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Nano Mechanics and Materials: Theory, Multiscale Methods and Applications by Wing Kam Liu, Eduard G. Karpov, Harold S. Park
4. Methods of Thermodynamics and Statistical Mechanics
Basic features of the thermodynamic method: Multi-particle physical systems is described by means of a small number of macroscopically measurable parameters, the thermodynamic parameters: V, P, T, S (volume, pressure, temperature, entropy), and others. Note: macroscopic objects contain ~ 10 23 …10 24 atoms (Avogadro's number ~ 6 x 10 23 mol –1 ). The connections between thermodynamic parameters are found from the general laws of thermodynamics. The laws of thermodynamics are regarded as experimental facts. Therefore, thermodynamics is a phenomenological theory. Thermodynamics is in fact a theory of equilibrium states, i.e. the states with time- independent (relaxed) V, P, T and S. Term "dynamics" is understood only in the sense "how one thermodynamic parameters varies with a change of another parameter in two successive equilibrium states of the system". Thermodynamics is a macroscopic, phenomenological theory of heat. Definition and Features the Thermodynamic Method
Internal and external parameters: External parameters can be prescribed by means of external influences on the system by specifying external boundaries and fields. Internal parameters are determined by the state of the system itself for given values of the external parameters. Note: the same parameter may appear as external in one system, and as internal in another system. Intensive and extensive parameters: Intensive parameters are independent of the number of particles in the system, and they serve as general characteristics of the thermal atomic motion (temperature, chemical potential). Extensive parameters are proportional to the total mass or the number of particles in the system (internal energy, entropy). Note: this classification is invariant with respect to the choice of a system. Classification of Thermodynamic Parameters
A same parameter may appear both as external and internal in various systems: System A System B P V = Const M P = Const V External parameter: V External parameter: P, P = Mg/A Internal parameter: P Internal parameter: V, V = Ah Internal and External Parameters: Examples
Application of the thermodynamic method implies that the system if found in the state of thermodynamic equilibrium, denoted X, which is defined by time-invariant state parameters, such as volume, temperature and pressure: The parameters (V,T,P) are macroscopically measurable. One or two of them may be replaced by non-measurable parameters, such internal energy or entropy. Note that only the mean quantity of a state parameter A is time-invariant, see the plot. A mathematical relationship that involve a complete set of measurable parameters (V,T,P) is called the thermodynamic state equation Here, ξ is the vector of system parameters State Vector and State Equation
The knowledge of an equation of state allows evaluation of a group of the microscopic system parameters, such as the compressibility, expansion and pressure coefficients: 1) Isothermal compressibility coefficient 2) Isobaric thermal expansion coefficient 3) Isochoric pressure coefficient Analysis of the State Equation: System Parameters
Standard forms of the state equations are readily available for ideal gases, real (Van der Waals) gases, homogeneous liquid and homogeneous isotropic solids. Ideal gas Van der Waals gas (pair wise interaction V of gas molecules is taken into account) Homogeneous isotropic liquid or solid d – effective diameter of the molecules W – pairwise potential Examples of the State Equation
The temperature is introduced as a parameter, which: 1) serves as an intrinsic characteristic of any equilibrium system (similar to V and P) 2) determines thermodynamic equilibrium between two systems in thermal contact Thus, it is postulated that: If two adiabatically isolated systems in equilibrium are brought into thermal contact with each other, their states of equilibrium will not be altered and the total system will be in equilibrium, only if initial systems have the same temperature. (Also known as the zeroth law of thermodynamics) Any state of thermodynamic equilibrium of an arbitrary system in entirely determined by the set of external parameters and temperature. Consequently, All internal parameters of an equilibrium system are functions of the external parameters and temperature. The Postulate on Existence of Temperature
The first law of thermodynamics is essentially a form of the energy conservation law, written in relation to thermodynamic systems: An amount of heat absorbed by the system is equal to the summary change of its internal energy and the work done by the system over external bodies. Note: The internal energy U is defined solely by the state of system, while the external thermal energy Q and the mechanical work W may depend both on the internal state of the system and other factors. The First Law of Thermodynamics
The second law of thermodynamics specifies the direction of thermodynamic processes. The simplest form of the second law is given by Clausius' postulate: Heat cannot flow spontaneously from a colder to a hotter system. This is equivalent to the following (Kelvin's postulate): It is impossible to devise an engine (a perpetuum mobile of the second kind) which, working in a cycle, would produce no other effect than the transformation of heat extracted from a reservoir completely into work. The Second Law of Thermodynamics
The most important consequence of the second law of thermodynamics is that it asserts the existence of a new function of state, namely the entropy, S. The concept of entropy plays a crucial role in statistical mechanics. For quasistatic processes, entropy is an extensive state function, which is defined by the relation Based on the first law of thermodynamics we obtain the fundamental differential equation Alternative form of the second law of thermodynamics: All spontaneous processes in adiabatically isolated systems, δQ = 0, occur at a constant or growing entropy: Entropy
The second law and the original definition of entropy does not specify the absolute value of entropy, whose value is provided up to a constant value. The third law claims that All thermodynamic processes at T = 0 occur without a change of the entropy. This allows establishing an absolute scale for measuring the entropy; so that Also, The Third Law of Thermodynamics
The method of thermodynamic potentials is a powerful tool of thermodynamics. Thermodynamic potentials are functions that uniquely describe the state of the system. The relevant thermodynamic parameters are found as derivatives of the potentials. The simplest thermodynamic potential is the internal energy, given by the first law, Other thermodynamic potentials for systems with constant number of particles: free energy Gibbs potential enthalpy Exercise 3-1 (can be done in class): derive the differentials of the free energy, Gibbs potential and enthalpy, by utilizing the definitions of these potentials and the first law of thermodynamics. Thermodynamic Potentials
4.1 Basic Results of the Thermodynamic Method Differentiation of the thermodynamic potentials gives the thermodynamic parameters: Also, system parameters can be evaluated using their relationship with the above state parameters (see reading assignment [1], Section 4.1.5)
Hamiltonian of the system and the generalized momentum: Equations of motion: Cartesian coordinates: Hamiltonian Mechanics
In classical (deterministic) mechanics, the state of the system is completely described by the phase vector Q. Such a state is called a microscopic state, and the corresponding model of matter is called a micromodel. The microstate is completely defined by specifying values of all canonical variables, the components of the phase vector, This approach is not tractable in modeling macroscopic objects. Thermodynamics provides a macromodel; the state of the a system is determined by a very limited number of thermodynamic parameters, which are sufficient for macroscopic characterization of the system. The prescription of these parameters, measured in a macroscopic experiment, determines the macroscopic state the system. A key point is that a single macroscopic state of the system corresponds to a great number of different microscopic states. Micromodel vs. Macromodel
4.2 Statistics of Multiparticle Systems in Thermodynamic Equilibrium However, the specification of all the macroparameters X does not determine a unique microstate, Consequently, on the basis of macroscopic measurements, one can make only statistical statements about the values of the microscopic variables. The macroscopic thermodynamic parameters, X = (V,P,T,…), are macroscopically observable quantities that are, in principle, functions of the canonical variables, i.e.
Statistical description of mechanical systems is utilized for multi-particle problems, where individual solutions for all the constitutive atoms are not affordable, or necessary. Statistical description can be used to reproduce averaged macroscopic parameters and properties of the system. Comparison of objectives of the deterministic and statistical approaches: Deterministic particle dynamicsStatistical mechanics Provides the phase vector, as a function of time Q(t), based on the vector of initial conditions Q(0) Provides the time-dependent probability density to observe the phase vector Q, w(Q,t), based on the initial value w(Q,0) Statistical Description of Mechanical Systems
From the contemporary point of view, statistical mechanics can be regarded as a hierarchical multiscale method, which eliminates the atomistic degrees of freedom, while establishing a deterministic mapping from the atomic to macroscale variables, and a probabilistic mapping from the macroscale to the atomic variables: Microstates Macrostates deterministic conformity probabilistic conformity XkXk (p,q) k Statistical Description of Mechanical Systems
Though the specification of a macrostate X i cannot determine the microstate (p,q) i = (p 1,p 2,…,p s ; q 1,q 2,…,q s ) i, a probability density w of all the microstates can be found, or abbreviated: The probability of finding the system in a given phase volume G: The normalization condition: Distribution Function
Within the statistical description, the motion of one single system with given initial conditions is not considered; thus, p(t), q(t) are not sought. Instead, the motion of a whole set of phase points, representing the collection of possible states of the given system. Such a set of phase points is called a phase space ensemble. If each point in the phase space is considered as a random quantity with a particular probability ascribed to every possible state (i.e. a probability density w(p,q,t) is introduced in the phase space), the relevant phase space ensemble is called a statistical ensemble. G – volume in the phase space, occupied by the statistical ensemble. p q t = t 1 : G 1 t = t 2 : G 2 Statistical Ensemble
Statistical average (expectation) of an arbitrary physical quantity F(p,q), is given most generally by the ensemble average, The root-mean-square fluctuation (standard deviation): The curve representing the real motion (the experimental curve) will mostly proceed within the band of width 2Δ(F) For some standard equilibrium systems, thermodynamic parameters can be obtained, using a single phase space integral. This approach is discussed below. True value F t Statistical Averaging
Evaluation of the ensemble average (previous slide) requires the knowledge of the distribution function w for a system of interest. Alternatively, the statistical average can be obtained by utilizing the ergodic hypothesis in the form, Here, the right-hand side is the time average (in practice, time t is chosen finite, though as large as possible) This approach requires F as a function of the generalized coordinates. Some examples More examples are given in Ref. [1]. Ergodic Hypothesis and the Time Average
A statistical ensemble is described by the probability density in phase space, w(p,q,t). It is important to know how to find w(p,q,t) at an arbitrary time t, when the initial function w(p,q,0) at the time t = 0 is given. In other words, the equation of motion satisfied by the function w(p,q,t) is needed. p q w(p,q,0) Γ2Γ2 Γ0Γ0 Γ1Γ1 w(p,q,t 1 ) w(p,q,t 2 ) The motion of of an ensemble in phase space may be considered as the motion of a phase space fluid in analogy to the motion of an ordinary fluid in a 3D space. Liouville's theorem claims that Due to Liouville's theorem, the following equation of motion holds Law of Motion of a Statistical Ensemble
Exercise: Check the above equality. A direct solution of this equation is not tractable. Therefore, the ergodic hypothesis (in a more general form) is utilized: the probability density in phase space at equilibrium depends only on the total energy: Notes: the Hamiltonian gives the total energy required; the Hamiltonian may depend on the values of external parameters a = (a 1, a 2,…), besides the phase vector X. This distribution function satisfies the equilibrium equation of motion, because For a system in a state of thermodynamic equilibrium the probability density in phase space must not depend explicitly on time, Thus, the equation of motion for an equilibrium statistical ensemble reads Equilibrium Statistical Ensemble: Ergodic Hypothesis
After adoption of the ergodic hypothesis, it then remains to determine the actual form of the function φ(H). This function depends on the type of the thermodynamic system under consideration, i.e. on the character of the interaction between the system and the external bodies. We will consider canonical ensembles of two types of systems: 1) Adiabatically isolated systems that have no contact with the surroundings and have a specified energy E. The corresponding statistical ensemble is referred to as the microcanonical ensemble, and the distribution function – microcanonical distribution. 2) Closed isothermal systems that are in contact and thermal equilibrium with an external thermostat of a given temperature T. The corresponding statistical ensemble is referred to as the canonical ensemble, and the distribution function – Gibbs' canonical distribution. Both systems do not exchange particles with the environment. Canonical Ensembles
For an adiabatically isolated system with constant external parameters, a, the total energy cannot vary. Therefore, only such microstates X can occur, for which This implies (δ – Dirac's delta function) and finally: where Ω is the normalization factor, E, a (P,T,V,…) Within the microcanonical ensemble, all the energetically allowed microstates have an equal probability to occur. Microcanonical Distribution
The normalization factor Ω is given by where Γ is the integral over states, or phase integral: Γ(E,a) represents the normalized phase volume, enclosed within the hypersurface of given energy determined by the equation H(X,a) = E. Phase integral Γ is a dimensionless quantity. Thus the normalization factor Ω shows the rate at which the phase volume varies due to a change of total energy at fixed external parameters. Phase volume Microcanonical Distribution: Integral Over States
The integral over states is a major calculation characteristic of the microcanonical ensemble. The knowledge of Γ allows computing thermodynamic parameters of the closed adiabatic system: (These are the major results in terms of practical calculations over microcanonical ensembles.) Microcanonical Distribution: Integral Over States
We will consider one-dimensional illustrative examples of computing the phase integral, entropy and temperature for microcanonical ensembles: Spring-mass harmonic oscillator Pendulum (non-harmonic oscillator) We will use the Hamiltonian equations of motion to get the phase space trajectory, and then evaluate the phase integral. Microcanonical Ensemble: Illustrative Examples
Hamiltonian: general form Kinetic energy Potential energy The total Hamiltonian Potential energy is a quadratic function of the coordinate (displacement form the equilibrium position) m k x Harmonic Oscillator: Hamiltonian
Hamiltonian and equations motion: Initial conditions (m, m/s): Harmonic Oscillator: Equations of Motion and Solution
Total energy: Harmonic Oscillator: Total Energy
Phase integral: A2A2 A3A3 A1A1 For the harmonic oscillator, phase volume grows linearly with the increase of total energy. Harmonic Oscillator: Phase Integral
Entropy: Temperature: We perturb the initial conditions (on 0.1% or less) and compute new values The temperature is computed then, as Harmonic Oscillator: Entropy and Temperature
Total energy: Pendulum: Total Energy
Phase integral: For the pendulum, phase volume grows NON-linearly with the increase of total energy at large amplitudes. A2A2 A3A3 A1A1 Pendulum: Phase Integral
Entropy: Temperature: We perturb the initial conditions (on 0.1% or less) and compute new values The temperature is computed then, as Pendulum: Entropy and Temperature
1.Analyze the physical model; justify applicability of the microcanonical distribution. 2.Model individual particles and boundaries. 3.Model interaction between particles and between particles and boundaries. 4.Set up initial conditions and solve for the deterministic trajectories (MD). 5.Compute two values of the total energy and the phase integral – for the original and perturbed initial conditions. 6.Using the method of thermodynamic parameters, compute entropy, temperature and other thermodynamic parameters. If possible compare the obtained value of temperature with benchmark values. 7.If required, accomplish an extended analysis of macroscopic properties (e.g. functions T(E), S(E), S(T), etc.) by repeating the steps 4-7. Summary of the Statistical Method: Microcanonical Distribution
Canonical Distribution: Preliminary Issues One important preliminary issue related to the use of Gibbs' canonical distribution is the additivity of the Hamiltonian of a mechanical system. Structure of the Hamiltonian of an atomic system: Here, kinetic energy and the one-body potential are additive, i.e. they can be expanded into the components, each corresponding to one particle in the system: Two-body and higher order potentials are non-additive (function Q 2 does not exist),
Canonical Distribution: Preliminary Issues Thus, if the inter-particle interaction is negligible, the system is described by an additive Hamiltonian, Here, H is the total Hamiltonian, and h i is the one-particle Hamiltonian. For the statistical description, it is sufficient that this requirement holds for the averaged quantities only. The multi-body components, W >1, cannot be completely excluded from the physical consideration, as they are responsible for heat transfer and establishing the thermodynamic equilibrium between constitutive parts of the total system. A micromodel with small averaged contributions to the total energy due to particle-particle interactions is called the ideal gas. Example: particles in a circular cavity. Statistically averaged value W 2 is small:
Canonical Distribution Suppose that system under investigation Σ 1 is in thermal contact and thermal equilibrium with a much larger system Σ 2 that serve as the thermostat, or "heat bath" at the temperature T. From the microscopic point of view, both Σ 1 and Σ 2 are mechanical systems whose states are described by the phase vectors (sets of canonical variables X 1 and X 2 ). The entire system Σ 1 +Σ 2 is adiabatically isolated, and therefore the microcanonical distribution is applicable to Σ 1 +Σ 2, Assume N 1 and N 2 are number of particles in Σ 1 and Σ 2 respectively. Provided that N 1 << N 2, the Gibbs' canonical distribution applies to Σ 1 : Thermostat T N 1 Σ 1 N 2 Σ 2
Canonical Distribution: Partition Function The normalization factor Z for the canonical distribution called the integral over states or partition function is computed as Thermostat T N 1 Σ 1 N 2 Σ 2 Before the normalization, this integral represents the statistically averaged phase volume occupied by the canonical ensemble. The total energy for the canonical ensemble is not fixed, and, in principle, it may occur arbitrary in the range from – to (for the infinitely large thermostat, N 2 ).
Partition Function and Thermodynamic Properties The partition function Z is the major computational characteristic of the canonical ensemble. The knowledge of Z allows computing thermodynamic parameters of the closed isothermal system (a V, external parameter): These are the major results in terms of practical calculations over canonical ensembles. Class exercise: check the last three above formulas with the the method of thermodynamic potentials, using the first formula for the free energy. Free energy: (relates to mechanical work) Entropy (variety of microstates) Pressure Internal energy
Free Energy and Isothermal Processes Free energy, also Helmholtz potential is of importance for the description of isothermal processes. It is defined as the difference between internal energy and the product of temperature and entropy. Since free energy is a thermodynamic potential, the function F(T,V,N,…) guarantees the full knowledge of all thermodynamic quantities. Physical content of free energy: the change of the free energy dF of a system at constant temperature, represents the work accomplished by, or over, the system. Indeed, Isothermal processes tend to a minimum of free energy, i.e. due to the definition, simultaneously to a minimum of internal energy and maximum of entropy.
Canonical vs. Microcanonical: Factorization of the Partition Function In terms of practical calculations, there exists one major difference between the canonical and microcanonical distributions: For additive Hamiltonians, the canonical distribution factorizes, Note that this property does not hold for the microcanonical distribution, Thermostat T 6 N 1 Σ 1 N 2 Σ 2 E, a z i is the one-particle partition function
Factorization of the Partition Function: Computational Issues Factorization of the canonical distribution is crucial in terms of practical calculations over real-life systems. In computing the partition function Z, this property reduces the calculation of a 6N- dimensional phase integral to a product of N 6-dimensional integrals: Here, z i is the one-particle partition function, and h i is the one-particle Hamiltonian, In case that the system is comprised of identical particles, calculation of Z requires evaluation of a single 6-dimensional integral z: The factorized canonical distribution can be very effective computationally.
Analytical Example: Non-Interactive Ideal Gas The canonical distribution allows an exact solution for the non-interactive ideal gas: Analytical results for this system are useful, because they provide acceptable "first guess" assessments for a wide class of systems. One-particle partition function: Partition function (total system):
Non-Interactive Ideal Gas: Thermodynamic Parameters Partition function: Free energy (recall the method of thermodynamic potentials) Entropy Pressure Total internal energy (differs form the earlier MD definition)
Numerical Example: Interactive Gas Repulsive interaction between the particles and the wall is described by the "wall function", a one-body potential that depends on r i – distance between the particle i and the chamber's center): Interaction between particles is modeled with the two-body Lennard-Jones potential (r ij – distance between particles i and j): The Hamiltonian: y x riri R r ij rjrj One particle is initially at rest. This illustrates the concept of heat exchange between the smaller subsystem, for which the canonical distribution holds, and the external thermostat.
Interactive Gas: Equations of Motion and Solution The total potential: Equations of motion: Parameters: Initial conditions (nm, nm/s):
Interactive Gas: Temperature Time averaged kinetic energy vs. time (five particles) Information on temperature allows computing the partition function (integral over states), using canonical distribution. Subsequently, the partition function, computed at various temperatures, can provide all the remaining thermodynamic parameters. For sufficiently long simulations, the value of temperature does not depend on the choice of a subsystem (particle). Time averaged kinetic energy of particles is approaching the value which corresponds to temperature
Interactive Gas: Partition Function and Free Energy Hamiltonian (can be viewed as additive in the statistical sense, due to smallness of the time averaged pair-wise interaction) One-particle partition function (value at given T and V = πR 2 ) Partition function (total system) Free energy
Interactive Gas: Thermodynamic Parameters In order to compute the thermodynamic quantities, it necessary to evaluate 2 values of the partition function: 1) Z – for the initially computed temperature T, 2) – for a perturbed temperature T +ΔT (ΔT/T < 0.1%). Note: the simulation needs to be run once only (not two times). Entropy: Pressure: Internal energy: Ideal gas benchmark: Other parameters can be computed using the method of thermodynamic potentials
Phase Integral, Free Energy and Entropy vs. Temperature Assume that we observe the same isothermal system at various temperatures of thermostat. The following trends are available: Partition function Free energy Entropy Partition function, and therefore the phase volume occupied by this canonical ensemble, grows exponentially vs. temperature. Free energy decreases linearly; the work done by the system does not depend on temperature. Entropy decays vs. temperature. Physical implication (according to the second law): temperature cannot grow spontaneously in an isothermal system, once thermal equilibrium with the thermostat is established.
Specifics of Calculations for Liquids and Solids In liquids, the energy due to pair-wise interaction between particles is close to the kinetic energy (per particle). However, interaction, w ij, between separate constitutive parts (subdomains) i and j is still weak, if compared with the total kinetic energy of the smaller domain. Indeed, the kinetic energy depends on the subdomain volume, while w ij depends on the surface area. Therefore, the Hamiltonian can be expanded into h i – Hamiltonians of the sufficiently large subdomains. Partition function (z – partition functions for N identical subdomains, n – number of subdomain particles) For reasonably small subdomains, numerical evaluation of the liquid's partition function can be effective. A similar approach is also applicable to solids. Example: H hihi i j Note: In case of large w ij, the micro- canonical distribution should be utilized.
1.Analyze the physical model; justify applicability of the Gibbs' canonical distribution. 2.Model individual particles and boundaries. 3.Model interaction between particles and between particles and boundaries. 4.Set up initial conditions and solve for the deterministic trajectories (MD). 5.Compute the averaged kinetic energy and temperature, or assume T given. 6.Based on the canonical distribution, compute two values of the partition function: for the original and perturbed temperatures. 7.Compute the free energy and other thermodynamic parameters, using the method of thermodynamic potentials. If possible compare the obtained value of internal energy with a benchmark value. 8.If required, accomplish an extended analysis of macroscopic properties (e.g. dependences P(T), P(N), S(T), etc.) by repeating the steps 4-7. Summary of the Statistical Method: Canonical Distribution
4.3 Numerical Heat Bath Techniques Berendsen thermostat Adelman-Doll thermostatting GLE Phonon heat bath Time-history kernel and transform techniques Random force and lattice normal modes
Finite Temperatures A heat bath technique is required to represent a peripheral region at finite temperatures Berendsen thermostat for a standard Langevin equation Berendsen et al., JCP 81(8), 1984
Finite Temperatures Adelman-Doll's thermostatting GLE for gas-solid interface Adelman, Doll et al., JCP 64(6), 1976 Almost exactly what we seek, however, the update is needed: gas/solid interface -> solid/solid interface
Phonon Heat Bath Phonon heat bath represents energy exchange due to correlated motion of lattice atoms along an imaginary atomic/continuum (solid-solid) interface Phonon heat bath is a configurational method t Karpov, Liu, preprint. atom next to the interface
Time History Kernel (THK) The time history kernel shows the dependence of dynamics in two adjacent cells. Any time history kernel is related to the response function. … -2 -1 0 1 2 … f(t)
Elimination of Degrees of Freedom: T = 0 Equations for the DoF n>0 are no longer required. We have taken them into account implicitly. … -2 -1 0 1 2 … … … Domain of interest Eliminated degrees of freedom
Bridging Scale at T = 0: Impedance Boundary Conditions MD degrees of freedom outside the localized domain are solved implicitly + Due to atomistic nature of the model, the structural impedance is evaluated computed at the molecular scale. The MD domain is too large to solve, so that we eliminate the MD degrees of freedom outside the localized domain of interest. Collective atomic behavior of in the bulk material is represented by an impedance force applied at the formal MD/continuum interface: FE + Reduced MD + Impedance BC MD FE
Dynamic Response Function: 1D Illustration Assume first neighbor interaction only: … n-2 n-1 n n+1 n+2 … Displacements Velocities Illustration Transfer of a unit pulse due to collision ( movie ):
Discrete Fourier Transform (DFT) Discrete convolution Discrete functional sequences DFT of infinite sequences p – wavenumber, a real value between – and DFT of periodic sequences Here, p – integer value between –N/2 and N/2
Numerical Laplace Transform Inversion – Laguerre polynomials, – coefficients computed using F(s) Weeks algorithm (J Assoc Comp Machinery 13, 1966, p.419) Sin-series expansion (J Assoc Comp Machinery 23, 1976, p.89) For an odd function f gives Most numerical algorithms for the Laplace transform inversion utilize series decompositions of the sought originals f(t) in terms of functions whose Laplace transform is tabulated. The expansion coefficients are found numerically from F(s). Examples:
Elimination of Degrees of Freedom at T > 0 Equations for the DoF n>0 are no longer required. We have taken them into account implicitly: - mechanical response is described by the THK - thermal contact is described by the randon force R … -2 -1 0 1 2 … … … Domain of interestHeat bath Compare with:
Random Force Term ( g – the lattice response function ) Is there a more effective way to compute R(t) ?
Gibbs Distribution and Lattice Hamiltonian Gibbs distribution Lattice Hamiltonian Normal modes decomposition
Random Force Term via Lattice Normal Modes Random force Distribution of the normal amplitudes and phases
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Shawn Kemp was one of the hardest dunkers in the NBA before he went on a see-food diet and ate himself out of the league. His behavior didn't help, but his weight was a big issue. Hell, he was the most gifted fatman I've ever seen play (John "Hot Plate" Williams was up there as well).
Well the "Reignman" wasn't all that impressed with Blake Griffin's winning dunk at the slam dunk contest.
Kemp classified the dunk as weak and feels he could do better, even at age 41.
"I'm a big Blake Griffin fan, but that dunk at the contest might've been the weakest dunk in the dunk contest that I've seen in a long time. I love the choir and all that stuff was great, but you at least gotta jump over the car though right? He swung over the car and landed on the hood of the car. I think he should at least be able to jump over the front of the car. I'm 41 years old and right now I could do it. Two Smart Cars."
Ok he's right, but saying he could do it over two Smart cars. Seeing is believing. And until we see Kemp do it, it's all talk and wishful thinking. Good luck in training for that feat Shawn.
Wednesday, February 23, 2011
Shawn Kemp Not Impressed With Blake Griffin's Dunk
Blake Griffin,
Shawn Kemp
3 comments:
It doesn't matter if he swung back and forth and stayed on the car, do you know why? Because it was good enough to WIN.
- February 24, 2011 at 12:41 PM
Yeah well everyone knew, even before All-Star weekend, the dunk contest was going to be rigged for Griffin to win.
- February 24, 2011 at 1:08 PM
- c note said...
They weren't going to let JaVale McGee win, but Griffin's final dunk hadn't been done before and it was good enough to win.
- February 27, 2011 at 2:24 PM
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The Question: Why don't the feet of a duck (seagull, goose, or other winter bird) freeze when they spend the night apparently sleeping on ice in sub-zero temperatures? Also, do you know if they stand on one foot and then the other going back and forth as a strategy to help with this? Submitted by: Ken L., Milwaukee, WI |
Category Archives: Uncategorized
Are Snakes Useful?
The Question: "Are snakes useful to humans? And what role do they play in nature? Submitted by: John L., Texas (John found three beautiful rat snakes when he lifted a tarp on some stored wood. When he posted his photos on FaceBook with enthusiasm, he was shocked that so many people responded by saying, "Kill them!!" Thanks to John for the picture printed below.) |
Where Does Trash End Up?
I was very much affected by these photos in the latest issue of Audubon Magazine: http://www.audubonmagazine.org/onepicture/onepicture1003.html. For some reason, they reproduced it in a small, low-res format. To see a better version, go to this pdf and go to page 21 of this presentation: http://faculty.philau.edu/AshleyJ/Philly_U_MD_Bamford.pdf (if you want to get really depressed, read the whole presentation.)
If you've ever wondered whether a little trash makes any difference, this picture gives a moving answer. The bottle caps, cigarette lighters, and hundreds of other pieces of trash that killed this albatross may have come from half way around the world. Albatross will scoop up just about anything they see on the surface of the ocean because in pre-plastic days, virtually anything floating on the ocean was food. Also, apparently, flying fish lay their eggs in long strings attached to floating objects, and albatross feed on them by scooping up whatever they see floating. Then they go back and regurgitate to their chicks. Unfortunately, all the plastic junk the parents have ingested ends up in the chicks. In this case, it was enough to kill the chick.
These photos are a tragic demonstration of the interconnectedness of our environment. Every bottle cap or plastic bag we throw away on the sidewalk can end up washing into a storm grate, into a river, out into the ocean, and eventually into the gut of an albatross chick.
Spider Mites
The Question: Every summer I see teeny tiny red bugs crawling around, usually on something like concrete. What are those? Submitted by: Rick P., Queens, NY |


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For some unknown reason, whilst trying to install Windows 7 to a new drive on a dual boot with Vista Ultimate, towards the end of the installation it said that it could not continue and I had to run chkdsk on the C: drive. I waited and chkdsk did run giving all sorts of errors but then the installation would not complete with the same message. The next try failed also, as did the next. I then tried to boot again from the CD, but that also failed - same problem. I am now left with an ineffective triple boot system. The options are Windows 7, Windows 7 and Vista Ultimate. How do I remove those choices so that I have only Vista? I am reformatting the offending drive to try again, and really do not want three Windows 7 choices. Any suggestions? David
Hi, You can do it by typing msconfig in Start search box. Click it when it pops up, then click the Boot Tab. Highlight the entry you don't want and click delete. Then click Apply and OK.


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Gavin Bieber
Gavin Bieber was born in Halifax, Nova Scotia. He developed a very early interest in birds, fish, amphibians and reptiles and has steadily pursued these interests while growing up in British Columbia, Virginia Beach, Great Britain and Denmark. Gavin graduated from the University of Victoria with a degree in Biology and a minor in Environmental Studies. He studied for a year at the University of Southern Mississippi where he collaborated with their Migratory Bird Study Group. While still in university he taught waterfowl, shorebird and passerine identification workshops for the Victoria Natural History Society and led field trips for the university's ornithology classes. Since graduating, Gavin has worked as a field assistant on a variety of ornithological research projects including studies of the wintering ecology of Henslow's Sparrow, the breeding biology of the Interior Least Tern, the stopover ecology of Swainson's Thrush and Gray Catbird and a population fitness study of auklets. In addition he conducted point counts for the National Park Service in Arizona and New Mexico and assisted in setting up a riparian bird survey for the University of Arizona. From 2002 onwards he has maintained a long-term interest in the avifauna of the Pribilof Islands, AK, spending a cumulative two years living on Saint Paul Island. He has also traveled extensively through much of Western Europe, parts of Africa and South America, Thailand, the Philippines, New Guinea and Australia. Gavin enjoys sharing his knowledge and enthusiasm of the natural world with others, and welcomes the chance to share his love of the natural world with new people.
Moving to Tucson in 2000 he has become involved in the environmental community, serving as a board member for the Tucson Audubon Society, and on the Arizona Bird Committee from 2007-2010. He currently lives in Tucson, with his wife Celina, his newly minted son Roland, a loveable Labradoodle, and an overly large fish tank.
- The Dominican Republic (Mar 25 to Apr 2, 2017)
- Colorado: Lekking Grouse (Apr 7-17, 2017)
- Florida: The South, the Keys and the Dry Tortugas (Apr 22-29, 2017)
- Arizona: Owls and Warblers (May 6-14, 2017)
- Alaska: Gambell (May 28 to Jun 6, 2017 with extensions to 9 Jun and to 11 Jun)
- Alaska: Majesty of the North (Jun 11-23, 2017 with extensions from 8 Jun and to 26 Jun)
- Alaska: Fall Migration at Gambell and the Pribilofs (Aug 25 to Sep 2, 2017 with extension to 8 Sep)
- Alaska: The Pribilofs in Fall (Sep 2-8, 2017)
- Australia: Western Australia and Northern Territory - Brushtails, Baobabs and Bowerbirds (Sep 29 to Oct 15, 2017)
- Australia: Queensland and New South Wales - Riflebirds, Reefs and Rainforests (Oct 15-28, 2017) One space remains
- Panama: Fall at the Canopy Tower (Nov 12-18, 2017)
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- Panama: Spring at the Canopy Tower (Mar 24-30, 2018 with extension to 4 Apr)
- Texas: The Rio Grande Valley in Spring (Apr 7-16, 2018)
- Florida: The South, the Keys and the Dry Tortugas (Apr 21-28, 2018)
- Alaska: Majesty of the North (Jun 10-22, 2018 with extensions from 7 Jun and to 25 Jun)
- Australia: Victoria and Tasmania - Plains-wanderer, Pardalotes, and Penguins (Sep 20 to Oct 7, 2018)
- Australia: Queensland and New South Wales - Riflebirds, Reefs and Rainforests (Oct 7-20, 2018)
- Panama: Fall at the Canopy Tower (Nov 11-17, 2018)
- Panama: Bocas del Toro and the Western Highlands (Nov 16-25, 2018)
- Panama: Darién Lowlands (Nov 24 to Dec 1, 2018)
- Australia: Western Australia and Northern Territory - Brushtails, Baobabs and Bowerbirds (Sep 27 to Oct 13, 2019)
Updated: May 2013


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Help smileys find their perfect friend!
Thank you for downloading Smileyville from our download portal.
Current files are located on the following IPs: 22.214.171.124
Outer mirror site one (www.interactionstudios.com)
Note: We prefer to use WinZip, WinRar, WinAce, 7zip to extract zip, rar, 7z, ace files. For data iso files we recommend you use freeware Daemon Toos lite.
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INTERACTION STUDIOS DISTRIBUTION AGREEMENT You may freely distribute, transmit and store the DEMO version of the Software on any electronic media, including but not limited to floppy diskette, hard disk, CD-ROM or other storage device, provided that you do not remove, edit, modify, or otherwise alter the original files of the Software. You may NOT sell, resale, rent, lease, display or offer the DEMO version of the Software on a pay-per-play, coin-op or other for-charge basis. You may NOT distribute the FULL (registered) version of the software under any circumstances.


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Our MSc Entrepreneurship and Innovation addresses critical issues that are central to economic growth and social transformation. These are issues which are high on the agendas of business, governments, policy-makers, researchers, educators and wider communities of interest across the world, as the study of them has emerged as critical to our understanding of economic and social change.
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SSCNR Group B / C Jobs Details 2016 - Last Date 30 Sep 2016
SSCNR Group B / C recruitment has arrived. Read this post to apply in this recruitment. SSCNR Group B / C in the recruitment, candidate of the country can apply. The deadline to apply to the recruitment of SSCNR - 30 Sep 2016. SSCNR Group B / C recruit must have pass to UG PG Degree to apply. SSCNR Group B / C are being taken for recruiting 250 posts.Written Exam Date - Update Soon
SSCNR Group B / C Recruitment 2016
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| |
Post Name
Group B / C
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9300-34800 / 5200-20200
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Feed Type
http://www.venturedeal.com/Search/SearchResultTransactionDetail.aspx?TransactionId=0bb383fd-b76e-41b0-97ce-25dcb49fcdc4&Preview=1 -
8/11/2009 -
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DriveCam -
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8911 Balboa Ave. San Diego, CA 92123 -
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http://www.drivecam.com -
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$19,000,000 -
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LongHorn Steakhouse (Perimeter Parkway)
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09 January 2009
sneak peek and hiatus
happy new year. i hope 2009 has been everything that you all expected. above is a sneak peek of my 7' long that is going to a show called "the domestic life" at the sun valley center for the arts in ketchem, ID
the show includes work by these other amazing artists:
Julie Blackmon
María A. Lopez
Jim Richard
Martha Rosler [ Martha Rosler is someone who i've studied for so long. it's surreal to be in a show with her]
Megan Wilson
and is up from Jan 16- March 21, 2009
AND. .... i know i have been quite out of touch for sometime...and i just wanted to let you know..... there is a good reason for this.
i'm often conflicted about how much to share on this blog. it's private, it's public, who knows who is reading.... and as much as i write about my life and thoughts here, i'm still a fairly private person. i am just going to say that life has thrown me a couple of curve balls this week. and my heart and soul and energy need to be focused elsewhere right now.
if i owe you an email, or have been out of touch i apologize. this trend may continue for awhile - please bear withe me. i will post as i can and have the energy to do so, but i'm not sure how much i can participate elsewhere online. i hope you understand. i have been thinking a lot about all my friends "out here" and have missed knowing what is going on with your lives and look forward to catching up when i can.
if you are "friend/family" on my flickr account i have posted a picture that explains the situation in a bit more detail.
be well.
17 comments:
- wendy said...
much love to you.
- Fri Jan 09, 07:56:00 PM PST
- Shiny Black Shoes said...
Can't wait to see pics of the show! Hope everything is going to be ok!
- Fri Jan 09, 08:10:00 PM PST
- julie said...
you just take care of yourself and be well.
love the angle of the photo of your new piece.
xxx - Sat Jan 10, 01:49:00 AM PST
While I will miss your comments on this page, I understand your need to attend to the "curveballs" that have come your way.
I support your need to invest your time and energy on these.
I hope these are not terribly serious.
I also hope you are seeking and getting support from family and friends who are close to you.
TAKE CARE.... - Sat Jan 10, 05:03:00 AM PST
- Kathleen said...
Love seeing a sneak peak from your new show. I'm sorry to hear you are experiencing some trying times. Whatever is happening I am sure you are handling it with grace. I think these curve balls, while difficult, always happen for a greater purpose. They are the universe's way of opening our eyes and setting us on a path we need to travel. I hope everything and everyone is well in your world. Much love to you dear Lisa.
- Sat Jan 10, 08:13:00 AM PST
- Patricia said...
I love your sneak peek. Can't wait to see more.
I can totally relate with your comments about privacy issues on a blog. I struggle with that almost on everyone of my posts. It's hard to edit and give only a partial picture of my life but at the same time I can't imagine it all being 'out' there.
I hope that whatever it is that is worrying you it gets resolved quickly and with the best of results. - Sat Jan 10, 08:33:00 AM PST
- jenifer74 said...
rest up, take care, & be well lisa. xxx.
- Sat Jan 10, 09:44:00 AM PST
- louise said...
Take all the time you need dear friend. Sending all my love. xo lj
- Sat Jan 10, 04:30:00 PM PST
- comfies said...
sending good and warm thoughts your way, lisa...xox.
- Sat Jan 10, 09:24:00 PM PST
- Esti said...
take care of yourself, lisa. I hope everything goes well in your life :)
- Mon Jan 12, 05:55:00 AM PST
- Anke said...
Sweetest Lisa - I just saw the picture over on flickr and will leave a comment there...wow - 2009 will hold a lot of excitement for your. Take good care of yourself. And thank you for your sweet christmas card...I've been a card slacker as usual, so sorry! But something is on the way... Lots of love, Anke.
- Mon Jan 12, 07:41:00 AM PST
- gracia said...
Ah, dear Lisa... wishing you good health, rest and calm.
big hugs, g xo
(P.S. That is such a beautiful photo of you.) - Mon Jan 12, 10:40:00 PM PST
- sophia said...
always enjoy seeing what you're working on.
hope you will work through whatever you have on your plate. look forward to seeing you when you are ready to come back to this space.
all my best,
sophia - Tue Jan 13, 07:44:00 AM PST
- Venetian Blue said...
I will miss your inspiration and posts but hope that everything is alright with you.
Jacqui - Sat Jan 17, 01:02:00 PM PST
- Katrina said...
take care of your dear self, dear lisa, and post when you feel inspired. we will wait patiently until your attention might turn back to this amazing corner of the blogosphere. sending nothing but love, love. xoxo, k.
- Tue Jan 20, 04:52:00 PM PST
- life in yonder said...
Ohhh you are such a tease, just showing a tiny piece of something that looks wonderful. Looking forward to we get to see the rest (...if we do?)
- Wed Jan 28, 09:05:00 AM PST
- stephanie levy said...
Hi Lisa,
Just wanted to touch base. Good luck with all of what is going on for you. I have had a long break as well.
I did want to let you know that I have compiled all of the "artists who blog" interviews (older and newer posts, your interview included of course) onto a new site: www.artistswhoblog.blogspot.com
I felt like the interviews needed their own space.
Take care and it's always nice to hear from you!
Stephanie - Sun Feb 01, 03:48:00 AM PST


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Red Lodge names four finalists for Chief's position
After 59 applicants, 7 from Montana, the City of Red Lodge has named four finalists for the posi t ion of Red Lodge police chief. The four candidates will be in Red Lodge for a public meet and greet at the Elks on May 21 from 5 p.m. - 7 p.m.
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On May 22 the candidates will be interviewed. Each interview panel will consist of three or four people and will include: professional panel; community panel; city council panel and mayor panel.


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Bhubaneswar, June 3 (IANS) There is an urgent need to enhance India's agricultural productivity and develop strong forward-backward linkages along the entire agri-value chain, considering the rising demand of food products, an industry association said Monday.
Despite record food grain production during the course of past few years, the share of agriculture and allied sectors in India's gross domestic product (GDP) declined by over 4.5 per cent between 2004-05 and 2010-11, Associated Chambers of Commerce and Industry of India (Assocham) said here in a release.
The share of agriculture and allied sectors in the gross state domestic product (GSDP) of top 19 states in India declined significantly during the aforesaid five-year period, thereby registering a fall ranging between about two to about 12 per cent in the GSDP, Assocham said citing the finding of a sector specific analysis it carried out recently.
Share of agri and allied sectors in the GSDP has fallen drastically in Bihar (12 per cent fall), Punjab (nine per cent fall), Uttar Pradesh (seven per cent), Haryana (six per cent), Madhya Pradesh (five per cent), West Bengal (six per cent) and Odisha (six per cent). These states, the major agriculture producing states in India, have registered a drop ranging between 5-12 per cent, it said.
"Jharkhand is the only state across top 20 states in India to have witnessed a surge of over three per cent and about 11 per cent in the share of agriculture-allied activities and services sector respectively in its GSDP," Assocham secretary general D.S. Rawat said in a release.
Expressing concern over decline in the share of agri-allied activities in the GSDP of almost all the states, Rawat said, "This calls for increased investments in research and development for speedy improvement in yield, besides, addressing infrastructure requirements in storage, communication, roads and market in the agriculture sector must also be prioritised."
"The government's decision to allow Foreign Direct Investment (FDI) in multi-brand retail would improve agriculture marketing, attracting significant investments in back-end supply chain and promote cluster farming in the long run considering that large number of farmers in India have small land holdings," added Rawat.
"There is an urgent need to enhance agricultural productivity and develop strong forward-backward linkages along the entire agri-value chain considering rising demand of food products" he said.


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Aug 7 2012, 11:09 PM | #1 |
Junior Member
Join Date: Aug 2012
Location: S
Gender: F
Fan of: Crystal Singer Trilogy
Now Reading: Hunger Games
Anyone else wish we had known more about Shillawn? Was he happy in research? Was he disappointed not to become a singer? Did him and Rimbol continue to meet up and hang out?
Aug 8 2012, 05:57 PM | #2 |
Ballybran Resident
Tuner Join Date: Mar 2008
Location: Somewhere in the USA
Gender: F
Fan of: Nimisha's Ship
Now Reading: Crystal Line
Re: Shillawn
I'll agree. I've always wondered. I suppose the way that society had developed it was unlikely for him to remain friends with the rest of his class, but a bit about him somewhere (developing a new use for crystal?) would have been interesting.
Kevia |
Aug 10 2012, 08:49 PM | #3 |
Junior Member
Join Date: Aug 2012
Location: S
Gender: F
Fan of: Crystal Singer Trilogy
Now Reading: Hunger Games
Re: Shillawn
You're absolutely right, the way their society worked it would've been impossible for them to remain friends. I was hoping all the way until the end though that there might be some mention of him. Maybe someone out there will write some fanfiction about Shillawn as a researcher... but I have to admit it doesn't sound that exciting. I always felt compassion towards him though, he seemed so concerned that people weren't nice, he was always trying to be helpful... poor guy.
Tags |
crystal singer, shillawn |
Thread Tools | |


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Multiple clip launch volume issue
When I am playing one or two clips together the volume is fine but when I add my whole scene (about 6 or 7 clips together) the volume seems to go down on everything across the board. I want to keep my main starting clip just as loud when the others are added but the peak of the volume never seems to reach where I have my sliding point set on any track after I add more than a few tracks together. Is there something I maybe clicked or overlooked? thank you in advance for any help!
1 answer
Mark Onecontribution
68 answers
156 votes received1 voteAssuming that when you say 'seems to go down' that it actually isn't going down in real terms (ie the peak value on the VU for that track remains the same). What you're experiencing is the masking of sounds due to the competition for frequencies between parts and the increased overall loudness of the sound due to layering of multiple parts.
If this is the case then you need to learn about mixing (volume, eq and pan)
It could be that you have a compressor on the master track. As you increase the input volume by launching more clips you increase the amount of compression.
If this is the case then you need to learn about compression.
If this is not the case then strange things are going on and I suggest you submit a bug report to Ableton.
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About QVH
Queen Victoria Home is located in Lindisfarne, a suburb of Hobart, on the Eastern Shore of the Derwent River, less than ten minutes from the City Centre.
The philosophy of the Board and staff of the Home is to actively support the independence of each resident. Care is offered in a manner that will preserve the dignity and self esteem of residents, by staff who are conscious of their roles as facilitators of independence.
Queen Victoria Home is a Not for Profit community based organisation, operated by a Board on a not-for-profit basis.
Queen Victoria Home is home to over 190 residents from all walks of life. It is licensed for 139 residents receiving government subsidised residential aged care.
Supporting a philosophy of "ageing in place", Queen Victoria Home caters for a comprehensive range of differing care needs. From Low Level (Hostel) in one of our Lincoln Street units through to High Level (Nursing) care in a private en-suite room within the Home itself, we can tailor our care to exactly meet your on-going needs.
The Home also operates 24 independent living units known as "Victoria Mews", 10 independent living apartments "Victoria Apartments" within the QVH complex and independent living units at Victoria Court, a short distance away.
Our Lincoln Street units often suit couples with differing care needs. Assistance and help can be arranged on a fee-for-service basis.
Queen Victoria Home employs over 180 staff members to provide care and associated services to our residents.
The Home is accredited by the Aged Care Standards and Accreditation Agency.
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QVH Annual Report 2014-2015.pdf
Find out more …History of the Queen Victoria Home
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Principal Analyst: FP&A - Mountain Finance
Apply now »Date: Mar 7, 2017
Location: Broomfield, CO, US
Reach Your Peak at Vail Resorts. You're someone who pushes boundaries and challenges the status quo. You're brave, ambitious and passionate in everything you do. And we want you on our team. Pursue your fullest potential and never settle in the quest to deliver extraordinary guest service. Join one of the world's 50 most innovative companies as named by Fast Company, and re-imagine a mountain resort experience with us. Welcome to Vail Resorts. Reach Your Peak.
Welcome to Vail Resorts. Reach Your Peak.
Principal Analyst, Mountain Finance Broomfield
The Finance Team is committed to Building Leaders and Driving Value. The Mountain Finance team performs comprehensive financial planning, forecasting and analysis to enable the company to align its resources with the achievement of its strategic goals - both long term and short term. The team works closely with the resort finance and leadership teams, along with the broader Finance organization in Broomfield. This position will report to the Director of Mountain Finance and support the major Financial Planning & Analysis functions within the company.
Essential job responsibilities include expertise in the Summer, Ski School and Lift Revenue lines of business in the Mountain segment, specifically as relates to the following:
- Delivering business insights by:
- Providing cross-resort comparisons and analytics
- Analyzing trends in the business to support decision making
- Evaluating labor and expense margins and cost saving opportunities
- Execute value-added analysis and decision support for business projects and initiatives
- Review and own major financial planning processes (operating budget, capital budget, forecasts)
- Develop finance & business presentations for Mountain leadership, Executive Committee and Board of Directors that can effectively summarize materials into key assumptions, risks/opportunities and decision points
- Coordinate all aspects of cross-resort reporting, including standardization of materials and ensuring consistency in reporting
- Assist with the reporting for executive dashboards, business intelligence and other operational analytics
5+ years experience (or 3 years equivalent with MBA or other graduate degree) in finance with demonstrated success in financial modeling and analysis. The ideal candidate should have experience coordinating all financial planning and analysis functions, including annual budget, capital budgeting, long-term strategic planning and resource allocation processes.
Additionally the ideal candidate should have:
- Brave, Ambitious and Courageous
- Outstanding academic credentials
- Strong project management skills
- Excellent individual initiative and objective-oriented drive
- Ability to multi-task and manage numerous simultaneous priorities
- Outstanding problem solving skills
- A record of accomplishment and excellence
- Highly collaborative team approach to work
- Ability to adapt to and excel in a fast-paced environment
- High energy and the ability to work highly independently
- Expertise in quantitative analysis and presentation. High degree of proficiency with Excel and PowerPoint (PeopleSoft also desirable)
We offer a variety of career opportunities at our world-class resorts and corporate headquarters near Boulder, Colorado in fields like Finance & Accounting, Human Resources, Information Technology, Legal, Public Affairs & Sustainability, Marketing, Sales & Communications and more. Our corporate team shares both a passion for the outdoors and a drive to re-imagine the mountain resort experience around the world. Learn more at www.vailresortscareers.com
Vail Resorts is an equal opportunity employer. Qualified applicants will receive consideration for employment without regard to race, color, religion, sex, national origin, sexual orientation, gender identity, disability, protected veteran status or any other status protected by applicable law.
Requisition ID 133056
Nearest Major Market: Denver


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Comotomo Natural-Feel Pure Medical Grade Silicone Baby Bottle - Green - 5 oz
Make the transition from breast to bottle smooth and simple with the Comotomo Natural-Feel Silicone Baby Bottle - Green - 5 oz. Babies can be extremely picky, so Comotomo's innovative design mimics natural breastfeeding as closely as possible. Some have called this bottle "breastfeeding in a bottle", but Comotomo simply calls it the next best thing to mom. The nipples on this bottle are naturally shaped, just like a mother's breast, and they're made of soft, pliable silicone - it's as close to real skin as you can get! To help babies latch properly, this bottle is also designed with a super-wide mound to help your little one make a seamless switch. In addition to naturally-shaped nipples, the bottle itself is rounded, soft, and squeezable, and also made of silicone, so it feels like skin, too. If there were any worries about the safety of this bottle, you can rest assured that 100% medical-grade hygienic silicone is one the safest materials available. No change of the silicone breaking down or leaching into your baby's milk. While this bottle would make any baby happy, it's ideal for babies who are having a bit of trouble transitioning from nursing to bottle feeding. These bottles are equipped with not one, but two brilliantly designed vents which prevent colic and guard against messy leaks. These vents completely eliminate additional air intake, so you can say goodbye to colic. This bottle also has perks for parents. The wide-neck design requires no brush and no stress to wash. Plus, silicone is extremely resistant to heat, so you can sterilize these bottles by boiling or even toss them in the dishwasher. Easy, peasy. Please note that the 5oz bottles come with truly slow flow nipples (1 hole), which are specially designed to feed newborns up to 3-month-old babies.
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My 1 month old, exclusively breastfed baby took to this bottle without skipping a beat on his first try. I am only gone from baby twice a week, so bottle feeding is a rare occurrence. I needed a bottle that would be as similar to breastfeeding as possible. This bottle is absolutely the best I have found. The nipple is truly soft and mimics momma's skin better than any other breastfeeding friendly bottle we have tried. It is shaped so that baby can feed just like when nursing and the "latch" on the bottle is very easy for baby. The only complaint is that when the milk in the bottle gets below 1 ounce left, you have to tip it almost vertical (so baby feeds lying on his back to drink the rest). Most exclusively BF babies feed best from a bottle when sitting up and having the liquid in the bottle stay horizontal while eating. Regardless, I highly recommend this to mommas who need that "occasional" bottle for a date night out or those who are returning to the workplace.
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Travel tidily.
If you're sick of the clothes-explosion that usually happens as soon as you get to your destination and need to change, the Eagle Creek Pack-It Starter Set will tote your travel togs in organized fashion. This hat-trick of clothing holders offers the same storage as Eagle Creek's Pack-It Specter Starter Set, just made with a different material that isn't quite as ultralight as the Specter. This stunning threesome is made from 300D polyester micro-weave for robust protection. The half cube, cube, and garment folder organize your items, and quick-grab handles make it easy to snatch your stored socks and run, in the event you find yourself on the lam and in need of clean socks.
- 300D polyester micro-weave
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I love the pack-starter kit. It makes packing so much easier than the traditional packing experience. Shirts are easily folded and transported without too many wrinkles. T-shirts and socks have their own place. If you have Eagle Creek luggage this kit will fit right in. Everything stays snug and doesn't move.


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Spike activation of the motoneurons innervating uropod muscles in crayfish is controlled by anaxonic interneurons located within the terminal (the 6th abdominal) ganglion. These neurons do not generate spikes either spontaneously at the resting potential level or in response to current injection of either polarity. Yet the change in the membrane potential… (More)
More than half of the identified ascending interneurons originating in the terminal abdominal ganglion of the crayfish received inhibitory sensory inputs from hair afferents innervating the tailfan on the side contralateral to their main branches. Biochemical aspects of this transverse lateral inhibition of ascending interneurons were examined by the use of… (More)
Unilateral mechanical stimulation of a uropod elicited an avoidance reaction in the crayfish Procambarus clarkii. Depending upon the animal's size, either one of two alternative behavioral acts emerged as the avoidance reaction to similar stimuli. A stationary resting posture of the crayfish and a passive extension of the abdomen were prerequisite… (More)
The occurrence of the uropod steering response as one of the equilibrium reflexes to body rolling in crayfish is significantly facilitated if the stimulus is given while the animal is performing the abdominal posture movement. This facilitation of the descending statocyst pathway by the abdominal posture system takes place between the uropod motor neurons… (More)
A characteristic physiological property of the neuromuscular junction between giant motor neurones (MoGs) and fast flexor muscles in crayfish is synaptic depression, in which repetitive electrical stimulation of the MoG results in a progressive decrease in excitatory junction potential (EJP) amplitude in flexor muscle fibres. Previous studies have… (More)
Uropod motor neurons in the terminal abdominal ganglion of crayfish are continuously excited during the abdominal posture movement so that subthreshold excitatory postsynaptic potentials from the descending statocyst pathway can elicit spike activity in the motor neurons only while the abdominal posture system is in operation. Local nonspiking interneurons… (More)
refers to surgical treatments that impose less impact on the human body. For example, surgical technique with smaller incisions would be less invasive, and could be expected to result in effects like a reduced burden on the patient, shortened hospital stay, and better post-operative recovery period. However, remote operation is based on limited information,… (More)
1. Each abdominal ganglion of the crayfish contains peripheral inhibitors of the fast flexor muscles. These flexor inhibitors (FIs), which can effectively inhibit tension development in the tailflip powerstroke muscles, are excited by a delayed central pathway from the same giant axons which trigger escape (33). The FIs also received sensory input, which… (More)


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Sero and serenity smash repairs did a great job repairing the paint damage on my car. The car looks brand new.
My car is a Holden Statesman special vehicle 1997. It had damage to the front and back. Sero gave a competitive quote explaining how he was going to replace the damage. He did an excellent job. I am exceedingly happy with the result. He delivered the car in a brand new conditi..
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Holden Caprice front driver side damage to bonnet, front bumper, front guard, driver side panel, driver side headlight. This is all the damage I can see. It drives fine. Look forward to your assist...
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text: Welcome to Black Bat squadron's Interweb Babble Script site. We are constantly working on content and we hope you will find our scribblings illuminating. various contributers add to our records from the Brig himself, to Lady Beatrice and even occasionally my good self, Flight Sergeant Ignatius Pew (BBS Librarian). |


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0 ssdeep 9 5 Years Ago i am doing a project in which i simulate symmetric encryption in routers.so hav to store secret keys for mac encryption in a symmetric matrix.how do i do it?????????should i convert them to strings and then store strings in a matrix??????? URGENT HELP NEEDED!!!!!!!!! cryptography java key mac
0 NormR1 563 5 Years Ago There is too much jargon in your question and not enough java. A lot depends on how you want to access the stored data and what you want to do with it while it is stored.
0 OPDiscussion Starter ssdeep 9 5 Years Ago okay,there is a SecretKey class in javax.crypto,i want to store a 2-D array of such keys, like i want to declare "SecretKey key[8][8]" so that key[j]=key[j] therefore the key between router-i and router-j is the same and i can perform symmetric encryption.
0 NormR1 563 5 Years Ago Can you explain what your problem is? Is it a logic problem with controlling the indexes for the contents of a two dimensional array? How do you determine the indexes you want to store the data at?
0 OPDiscussion Starter ssdeep 9 5 Years Ago lets say i hav a list of routers from 0 to 7(8 routers),in a 2-D array of size 8X8 i store SecretKey's.I use symmetric encripton so if i am sending a packet from router-i to router-j at router-i i use secretkey[j] to perform encryption at router-j i perform decryption by using secretkey[j].


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Laura Geller Spackle Mist.Prime, hydrate, and set your make-up with just one spray. This multi-tasking mist instantly absorbs into skin to create a perfect canvas for extended make-up wear and can also be used over make-up for a flawless finish. Soothing Aloe Vera Extract and Vitamin B5 help keep skin hydrated, while refreshing Cucumber Extract helps to reduce puffiness. Silicone and oil-free.
- All skin types
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Capsaicin is the substance in chili peppers that gives them their heat,1 but capsaicin has a lot more to offer than just spicing up your meals. In fact, it's a powerful natural pain reliever2 that's been used to help control joint and muscle discomfort for centuries.3 Substance P is a chemical in ... Read More ›
muscle pain
September 1, 2016
Study links widely prescribed pain pill to birth defects
Is there anything more exciting than the birth of a child? If there is, I sure don't know what it is. Welcoming a new life to the family—whether you're a parent, grandparent, aunt, uncle or sibling—is a joyous occasion. We all just want one thing, and that's for the little one to come into this ... Read More ›
October 3, 2016
Statins side effects: Statin drugs trigger painful autoimmune condition
If you or a loved one has ever been on a statin drug I probably don't need to tell you about the muscle aches and pains that can sometimes strike out of nowhere when you're on them. In fact, when I talk with folks about statin side effects, it's often top on people's lists of concerns. Maybe you ... Read More ›
September 14, 2016
Could your artificial sweetener be causing muscle pain?
I'm no fan of the artificial sweetener aspartame. Not only is there no good evidence that artificial sweeteners aid weight control, there is also evidence linking aspartame to adverse effects on health. For example, aspartame liberates methanol into the body which can be converted to ... Read More ›
September 14, 2016
Lights powerful painkilling properties
I am writing this on a train, and as I look out of the window I can see the British West Country go by. It's bathed in sunlight. And this stunning day reminds me of the last few days we've had here in the UK that have been cold, wet and grey. The general lack of sunlight during the winter months can ... Read More ›


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