Deterministic lattice Lorentz gas. I. Chiral model

The author studies diffusion by using a specific type of cellular automaton, where particles move in an environment of scatterers. The deterministic collision rules, used in the model, give rise to certain difficulties related to nonergodicity. The class of models, introduced by Gunn and Ortuno (1985), also contains the model studied by Gates (1972). Previously developed theory, including the Boltzmann approximation, the ring and repeated-ring approximations and the effective medium approximation (EMA), is generalized for this model. The validity is further investigated using computer simulations. In the presence of reflecting scatterers EMA yields low-density results that show the breakdown of the Boltzmann equation, while they agree quantitatively with the low-density simulations. EMA also agrees with a phase transition that occurs for some parameter choices.