT protocols involving tube current modulation (TCM), variable pitch or pitch modulation (PM), and variable aperture a(t), the interpretation of the scanner-reported CTDI{sub vol} is called into question. This was addressed for TCM in their previous paper published by Dixon and Boone [Med. Phys. 40, 111920 (14pp.) (2013)] and is extended to PM and concurrent TCM/PM as well as variable aperture in this work. Methods: Rigorous convolution equations are derived to describe the accumulated dose distributions for TCM, PM, and concurrent TCM/PM. A comparison with scanner-reported CTDI{sub vol} formulae clearly identifies the source of their differences with the traditional CTDI{sub vol}. Dose distribution simulations using the convolution are provided for a variety of TCM and PM scenarios including a helical shuttle used for perfusion studies (as well as constant mA)�all having the same scanner-reported CTDI{sub vol}. These new convolution simulations for TCM are validated by comparison with their previous discrete summations. Results: These equations show that PM is equivalent to TCM if the pitch variation p(z) is proportional to 1/i(z), where i(z) is the local tube current. The simulations show that the local dose at z depends only weakly on the local tube current i(z) or local pitch p(z) due to scatter from all other locations along z, and that the �local CTDI{sub vol}(z)� or �CTDI{sub vol} per slice� do not represent a local dose but rather only a relative i(z) or p(z). The CTDI-paradigm does not apply to shift-variant techniques and the scanner-reported CTDI{sub vol} for the same lacks physical significance and relevance. Conclusions: While the traditional CTDI{sub vol} at constant tube current and pitch conveys useful information (the peak dose at the center of the scan length), CTDI{sub vol} for shift-variant techniques (TCM or PM) conveys no useful information about the associated dose distribution it purportedly represents. On the other hand, the total energy absorbed E (�integral dose�) as well as its surrogate DLP remain robust (invariant) with respect to shift-variance, depending only on the total mAs = ?i?t{sub 0} accumulated during the total beam-on time t{sub 0} and aperture a, where ?i? is the average current.
Ab initio molecular orbital-configuration interaction based quantum master equation (MOQME) approach to the dynamic first hyperpolarizabilities of asymmetric π-conjugated systems
Kishi, Ryohei; Fujii, Hiroaki; Minami, Takuya; Shigeta, Yasuteru; Nakano, Masayoshi
In this study, we apply the ab initio molecular orbital - configuration interaction based quantum master equation (MOQME) approach to the calculation and analysis of the dynamic first hyperpolarizabilities (β) of asymmetric π-conjugated molecules. In this approach, we construct the excited state models by the ab initio configuration interaction singles method. Then, time evolutions of system reduced density matrix ρ(t) and system polarization p(t) are calculated by the QME approach. Dynamic β in the second harmonic generation is calculated based on the nonperturbative definition of nonlinear optical susceptibility, using the frequency domain system polarization p(ω). Spatial contributions of electrons to β are analyzed based on the dynamic hyperpolarizability density map, which visualizes the second-order response of charge density oscillating with a frequency of 2ω. We apply the present method to the calculation of the dynamic β of a series of donor/acceptor substituted polyene oligomers, and then discuss the applicability of the MOQME method to the calculation and analysis of dynamic NLO properties of molecular systems.
Understanding composite explosive energetics: 4. Reactive flow modeling of aluminum reaction kinetics in PETN and TNT using normalized product equation of state
Tao, W.C.; Tarver, C.M.; Kury, J.W.; Lee, C.G.; Ornellas, D.L.
Using Fabry-Perot interferometry techniques, we have determined the early time rate of energy release from detonating PETN and TNT explosives filled with 5 to 20 wt % of either 5 {mu}m or 18 {mu}m spherical aluminum with the detonation products, and calculate the extent of reaction at 1--3 {mu}s after the detonation. All of the metal in PETN formulations filled with 5 wt % and 10 wt % of either 5 {mu}m or 18 {mu}m aluminum reacted within 1.5 {mu}s, resulting in an increase of 18--22% in energy compared to pure PETN. For TNT formulations, between 5 to 10 wt % aluminum reacts completely with the same timeframe. A reactive flow hydrodynamic code model based on the Zeldovich-von Neumann-Doring (ZND) description of the reaction zone and subsequent reaction product expansion (Taylor wave) is used to address the reaction rate of the aluminum particles with detonation product gases. The detonation product JWL equation of state is derived from that of pure PETN using a parametric normalization methodology.
Equations of state of anhydrous AlF{sub 3} and AlI{sub 3}: Modeling of extreme condition halide chemistry
Stavrou, Elissaios; Zaug, Joseph M. Bastea, Sorin; Crowhurst, Jonathan C.; Radousky, Harry B.; Armstrong, Michael R.; Roberts, Sarah K.; Plaue, Jonathan W.; Goncharov, Alexander F.
Pressure dependent angle-dispersive x-ray powder diffraction measurements of alpha-phase aluminum trifluoride (?-AlF{sub 3}) and separately, aluminum triiodide (AlI{sub 3}) were conducted using a diamond-anvil cell. Results at 295 K extend to 50 GPa. The equations of state of AlF{sub 3} and AlI{sub 3} were determined through refinements of collected x-ray diffraction patterns. The respective bulk moduli and corresponding pressure derivatives are reported for multiple orders of the Birch-Murnaghan (B-M), finite-strain (F-f), and higher pressure finite-strain (G-g) EOS analysis models. Aluminum trifluoride exhibits an apparent isostructural phase transition at approximately 12 GPa. Aluminum triiodide also undergoes a second-order atomic rearrangement: applied stress transformed a monoclinically distorted face centered cubic (fcc) structure into a standard fcc structural arrangement of iodine atoms. Results from semi-empirical thermochemical computations of energetic materials formulated with fluorine containing reactants were obtained with the aim of predicting the yield of halogenated products.
Deaton, M. Brett; Duez, Matthew D.; Foucart, Francois; O'Connor, Evan; Ott, Christian D.; Scheel, Mark A.; Szilagyi, Bela; Kidder, Lawrence E.; Muhlberger, Curran D. E-mail: firstname.lastname@example.com
Neutrino emission significantly affects the evolution of the accretion tori formed in black hole-neutron star mergers. It removes energy from the disk, alters its composition, and provides a potential power source for a gamma-ray burst. To study these effects, simulations in general relativity with a hot microphysical equation of state (EOS) and neutrino feedback are needed. We present the first such simulation, using a neutrino leakage scheme for cooling to capture the most essential effects and considering a moderate mass (1.4 M{sub ?} neutron star, 5.6 M{sub ?} black hole), high-spin (black hole J/M {sup 2} = 0.9) system with the K{sub 0} = 220 MeV Lattimer-Swesty EOS. We find that about 0.08 M{sub ?} of nuclear matter is ejected from the system, while another 0.3 M{sub ?} forms a hot, compact accretion disk. The primary effects of the escaping neutrinos are (1) to make the disk much denser and more compact, (2) to cause the average electron fraction Y{sub e} of the disk to rise to about 0.2 and then gradually decrease again, and (3) to gradually cool the disk. The disk is initially hot (T ? 6 MeV) and luminous in neutrinos (L{sub ?} ? 10{sup 54} erg s{sup �1}), but the neutrino luminosity decreases by an order of magnitude over 50 ms of post-merger evolution.
AB INITIO EQUATIONS OF STATE FOR HYDROGEN (H-REOS.3) AND HELIUM (He-REOS.3) AND THEIR IMPLICATIONS FOR THE INTERIOR OF BROWN DWARFS
Becker, Andreas; Lorenzen, Winfried; Sch�ttler, Manuel; Redmer, Ronald; Fortney, Jonathan J.; Nettelmann, Nadine
We present new equations of state (EOSs) for hydrogen and helium covering a wide range of temperatures from 60 K to 10{sup 7} K and densities from 10{sup �10} g cm{sup �3} to 10{sup 3} g cm{sup �3}. They include an extended set of ab initio EOS data for the strongly correlated quantum regime with an accurate connection to data derived from other approaches for the neighboring regions. We compare linear mixing isotherms based on our EOS tables with available real mixture data. A first important astrophysical application of this new EOS data is the calculation of interior models for Jupiter and comparison with recent results. Second, mass-radius relations are calculated for Brown Dwarfs (BDs) which we compare with predictions derived from the widely used EOS of Saumon, Chabrier, and van Horn. Furthermore, we calculate interior models for typical BDs with different masses, namely, Corot-3b, Gliese-229b, and Corot-15b, and the giant planet KOI-889b. The predictions for the central pressures and densities differ by up to 10% dependent on the EOS used. Our EOS tables are made available in the supplemental material of this paper.
Thermal equation of state of solid naphthalene to 13 GPa and 773 K: In situ X-ray diffraction study and first principles calculations
Likhacheva, Anna Y.; Rashchenko, Sergey V.; Chanyshev, Artem D.; Litasov, Konstantin D.; Department of Geology and Geophysics, Novosibirsk State University, Novosibirsk 630090 ; Inerbaev, Talgat M.; Kilin, Dmitry S.
In a wide range of P-T conditions, such fundamental characteristics as compressibility and thermoelastic properties remain unknown for most classes of organic compounds. Here we attempt to clarify this issue by the example of naphthalene as a model representative of polycyclic aromatic hydrocarbons (PAHs). The elastic behavior of solid naphthalene was studied by in situ synchrotron powder X-ray diffraction up to 13 GPa and 773 K and first principles computations to 20 GPa and 773 K. Fitting of the P-V experimental data to Vinet equation of state yielded T 0 = 8.4(3) GPa and T' = 7.2 (3) at V0 = 361 �(3), whereas the thermal expansion coefficient was found to be extremely low at P > 3 GPa (about 10(-5) K(-1)), in agreement with theoretical estimation. Such a diminishing of thermal effects with the pressure increase clearly demonstrates a specific feature of the high-pressure behavior of molecular crystals like PAHs, associated with a low energy of intermolecular interactions.
The equation of state of 5-nitro-2,4-dihydro-1,2,4,-triazol-3-one determined via in-situ optical microscopy and interferometry measurements
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Stavrou, Elissaios; Zaug, Joseph M.; Bastea, Sorin; Crowhurst, Jonathan C.
Quasi-hydrostatic high-pressure equations of state (EOS) are typically determined, for crystalline solids, by measuring unit-cell volumes using x-ray diffraction (XRD) techniques. However, when characterizing low-symmetry materials with large unit cells, conventional XRD approaches may become problematic. To overcome this issue, we examined the utility of a "direct" approach toward determining high pressure material volume by measuring surface area and sample thickness using optical microscopy and interferometry (OMI) respectively. We have validated this experimental approach by comparing results obtained for TATB (2,4,6-triamino-1,3,5-trinitrobenzene) with an EOS determined from synchrotron XRD measurements; and, a good match is observed. We have measured the highmore » pressure EOS of 5-nitro-2,4-dihydro-1,2,4-triazol-3-one (α-NTO) up to 33 GPa. No high-pressure XRD EOS data have been published on α-NTO, probably due to its complex crystal structure. Furthermore, the results of this study suggest that OMI is a reliable and versatile alternative for determining EOSs, especially when conventional methodologies are impractical.« less
Equation of state and heavy-quark free energy at finite temperature and density in two flavor lattice QCD with Wilson quark action
Ejiri, S.; Maezawa, Y.; Ukita, N.; Aoki, S.; Hatsuda, T.; Ishii, N.; Kanaya, K.; Umeda, T.
We study the equation of state at finite temperature and density in two-flavor QCD with the renormalization group improved gluon action and the clover-improved Wilson quark action on a 16{sup 3}x4 lattice. Along the lines of constant physics at m{sub PS}/m{sub V}=0.65 and 0.80, we compute the second and forth derivatives of the grand canonical partition function with respect to the quark chemical potential {mu}{sub q}=({mu}{sub u}+{mu}{sub d})/2 and the isospin chemical potential {mu}{sub I}=({mu}{sub u}-{mu}{sub d})/2 at vanishing chemical potentials, and study the behaviors of thermodynamic quantities at finite {mu}{sub q} using these derivatives for the case {mu}{sub I}=0. In particular, we study density fluctuations at nonezero temperature and density by calculating the quark number and isospin susceptibilities and their derivatives with respect to {mu}{sub q}. To suppress statistical fluctuations, we also examine new techniques applicable at low densities. We find a large enhancement in the fluctuation of the quark number when the density increased near the pseudocritical temperature, suggesting a critical point at finite {mu}{sub q} terminating the first order transition line between hadronic and quark-gluon-plasma phases. This result agrees with the previous results using staggered-type quark actions qualitatively. Furthermore, we study heavy-quark free energies and Debye screening masses at finite density by measuring the first and second derivatives of these quantities for various color channels of heavy quark-quark and quark-antiquark pairs. The results suggest that, to the leading order of {mu}{sub q}, the interaction between two quarks becomes stronger at finite densities, while that between quark and antiquark becomes weaker.
Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations
Dahms, Rainer N.
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of previous temperature-dependent expressions, remains well-defined at supercritical temperatures, and is fully suitable for calculations of general multi-component two-phase interfaces.
Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Dahms, Rainer N.
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phasemore » components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of previous temperature-dependent expressions, remains well-defined at supercritical temperatures, and is fully suitable for calculations of general multi-component two-phase interfaces.« less
The high pressure structure and equation of state of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) up to 20 GPa: X-ray diffraction measurements and first principles molecular dynamics simulations
Stavou, Elissaios; Manaa, M. Riad; Zaug, Joseph M.; Kuo, I-Feng W.; Pagoria, Philip F.; Crowhurst, Jonathan C.; Armstrong, Michael R.; Kalkan, Bora
Recent theoretical studies of 2,6-diamino-3,5-dinitropyrazine-1-oxide (C4H4N6O5 Lawrence Livermore Molecule No. 105, LLM-105) report unreacted high pressure equations of state that include several structural phase transitions, between 8 and 50 GPa, while one published experimental study reports equation of state (EOS) data up to a pressure of 6 GPa with no observed transition. Here we report the results of a synchrotron-based X-ray diffraction study and also ambient temperature isobaric-isothermal atomistic molecular dynamics simulations of LLM-105 up to 20 GPa. We find that the ambient pressure phase remains stable up to 20 GPa; there is no indication of a pressure induced phase transition. We do find a prominent decrease in b-axis compressibility starting at approximately 13 GPa and attribute the stiffening to a critical length where inter-sheet distance becomes similar to the intermolecular distance within individual sheets. The ambient temperature isothermal equation of state was determined through refinements of measured X-ray diffraction patterns. The pressure-volume data were fit using various EOS models to yield bulk moduli with corresponding pressure derivatives. As a result, we find very good agreement between the experimental and theoretically derived EOS.
The high pressure structure and equation of state of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) up to 20 GPa: X-ray diffraction measurements and first principles molecular dynamics simulations
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Stavou, Elissaios; Manaa, M. Riad; Zaug, Joseph M.; Kuo, I-Feng W.; Pagoria, Philip F.; Crowhurst, Jonathan C.; Armstrong, Michael R.; Kalkan, Bora
Recent theoretical studies of 2,6-diamino-3,5-dinitropyrazine-1-oxide (C4H4N6O5 Lawrence Livermore Molecule No. 105, LLM-105) report unreacted high pressure equations of state that include several structural phase transitions, between 8 and 50 GPa, while one published experimental study reports equation of state (EOS) data up to a pressure of 6 GPa with no observed transition. Here we report the results of a synchrotron-based X-ray diffraction study and also ambient temperature isobaric-isothermal atomistic molecular dynamics simulations of LLM-105 up to 20 GPa. We find that the ambient pressure phase remains stable up to 20 GPa; there is no indication of a pressure induced phasemore » transition. We do find a prominent decrease in b-axis compressibility starting at approximately 13 GPa and attribute the stiffening to a critical length where inter-sheet distance becomes similar to the intermolecular distance within individual sheets. The ambient temperature isothermal equation of state was determined through refinements of measured X-ray diffraction patterns. The pressure-volume data were fit using various EOS models to yield bulk moduli with corresponding pressure derivatives. As a result, we find very good agreement between the experimental and theoretically derived EOS.« less
STOMP Subsurface Transport Over Multiple Phases Version 1.0 Addendum: ECKEChem Equilibrium-Conservation-Kinetic Equation Chemistry and Reactive Transport
White, Mark D.; McGrail, B. Peter
Geologic sequestration is currently being practiced and scientifically evaluated as a critical component in a broad strategy, comprising new practices and technologies, for mitigating global climate change due to anthropogenic emissions of CO2. Demonstrating that geologic sequestration of CO2 is safe and effective, and gaining public acceptance of sequestration technologies are critically important in meeting these global climate change challenges. Monitored field-scale demonstrations of geologic sequestration of carbon dioxide will contribute greatly toward growing trust and confidence in the technology; however, pilot demonstrations ultimately will not be the norm for new geological sequestration deployments. Instead, scientists, engineers, regulators, and ultimately the public will rely on numerical simulations to predict the performance of geologic repositories for carbon dioxide sequestration. The U.S. Department of Energy (DOE), through the National Environmental Technology Laboratory (NETL) has requested the development of numerical simulation capabilities for quantifying the permanent storage capacity, leakage rates, and public risks associated with geologic sequestration of CO2. In conjunction with this request. the Zero Emissions Research and Technology Center (ZERT) has been created with the mission of conducting basic and applied research that support the development of new technologies for minimizing emissions of anthropogenic carbon dioxide and other greenhouse gases that impact global climate change. As a member of the ZERT Center, the Pacific Northwest National Laboratory (PNNL) is conducting research associated with geologic sequestration of CO2 that includes the thermochemistry of supercritical CO2-brine mixtures, mineralization kinetics, leakage and microseepage of CO2, and new materials for CO2 capture. In addition to these research activities, PNNL is developing new scalable CO2 reservoir simulation capabilities for its multifluid subsurface flow and transport simulator, STOMP (Subsurface Transport Over Multiple Phases). Prior to these code development activities, the STOMP simulator included sequential and scalable implementations for numerically simulating the injection of supercritical CO2 into deep saline aquifers. Additionally, the sequential implementations included operational modes that considered nonisothermal conditions and kinetic dissolution of CO2 into the saline aqueous phase. This addendum documents the advancement of these numerical simulation capabilities to include reactive transport in the STOMP simulator through the inclusion of the recently PNNL developed batch geochemistry solution module ECKEChem (Equilibrium-Conservation-Kinetic Equation Chemistry). Potential geologic reservoirs for sequestering CO2 include deep saline aquifers, hydrate-bearing formations, depleted or partially depleted natural gas and petroleum reservoirs, and coal beds. The mechanisms for sequestering carbon dioxide in geologic reservoirs include physical trapping, dissolution in the reservoir fluids, hydraulic trapping (hysteretic entrapment of nonwetting fluids), and chemical reaction. This document and the associated code development and verification work are concerned with the chemistry of injecting CO2 into geologic reservoirs. As geologic sequestration of CO2 via chemical reaction, namely precipitation reactions, are most dominate in deep saline aquifers, the principal focus of this document is the numerical simulation of CO2 injection, migration, and geochemical reaction in deep saline aquifers. The ECKEChem batch chemistry module was developed in a fashion that would allow its implementation into all operational modes of the STOMP simulator, making it a more versatile chemistry component. Additionally, this approach allows for verification of the ECKEChem module against more classical reactive transport problems involving aqueous systems.
Separability of massive field equations for spin-0 and spin-1/2 charged particles in the general nonextremal rotating charged black hole spacetimes in minimal five-dimensional gauged supergravity
Wu Shuangqing
We continue to investigate the separability of massive field equations for spin-0 and spin-1/2 charged particles in the general, nonextremal, rotating, charged, Chong-Cvetic-Lue-Pope black holes with two independent angular momenta and a nonzero cosmological constant in minimal D=5 gauged supergravity theory. We show that the complex Klein-Gordon equation and the modified Dirac equation with the inclusion of an extra counterterm can be separated by variables into purely radial and purely angular parts in this general Einstein-Maxwell-Chern-Simons background spacetime. A second-order symmetry operator that commutes with the complex Laplacian operator is constructed from the separated solutions and expressed compactly in terms of a rank-2 Staeckel-Killing tensor which admits a simple diagonal form in the chosen pentad one-forms so that it can be understood as the square of a rank-3 totally antisymmetric tensor. A first-order symmetry operator that commutes with the modified Dirac operator is expressed in terms of a rank-3 generalized Killing-Yano tensor and its covariant derivative. The Hodge dual of this generalized Killing-Yano tensor is a generalized principal conformal Killing-Yano tensor of rank-2, which can generate a 'tower' of generalized (conformal) Killing-Yano and Staeckel-Killing tensors that are responsible for the whole hidden symmetries of this general, rotating, charged, Kerr-anti-de Sitter black hole geometry. In addition, the first laws of black hole thermodynamics have been generalized to the case that the cosmological constant can be viewed as a thermodynamical variable.
NREL Success Stories - SkyFuel Partnership Reflects Bright Future
Jorgensen, Gary; Gee, Randy
NREL Scientists and SkyFuel share a story about how their partnership has resulted in a revolutionary concentrating solar power technology ReflecTech Mirror Film.
Derivation of an Applied Nonlinear Schroedinger Equation.
Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens; Rambo, Patrick K.; Karelitz, David B.
We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release
Renormalization group functional equations (Journal Article)...
Office of Scientific and Technical Information (OSTI)
Publication Date: 2011-03-15 OSTI Identifier: 21537581 Resource Type: Journal Article Resource Relation: Journal Name: Physical Review. D, Particles Fields; Journal Volume: 83; ...
TH-E-BRE-01: A 3D Solver of Linear Boltzmann Transport Equation Based On a New Angular Discretization Method with Positivity for Photon Dose Calculation Benchmarked with Geant4
Hong, X; Gao, H
Purpose: The Linear Boltzmann Transport Equation (LBTE) solved through statistical Monte Carlo (MC) method provides the accurate dose calculation in radiotherapy. This work is to investigate the alternative way for accurately solving LBTE using deterministic numerical method due to its possible advantage in computational speed from MC. Methods: Instead of using traditional spherical harmonics to approximate angular scattering kernel, our deterministic numerical method directly computes angular scattering weights, based on a new angular discretization method that utilizes linear finite element method on the local triangulation of unit angular sphere. As a Result, our angular discretization method has the unique advantage in positivity, i.e., to maintain all scattering weights nonnegative all the time, which is physically correct. Moreover, our method is local in angular space, and therefore handles the anisotropic scattering well, such as the forward-peaking scattering. To be compatible with image-guided radiotherapy, the spatial variables are discretized on the structured grid with the standard diamond scheme. After discretization, the improved sourceiteration method is utilized for solving the linear system without saving the linear system to memory. The accuracy of our 3D solver is validated using analytic solutions and benchmarked with Geant4, a popular MC solver. Results: The differences between Geant4 solutions and our solutions were less than 1.5% for various testing cases that mimic the practical cases. More details are available in the supporting document. Conclusion: We have developed a 3D LBTE solver based on a new angular discretization method that guarantees the positivity of scattering weights for physical correctness, and it has been benchmarked with Geant4 for photon dose calculation.
Strategic Petroleum Reserve equation of state model development...
Office of Scientific and Technical Information (OSTI)
phase behavior modeling within the U.S. Strategic Petroleum Reserve vapor pressure program during the period 2004-2009. Improvements in quality control on phase behavior ...
Detonation equation of state at LLNL, 1995. Revision 3
Souers, P.C.; Wu, B.; Haselman, L.C. Jr.
JWL`s and 1-D Look-up tables are shown to work for ``one-track`` experiments like cylinder shots and the expanding sphere. They fail for ``many-track`` experiments like the compressed sphere. As long as the one-track experiment has dimensions larger than the explosive`s reaction zone and the explosive is near-ideal, a general JWL with R{sub 1} = 4.5 and R{sub 2} = 1.5 can be constructed, with both {omega} and E{sub o} being calculated from thermochemical codes. These general JWL`s allow comparison between various explosives plus recalculation of the JWL for different densities. The Bigplate experiment complements the cylinder test by providing continuous oblique angles of shock incidence from 0{degrees} to 70{degrees}. Explosive reaction zone lengths are determined from metal plate thicknesses, extrapolated run-to-detonation distances, radius size effects and detonation front curvature. Simple theories of the cylinder test, Bigplate, the cylinder size effect and detonation front curvature are given. The detonation front lag at the cylinder edge is shown to be proportional to the half-power of the reaction zone length. By calibrating for wall blow-out, a full set of reaction zone lengths from PETN to ANFO are obtained. The 1800--2100 K freezing effect is shown to be caused by rapid cooling of the product gases. Compiled comparative data for about 80 explosives is listed. Ten Chapters plus an Appendix.
On computing ``accurate'' derivatives of Equation-of-State variables
Shestakov, A. I.
We analyze a log-log interpolant for 2D EOS lookups, where the EOS independent variables are, say, T and ρ. If the data f (Ti, ρj) are in the form of a power law, even locally, the interpolant is exact.
Disastrous Equations J. Douglas Wright Drexel University Department
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
J. Douglas Wright Drexel University Department of Mathematics Science on Saturday 1 ... from shore... 16 Mathematics has played a crucial role in our understanding of tsunami. ...
Renormalization group equations in a model of generalized hidden...
Office of Scientific and Technical Information (OSTI)
10.1103PhysRevD.73.036004; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA) Country of Publication: United States Language: ...
NREL Compares State Solar Policies to Determine Equation for...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Non-policy issues that have implications for a solar market, such as the amount of sunlight available for potential solar generation, community interest in renewable energy, and ...
A Simple Empirical Equation to Calculate Cloud Optical Thickness...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
and high values of this quantity. With the above evidence in mind, we conclude that the empirical method described here is a useful tool for estimating cloud optical thickness at...
Majorana equations and the rest mass of neutrinos
von Borzeszkowski, H.; Treder, H.
As is well known, the law of parity conservation does not hold in weak interactions. This type of asymmetry created a number of theoretical problems which were solved, first of all, by a new understanding of the features of neutrinos and their role in weak interactions. These solutions were based, however, essentially on the handedness (chirality) of neutrinos which is closely related to their vanishing rest mass. The thesis of neutrinos with nonvanishing rest mass, newly considered in the literature, therefore requires a rediscussion of the early arguments concerning the relation between the neutrino theory and some weak interaction essentials. When one does this, as in the present paper, it is noted that neutrinos with rest mass lead to some difficulties, in particular to a violation of T invariance.
ARM - Lesson Plans: Why is it Hotter at the Equator?
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Black construction paper (one sheet per group of students) Stapler Several books to prop thermometers Metric ruler Scissors Graph paper Small ruler Pencil Important Points to...
Anisotropic Elastic Resonance Scattering model for the Neutron Transport equation
Mohamed Ouisloumen; Abderrafi M. Ougouag; Shadi Z. Ghrayeb
The resonance scattering transfer cross-section has been reformulated to account for anisotropic scattering in the center-of-mass of the neutron-nucleus system. The main innovation over previous implementations is the relaxation of the ubiquitous assumption of isotropic scattering in the center-of-mass and the actual effective use of scattering angle distributions from evaluated nuclear data files in the computation of the angular moments of the resonant scattering kernels. The formulas for the high order anisotropic moments in the laboratory system are also derived. A multi-group numerical formulation is derived and implemented into a module incorporated within the NJOY nuclear data processing code. An ultra-fine energy mesh cross section library was generated using these new theoretical models and then was used for fuel assembly calculations with the PARAGON lattice physics code. The results obtained indicate a strong effect of this new model on reactivity, multi-group fluxes and isotopic inventory during depletion.
Modeling Dynamic Ductility: An Equation of State for Porous Metals...
Office of Scientific and Technical Information (OSTI)
which a sector of a thin cylindrical shell is driven from the inside surface by SEMTEX high explosive (approx1 micros FWHM pressure pulse with peak pressure approx21.5 GPa). ...
An acoustic wave equation for modeling in tilted TI media
Office of Scientific and Technical Information (OSTI)
... conditions are applied on the other three boundaries of the model (Cerjan, et al, 1985). ... Kosloff, D., Kosloff, R., and Reshef, M., 1985, A nonreflecting boundary condition for ...
Modeling Dynamic Ductility: An Equation of State for Porous Metals...
Office of Scientific and Technical Information (OSTI)
for Porous Metals Enhanced heating from shock compression of a porous material can ... Physical Society Topical Conference on Shock Compression of Condensed Matter (APS...
A Reconstructed Discontinuous Galerkin Method for the Euler Equations...
Office of Scientific and Technical Information (OSTI)
(face-neighboring cells) and are compact and consistent with the underlying DG method. ... accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing ...
Quantum chaos in the Lorenz equations with symmetry breaking
Sarkar, S.; Satchell, J.S.
The role of phase diffusion for quantum chaos in the quantum-mechanical model of the laser in the Haken limit is discussed. Fractal properties of the support of the asymptotic attracting probability distribution for the system are studied.
An acoustic wave equation for modeling in tilted TI media
Office of Scientific and Technical Information (OSTI)
... In other words, a local symmetry assumption instead of a global one is more realistic. To ... The parameters and are zero in the water layer and linearly increase from 0 at the ...
Equation of state in ( 2 + 1 )-flavor QCD (Journal Article) ...
Office of Scientific and Technical Information (OSTI)
M. ; Karsch, F. ; Laermann, E. ; Levkova, L. ; Mukherjee, Swagato ; Petreczky, P. ; Schmidt, C. ; Schroeder, C. ; Soltz, R. A. ; Soeldner, W. ; Sugar, R. ; Wagner, M. ; Vranas, ...
Oxygen Catalysis: The Other Half of the Equation
Turner, J.
Artificial photosynthesis--splitting water with light--is an attractive way to make hydrogen, but what happens to the oxygen? A catalyst that aids in the efficient production of gaseous oxygen improves the viability of this approach.
Noise modeling from high-permeability shields using Kirchhoff equations
Sandin, Henrik J; Volegov, Petr L; Espy, Michelle A; Matlashov, Andrei N; Savukov, Igor M; Schultz, Larry J
Progress in the development of high-sensitivity magnetic-field measurements has stimulated interest in understanding magnetic noise of conductive materials, especially of magnetic shields (DC or rf) based on high-permeability materials and/or high-conductivity materials. For example, SQUIDs and atomic magnetometers have been used in many experiments with mu-metal shields, and additionally SQUID systems frequently have rf shielding based on thin conductive materials. Typical existing approaches to modeling noise only work with simple shield and sensor geometries while common experimental setups today consist of multiple sensor systems arbitrary shapes and complex shield geometries. With complex sensor arrays used in, for example, MEG and Ultra Low Field MRI studies the knowledge of the noise correlation between sensors is as important as the knowledge of the noise itself. This is crucial for incorporating efficient noise cancelation schemes for the system. We developed an approach that allows us to calculate the Johnson noise for any geometrically shaped shield and multiple sensor systems. The approach uses a fraction of the processing power of other approaches and with a multiple sensor system our approach not only calculates the noise for each sensor but it also calculates the noise correlation matrix between sensors. Here we will show the algorithm and examples where it can be implemented.
Equation of State Measurements by Radiography Provide Evidence...
Office of Scientific and Technical Information (OSTI)
Resource Type: Journal Article Resource Relation: Journal Name: Journal of ... PHYSICS; 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ...
Felix Bloch, Nuclear Induction, Bloch Equations, Bloch Theorem...
Office of Scientific and Technical Information (OSTI)
of the Swiss Physical Society and received honorary degrees from Grenoble University, Oxford University, the University of Jerusalem, and the University of Zurich. In 1965, he...
Green Computing Helps in Zero Energy Equation - News Feature | NREL
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Button App of the Week Part 1: Leafully Green Button App of the Week Part 1: Leafully July 12, 2012 - 3:02pm Addthis Leafully is an energy saving application that helps you understand your energy usage in meaningful terms, find ways to save and helps you track against your goals. Matthew Loveless Matthew Loveless Data Integration Specialist, Office of Public Affairs How can I participate? Check out Leafully and all the Apps for Energy winners. This is the first in a series highlighting the
Notes on the Lumped Backward Master Equation for the Neutron...
Office of Scientific and Technical Information (OSTI)
Notes on the Lumped Backward Master Equation for the Neutron...
Office of Scientific and Technical Information (OSTI)
with a knowledge of low order statistical averages (variance, correlation), provides an incomplete and very unsatisfactory description of the state of the neutron population. ...
Webinar: Fuzzy Mud and the Future of Alternative Fuels | Argonne National
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Laboratory Webinar: Fuzzy Mud and the Future of Alternative Fuels Share Browse By - Any - Energy -Energy efficiency --Vehicles ---Alternative fuels ---Automotive engineering ---Diesel ---Electric drive technology ---Hybrid & electric vehicles ---Hydrogen & fuel cells ---Internal combustion ---Powertrain research --Building design ---Construction --Manufacturing -Energy sources --Renewable energy ---Bioenergy ---Solar energy --Fossil fuels ---Natural Gas --Nuclear energy ---Nuclear
Equation of state and high-pressure/high-temperature phase diagram of
Office of Scientific and Technical Information (OSTI)
magnesium (Journal Article) | SciTech Connect W. ; MacLeod, S.G. ; Cynn, H. ; Errandonea, D. ; Evans, W.J. ; Proctor, J.E. ; Meng, Y. ; McMahon, M.I. [1] ; Edinburgh) [2] ; Valencia) [2] ; LLNL) [2] ; CIW) [2] ; ICL) [2] + Show Author Affiliations (RCaH) ( Publication Date: 2014-11-20 OSTI Identifier: 1162316 Resource Type: Journal Article Resource Relation: Journal Name: Phys. Rev. B; Journal Volume: 90; Journal Issue: (13) ; 10, 2014 Research Org: Advanced Photon Source (APS), Argonne
Equation of state and high-pressure/high-temperature phase diagram of
Office of Scientific and Technical Information (OSTI)
magnesium (Journal Article) | SciTech Connect W. ; MacLeod, S. G. ; Cynn, H. ; Errandonea, D. ; Evans, W. J. ; Proctor, J. E. ; Meng, Y. ; McMahon, M. I. Publication Date: 2014-10-20 OSTI Identifier: 1181305 Grant/Contract Number: AC52-07NA27344; FG02-99ER45775; NA0001974; AC02-06CH11357; W-7405-Eng-48 Type: Publisher's Accepted Manuscript Journal Name: Physical Review B Additional Journal Information: Journal Volume: 90; Journal Issue: 13; Journal ID: ISSN 1098-0121 Publisher: American
Pygmy Dipole Strength in Exotic Nuclei and the Equation of State
Klimkiewicz, A.; Adrich, P.; Paar, N.; Vretenar, D.; Fallot, M.; Boretzky, K.; Aksouh, F.; Chatillon, A.; Pramanik, U. Datta; Emling, H.; Ershova, O.; Geissel, H.; Gorska, M.; Heil, M.; Hellstroem, M.; Jones, K. L.; Kurz, N.; Litvinov, Y.; Mahata, K.; Simon, H.
A concentration of dipole strength at energies below the giant dipole resonance was observed in neutron-rich nuclei around {sup 132}Sn in an experiment using the FRS-LAND setup. This so-called 'pygmy' dipole strength can be related to the parameters of the symmetry energy and to the neutron skin thickness on the grounds of a relativistic quasiparticle random-phase approximation. Using this ansatz and the experimental findings for {sup 130}Sn and {sup 132}Sn, we derive a value of the symmetry energy pressure of p-bar{sub 0} = 2.2+-0.5 MeV/fm{sup 3}. Neutron skin thicknesses of R{sub n}-R{sub p} 0.23+-0.03 fm and 0.24+-0.03 fm for {sup 130}Sn and {sup 132}Sn, respectively, have been determined. Preliminary results on {sup 68}Ni from a similar experiment using an improved setup indicate an enhanced cross section at low energies, while the results for {sup 58}Ni are in accordance with results from photoabsorption measurements.
About vacuum solutions of Einstein's field equations with flat three-dimensional hypersurfaces
Wolf, T.
The class of vacuum space-times with a family of flat three-slices and a traceless tensor of exterior curvature K-italic/sub a-italic//sub b-italic/ is examined. Metrics without symmetry and solutions describing gravitational radiation are obtained. It turns out that there is a correlation between rank (K-italic/sub a-italic//sub b-italic/) and the Petrov type. Although the resulting solutions are already known, the richness of the class of space-times with flat slices becomes obvious. An example is given of a metric with one-parameter manifold of families of flat slices.
Tabulated equation of state for supernova matter including full nuclear ensemble
Buyukcizmeci, N.; Botvina, A. S.; Mishustin, I. N. [Frankfurt Institute for Advanced Studies, J.W. Goethe University, D-60438 Frankfurt am Main (Germany)
This is an introduction to the tabulated database of stellar matter properties calculated within the framework of the Statistical Model for Supernova Matter (SMSM). The tables present thermodynamical characteristics and nuclear abundances for 31 values of baryon density (10{sup �8} < ?/?{sub 0} < 0.32, ?{sub 0} = 0.15 fm{sup �3} is the normal nuclear matter density), 35 values of temperature (0.2 MeV < T < 25 MeV), and 28 values of electron-to-baryon ratio (0.02 < Y{sub e} < 0.56). The properties of stellar matter in ? equilibrium are also considered. The main ingredients of the SMSM are briefly outlined, and the data structure and content of the tables are explained.
First-principles high-pressure unreacted equation of state and...
Office of Scientific and Technical Information (OSTI)
Subject: 71 CLASSICAL AND QUANTUMM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY ...
The effects of QCD equation of state on the relic density of WIMP dark matter
Drees, Manuel; Hajkarim, Fazlollah; Schmitz, Ernany Rossi
Weakly Interactive Massive Particles (WIMPs) are the most widely studied candidate particles forming the cold dark matter (CDM) whose existence can be inferred from a wealth of astrophysical and cosmological observations. In the framework of the minimal cosmological model detailed measurements on the cosmic microwave background by the PLANCK collaboration fix the scaled CDM relic density to Ω{sub c}h{sup 2}=0.1193±0.0014, with an error of less than 1.5%. In order to fully exploit this observational precision, theoretical calculations should have a comparable or smaller error. In this paper we use recent lattice QCD calculations to improve the description of the thermal plasma. This affects the predicted relic density of "thermal WIMPs", which once were in chemical equilibrium with Standard Model particles. For WIMP masses between 3 and 15 GeV, where QCD effects are most important, our predictions differ from earlier results by up to 9% (12%) for pure S-wave (P-wave) annihilation. We use these results to compute the thermally averaged WIMP annihilation cross section that reproduces the correct CDM relic density, for WIMP masses between 0.1 GeV and 10 TeV.
Solitary Waves of a $$\\mathcal {P}$$ $$\\mathcal {T}$$-Symmetric Nonlinear Dirac Equation
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Cuevas-Maraver, Jesus; Kevrekidis, Panayotis G.; Saxena, Avadh; Cooper, Fred; Khare, Avinash; Comech, Andrew; Bender, Carl M.
In our study we consider we consider a prototypical example of a mathcalP mathcalT-symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the mathcalP mathcalT -phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the mathcalP mathcalT -symmetric model of the solutions of the corresponding Hamiltonian model and find that the solutions can be continued robustly as stable ones all the way up to the mathcalP mathcalT-transition threshold. In the latter, they degenerate into linear waves. We also examine themore » dynamics of the model. Given the stability of the waveforms in the mathcalP mathcalT-exact phase, we consider them as initial conditions for parameters outside of that phase. We also find that both oscillatory dynamics and exponential growth may arise, depending on the size of the corresponding "quench". The former can be characterized by an interesting form of bifrequency solutions that have been predicted on the basis of the SU symmetry. Finally, we explore some special, analytically tractable, but not mathcalP mathcalT-symmetric solutions in the massless limit of t- e model.« less
Equation of state and phase diagram of Fe-16Si alloy as a candidate...
Office of Scientific and Technical Information (OSTI)
Resource Relation: Journal Name: Earth and Planetary Science Letters; Journal Volume: 357-358 Publisher: Elsevier Research Org: Advanced Photon Source (APS), Argonne National ...
Residual Monte Carlo high-order solver for Moment-Based Accelerated Thermal Radiative Transfer equations
Willert, Jeffrey Park, H.
In this article we explore the possibility of replacing Standard Monte Carlo (SMC) transport sweeps within a Moment-Based Accelerated Thermal Radiative Transfer (TRT) algorithm with a Residual Monte Carlo (RMC) formulation. Previous Moment-Based Accelerated TRT implementations have encountered trouble when stochastic noise from SMC transport sweeps accumulates over several iterations and pollutes the low-order system. With RMC we hope to significantly lower the build-up of statistical error at a much lower cost. First, we display encouraging results for a zero-dimensional test problem. Then, we demonstrate that we can achieve a lower degree of error in two one-dimensional test problems by employing an RMC transport sweep with multiple orders of magnitude fewer particles per sweep. We find that by reformulating the high-order problem, we can compute more accurate solutions at a fraction of the cost.
A Unified Equation for the Reaction Rate in Dense Matter Stars
Gasques, L. R.; Wiescher, M.; Yakovlev, D. G.
We analyze thermonuclear and pycnonuclear reaction rates in multi-component dense stellar plasma. First we describe calculations of the astrophysical S-factor at low energies using the Sao Paulo potential on the basis of the barrier penetration model. Then we present a simple phenomenological expression for a reaction rate. The expression contains several fit parameters which we adjust to reproduce the best microscopic calculations available in the literature.
Finite Element Code For 3D-Hydraulic Fracture Propagation Equations (3-layer).
Energy Science and Technology Software Center (OSTI)
HYFRACP3D is a finite element program for simulation of a pseudo three-dimensional fracture geometries with a two-dimensional planar solution. The model predicts the height, width and winglength over time for a hydraulic fracture propagating in a three-layered system of rocks with variable rock mechanics properties.
Equation of state and high-pressure/high-temperature phase diagram...
Office of Scientific and Technical Information (OSTI)
W. ; MacLeod, S. G. ; Cynn, H. ; Errandonea, D. ; Evans, W. J. ; Proctor, J. E. ; Meng, Y. ; McMahon, M. I. Publication Date: 2014-10-20 OSTI Identifier: 1181305 GrantContract ...
Characterization of the {beta}-phase of the palladium-hydrogen equation of state
Fisher, K.J.
The {beta}-phase of the P-C-T curves of the palladium-hydrogen system is encountered at high pressures of gaseous hydrogen and low temperatures of this system. The {beta}-phase is characterized by an increase in the concentration of hydrogen in the palladium lattice with an increase in pressure of the free hydrogen gas surrounding the palladium. The P-C-T curves in this study are determined by gravimetric measurements of the hydrided palladium sample to determine the amount of hydrogen within the palladium lattice. The amount of hydrogen is kept constant within the experimental system and the temperature is varied which changes the pressures. The objective of this experimental thesis is to accurately determine the P-C-T curves of palladium in the {beta}-phase region to pressures of 20,000 psia and medium to low temperature region of {minus}60 C to 100 C.
Validity of equation-of-motion approach to kondo problem in the...
Office of Scientific and Technical Information (OSTI)
Close Cite: Bibtex Format Close 0 pages in this document matching the terms "" Search For Terms: Enter terms in the toolbar above to search the full text of this document for ...
Microbes in Thawing Permafrost: The Unknown Variable in the Climate Change Equation
Graham, David E; Wallenstein, Matthew D; Vishnivetskaya, T.; Waldrop, Mark P.; Phelps, Tommy Joe; Pfiffner, Susan M.; Onstott, T. C.; Whyte, Lyle; Rivkina, Elizaveta; Gilichinsky, David A; Elias, Dwayne A; Mackelprang, Rachel; Verberkmoes, Nathan C; Hettich, Robert {Bob} L; Wagner, Dirk; Wullschleger, Stan D; Jansson, Janet
Considering that 25% of Earth's terrestrial surface is underlain by permafrost (ground that has been continuously frozen for at least 2 years), our understanding of the diversity of microbial life in this extreme habitat is surprisingly limited. Taking into account the total mass of perennially frozen sediment (up to several hundred meters deep), permafrost contains a huge amount of buried, ancient organic carbon (Tarnocai et al., 2009).
Microbes in thawing permafrost: the unknown variable in the climate change equation
Graham, David E; Wallenstein, Matthew D; Vishnivetskaya, T.; Waldrop, Mark P.; Phelps, Tommy Joe; Pfiffner, Susan M.; Onstott, T. C.; Whyte, Lyle; Rivkina, Elizaveta; Gilichinsky, David A; Elias, Dwayne A; Mackelprang, Rachel; Verberkmoes, Nathan C; Hettich, Robert {Bob} L; Wagner, Dirk; Wullschleger, Stan D; Jansson, Janet
Considering that 25% of Earth s terrestrial surface is underlain by permafrost (ground that has been continuously frozen for at least 2 years), our understanding of the diversity of microbial life in this extreme habitat is surprisingly limited. Taking into account the total mass of perennially frozen sediment (up to several hundred meters deep), permafrost contains a huge amount of buried, ancient organic carbon (Tarnocai et al., 2009). In addition, permafrost is warming rapidly in response to global climate change (Romanovsky et al., 2010), potentially leading to widespread thaw and a larger, seasonally thawed soil active layer. This concern has prompted the question: will permafrost thawing lead to the release of massive amounts of carbon dioxide (CO2) and methane (CH4) into the atmosphere? This question can only be answered by understanding how the microbes residing in permafrost will respond to thaw, through processes such as respiration, fermentation, methanogenesis and CH4 oxidation (Schuur et al., 2009). Predicting future carbon fluxes is complicated by the diversity of permafrost environments, ranging from high mountains, southern boreal forests, frozen peatlands and Pleistocene ice complexes (yedoma) up to several hundred meters deep, which vary widely in soil composition, soil organic matter (SOM) quality, hydrology and thermal regimes (Figure 1). Permafrost degradation can occur in many forms: thaw can progress downward from seasonally-thawed active layer soils in warming climates or laterally because of changes in surface or groundwater flow paths (Grosse et al., 2011). Permafrost degradation can sometimes lead to dramatic changes in ecosystem structure and function
First-principles high-pressure unreacted equation of state and...
Office of Scientific and Technical Information (OSTI)
Language: English Subject: 71 CLASSICAL AND QUANTUMM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 37 INORGANIC, ORGANIC, PHYSICAL AND ...
Analysis of the Sultana-Dyer cosmological black hole solution of the Einstein equations
Faraoni, Valerio
The Sultana-Dyer solution of general relativity representing a black hole embedded in a special cosmological background is analyzed. We find an expanding (weak) spacetime singularity instead of the reported conformal Killing horizon, which is covered by an expanding black hole apparent horizon (internal to a cosmological apparent horizon) for most of the history of the Universe. This singularity was naked early on. The global structure of the solution is studied as well.
Equation of state and high-pressure/high-temperature phase diagram...
Office of Scientific and Technical Information (OSTI)
Argonne, IL (US) Sponsoring Org: FOREIGNDOE - BASIC ENERGY SCIENCES Country of Publication: United States Language: ENGLISH Word Cloud More Like This Full Text Journal Articles ...
Bodo, G.; Rossi, P.; Cattaneo, F.; Mignone, A.
We present a numerical study of turbulence and dynamo action in stratified shearing boxes with zero mean magnetic flux. We assume that the fluid obeys the perfect gas law and has finite (constant) thermal diffusivity. The calculations begin from an isothermal state spanning three scale heights above and below the mid-plane. After a long transient the layers settle to a stationary state in which thermal losses out of the boundaries are balanced by dissipative heating. We identify two regimes. The first is a conductive regime in which the heat is transported mostly by conduction and the density decreases with height. In the limit of large thermal diffusivity this regime resembles the more familiar isothermal case. The second is the convective regime, observed at smaller values of the thermal diffusivity, in which the layer becomes unstable to overturning motions, the heat is carried mostly by advection, and the density becomes nearly constant throughout the layer. In this latter constant-density regime we observe evidence for large-scale dynamo action leading to a substantial increase in transport efficiency relative to the conductive case.
Fully self-consistent solution of the Dyson equation using a...
Office of Scientific and Technical Information (OSTI)
Additional Journal Information: Journal Volume: 91; Journal Issue: 12; Journal ID: ISSN 1098-0121 Publisher: American Physical Society Sponsoring Org: USDOE Office of Science (SC), ...
Green's function partitioning in Galerkin-based integral solution of the diffusion equation
Haji-Sheikh, A. ); Beck, J.V. )
A procedure to obtain accurate solutions for many transient conduction problems in complex geometries using a Galerkin-based integral (GBI) method is presented. The nonhomogeneous boundary conditions are accommodated by the Green's function solution technique. A Green's function obtained by the GBI method exhibits excellent large-time accuracy. It is shown that the time partitioning of the Green's function yields accurate small-time and large-time solutions. In one example, a hollow cylinder with convective inner surface and prescribed heat flux at the outer surface is considered. Only a few terms for both large-time and small-time solutions are sufficient to produce results with excellent accuracy. The methodology used for homogeneous solids is modified for application to complex heterogeneous solids.
A New Lifshitz Transition and the Equation of State of Osmium...
Office of Scientific and Technical Information (OSTI)
... Accurate investigations of Ksub 0 and K'sub 0 simultaneously in materials such as Os requires very high resolution studies in the low pressure region (Ksub 0) and high ...