Extended mode coupling and simulations in cellular-automata fluids.

Abstract

The velocity autocorrelation function (VACF) of lattice-gas cellular-automata fluids has been calculated by mode-coupling (MC) theory for finite systems, including sound modes, and compared with computer simulations on small (N\ensuremath{\simeq}${10}^{3}$) and large (N\ensuremath{\simeq}${10}^{6}$) two- and three-dimensional (3D) systems for reduced densities f ranging from 0.05 to 0.8. For times t up to 6${\mathit{t}}_{0}$ (mean free times) the simulated VACF agrees with Boltzmann relaxation. In 2D the agreement with MC theory is excellent for t>9${\mathit{t}}_{0}$ and has been tested over intervals of several acoustic traversal times. In 3D the agreement is still good, but sets in after much larger times (150${\mathit{t}}_{0}$ at f=0.1 and 60${\mathit{t}}_{0}$ at f=0.8). However, there are disagreements in the smallest systems at the lowest densities, where the observed VACF at largest times is about 6% (f=0.1) and 9% (f=0.05) larger than the theoretical values.