BIASED DIFFUSION ON RANDOMLY GROWN PERCOLATING CLUSTERS

Abstract

Effect of bias on random walk diffusion on percolating system is examined in the framework of Monte Carlo simulation and recent theories. This chapter discusses the effects of bias on random walk diffusion on percolating system in the framework of Monte Carlo simulation and recent theories. The idea behind computer simulation described in the chapter is very simple. First, the sample was prepared by randomly occupying a fraction of a cubic lattice, which is called lattice realization. An occupied site called local origin was selected randomly and a diffuser, that is, blind ant was placed on it to execute its random walk with hopping probabilities in positive directions and in opposite directions. With this biased prescription, a neighboring site was chosen randomly and the diffuser was moved to this site if it was occupied otherwise it stayed at its old position. Each attempt, whether successful, was counted as a one-time step. Keeping track of time, the position of diffuser was updated to calculate root mean square (rms) displacement from its local origin. To get a reliable estimate of the rms, displacement simulation was performed on several independent lattice realizations each with many independent local origins. Fitting the data with power law equation, the effective exponent was calculated. The chapter also highlights the complexities and richness of the biased diffusion problems via illustrating various crossover effects in time, bias, and concentration.