-0.5 -0.3 -0.1 0.1 0.3 -3.5 < x < +3.5 T > T xx yy Q 0.0 0.5 1.0 1.5 2.0 2.5 -3.5 < x < +3.5 P > P xx yy e ρ Figure 3: A snapshot spatial profile of a nominally steady one-dimensional shockwave from molecular dynamics, using a short-ranged repulsive potential. Spatial one-dimensional averages of the temperatures and heat flux (left) and the pressures, density, and energy (right) have been computed with Lucy’s weight function using a range h = 3. The cold zero-pressure, zero- temperature triangular lattice is compressed to twice the initial density ( √ 4 / 3 → 2 √ 4 / 3) by the shockwave, just as in Figure 2. The cold and hot boundary conditions enclosing the shock are equilibrium ones imposed far from the shockfront so that the small-system surface effects complicating the number- dependence of nonequilibrium systems are minimized. In implementing these ideas no arbitrary or artificial assumptions have to be made. All the observed phenomena follow from the assumed form for the interparticle forces. Figures 3, 4, and 5 show typical results from molecular dynamics, as is described in more detail in Section II. Notice that the rise in longitudinal temperature T$_{xx}$ can be much larger and can occur somewhat earlier 12 than that of the transverse temperature T$_{yy}$ . In Section III we discuss the continuum mechanics of the same shockwave problem. Evidently any continuum formulation must first of all include the continuum conservation laws for mass, momentum, and energy: Here the pressure tensor P and heat flux vector Q measure the momentum and energy fluxes in the local “comoving” (or “Lagrangian”) coordinate frame moving with the mean velocity u ( x ). Now the superior dot notation is used to indicate the time derivatives of ˙ ρ = − ρ ∇ · u ; ρ ˙ u = −∇ · P ; ρ ˙ e = −∇ u : P − ∇ · Q .