Shock fluctuations in one-dimensional lattice fluids

We present results of computer simulations of the motion of shock fronts in a variety of one-dimensional stochastic lattice models with parallel and serial dynamics, infinite and finite temperatures, and ferromagnetic and antiferromagnetic particle interactions. We find that fluctuations in the shock location, about an average determined by evolving an ensemble of systems with the same initial conditions, generically grow in time like ${\mathit{t}}^{1/3}$. We discuss the robustness of the ${\mathit{t}}^{1/3}$ growth and determine the density dependence of the coefficient in a simple case. We compare this with models where the dynamics are specially tuned so that the growth is reduced to ${\mathit{t}}^{1/4}$, and with the situation where the ensemble members have different initial conditions, in which case the growth is like ${\mathit{t}}^{1/2}$.