Diffusion-limited aggregation on two-dimensional percolation clusters

Abstract

Diffusion-limited aggregation has been simulated on two-dimensional percolation clusters with the use of a modified Witten-Sander model. At low particle concentrations, the aggregate cluster has a fractal dimensionality of about 1.4, substantially lower both in absolute and relative terms than the dimensionality of a Witten-Sander cluster on a two-dimensional lattice ($\ensuremath{\approx}\frac{5}{3}$). The lower fractal dimensionality is attributed, at least in part, to the higher effective dimensionality (${D}_{t}$) of a random walk on a percolation cluster (${D}_{t}\ensuremath{\simeq}2.5\ensuremath{-}2.8$) compared to a random walk on a nonfractal lattice (${D}_{t}\ensuremath{\simeq}2.0$).