Diffusion on two-dimensional percolation clusters with multifractal jump probabilities

Abstract

By means of Monte Carlo simulations we studied the properties of diffusion limited recombination reactions (DLRR's) and random walks on two dimensional incipient percolation clusters with multifractal jump probabilities. We claim that, for these kind of geometric and energetic heterogeneous substrata, the long time behavior of the particle density in a DLRR is determined by a random walk exponent. It is also suggested that the exploration of a random walk is compact. It is considered a general case of intersection ind euclidean dimension of a random fractal of dimension DF and a multifractal distribution of probabilities of dimensionsD q (q real), where the two dimensional incipient percolation clusters with multifractal jump probabilities are particular examples. We argue that the object formed by this intersection is a multifractal of dimensionsD' q =D q +D F -d, for a finite interval ofq.