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

TL;DR

This study uses lattice gas automata to simulate 2D site-percolation diffusion, revealing configuration-dependent crossover behavior between diffusion regimes and the impact of ensemble averaging on these phenomena.

Contribution

It demonstrates the configuration dependence of diffusion crossover in 2D percolation lattices using lattice gas automata, highlighting the effects of ensemble averaging.

Findings

Observed anomalous sub-diffusion with decreasing exponent at lower site concentrations.

Detected configuration-dependent crossover between diffusion regimes.

Ensemble averaging removed the observable crossover effects.

Abstract

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.