In cellular automaton fluids, where binary collision laws admit reflections, the Stosszahl ansatz and the Boltzmann equation are no longer valid at low densities. This is proven for a class of Lorentz gas models, defined on cubic lattices, for which the diffusion coefficient is calculated from a self-consistent ring kinetic equation or effective medium theory. The calculated results are in excellent agreement with results from molecular dynamics simulations over the whole density interval.
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Ernst et al. (1989) studied this question.
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