0.0 0.1 0.2 0.3 h=3 0.4 < (V/N) < 0.9 T > T xx yy 0.0 0.5 1.0 1.5 2.0 2.5 h=3 0.4 < (V/N) < 0.9 P > P xx yy Figure 4: Volume dependence of the temperature tensor (left) and the pressure tensor (right) in the stationary shockwave of Figure 3, as calculated with molecular dynamics. Spatial averages have been computed with Lucy’s weight function using a range h = 3, as is discussed in Section II. 0.0 0.1 0.2 0.3 -3 < time < +3 T > T xx yy 0.0 0.5 1.0 1.5 2.0 2.5 -3 < time < +3 P > P xx yy e ρ Figure 5: Stationary temporal profile for the one-dimensional shockwave of Figure 3, using a short-ranged repulsive potential. Spatial averages of the temperatures (left) and the pressures, density, and energy (right) have been computed with Lucy’s weight function using a range h = 3. The initial stress-free cold triangular lattice is compressed to twice the initial density by the shockwave, as in Figure 2. The time origin has been chosen, arbitrarily, close to the shockfront. ρ , u , and e following the motion at velocity u . In the continuum description these field variables are continuous differentiable functions of space and time so that the spatial averaging (necessary to an analysis of molecular dynamics data) is unnecessary. The steady nature of the shock process makes it possible to use either space or time as an independent variable. On the average, the progress of a particle traveling through the shockwave follows from the integral of the flow velocity. To illustrate, consider again