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Theoretical analysis of random walk on percolation lattices has predictedthat, at the occupied site concentrations of above the threshold value, acharacteristic crossover between an initial sub-diffusion to a final classicaldiffusion behavior should occur. In this study, we have employed the latticegas automata model to simulate random walk over a square 2D site-percolationlattice. Quite good result was obtained for the critical exponent of diffusioncoefficient. The random walker was found to obey the anomalous sub-diffusionregime, with the exponent decreasing when the occupied site concentrationdecreases. The expected crossover between diffusion regimes was observed in aconfiguration-dependent manner, but the averaging over the ensemble of latticeconfigurations removed any manifestation of such crossovers. This may have beenoriginated from the removal of short-scale inhomogeneities in percolationlattices occurring after ensemble averaging.

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