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

摘要

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.