Cluster-approximation mean-field theory of a class of cellular automaton models

A cluster-approximation mean-field scheme, which maybe used to describe som e cellular automaton (CA) models, is introduced based on analyzing the evol ution of cluster states. Ln this scheme the description of microscopic proc esses is exact within a cluster, and approximate for the interaction betwee n clusters and the environment. The approach to building the theory is illu strated by a surface-reaction-like CA model very similar to the model of Zi ff, Gulari, and Barshad. A set of equations of motion concerning the evolut ion of microscopic cluster states is derived, and some results from these e quations are given. [S1063-651X(99)05105-3].