Microscopic Shock Structure in Model Particle Systems: The Boghosian-Levermore Cellular Automation Revisited

We carried out new computer simulations of the Boghosian-Levermore stochastic cellular automaton for the Burgers equation. The existence of an extra “conservation law” in the dynamics—even and odd lattice sites exchange their contents at every time step—implies that the automaton decomposes into two independent subsystems; the simulations show that the density from each subsystem exhibits a “shock front” which does not broaden with time. The location of the shock in a particular microscopic realization differs from that predicted by the Burgers equation by an amount which depends only on the initial microscopic density of the particle system, that is, fluctuations in the stochastic dynamics do not affect the shock profile on the time scale considered. This is in complete accord with theoretical expectations. The apparent broadening of the shock in the original Boghosian-Levermore simulations is shown to result from averaging the two subsystem densities.

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