Lattice Gas Automata Simulation of 2D site-percolation diffusion: Configuration dependence of the theoretically expected crossover of diffusion regime

Details Lattice Gas Automata Simulation of 2D site-percolation diffusion: Configuration dependence of the theoretically expected crossover of diffusion regime Lattice Gas Automata Simulation of 2D site-percolation diffusion: Configuration dependence of the theoretically expected crossover of diffusion regime

2010-01-17

arxiv.org/abs/1001.2875v1

Lecture Notes in Computer Science, 5191, pp 274-281, 2008

Nonlinear Sciences

Cellular Automata and Lattice Gases

8 pages, 6 figures

Scientific paper

Theoretical analysis of random walk on percolation lattices has predicted that, at the occupied site concentrations of above the threshold value, a characteristic crossover between an initial sub-diffusion to a final classical diffusion behavior should occur. In this study, we have employed the lattice gas automata model to simulate random walk over a square 2D site-percolation lattice. Quite good result was obtained for the critical exponent of diffusion coefficient. The random walker was found to obey the anomalous sub-diffusion regime, with the exponent decreasing when the occupied site concentration decreases. The expected crossover between diffusion regimes was observed in a configuration-dependent manner, but the averaging over the ensemble of lattice configurations removed any manifestation of such crossovers. This may have been originated from the removal of short-scale inhomogeneities in percolation lattices occurring after ensemble averaging.

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