A 2d Monte Carlo Simulation of Diffusion in a Disorder Media

Abstract

In this work, we present 2D Monte Carlo simulations of tracer in disorder media with obstacles distributed randomly. For diffusion of a particle, the mean-square displace ment of the diffusing species is linearly proportional to time for normal diffusion. But in disordered systems anomalous diffusion occurs, in which the means square displacement is proportional to a fractional power of time not equal to one.As the ob stacle concentration approaches the percolation threshold, diffusion becomes more anomalous for long times; the anomalous diffusion exponent increases.Simulation data show anomalous for short times and normal for long times below percolation threshold.Monte Carlo calculations are used to characterize anomalous diffusion for obstacle concentrations between zero and the percolation threshold.In addition,above percolation threshold anomalous for short times but for long time( t), < r2 > approx imate fixed point proportional to mean value of boundary condition.,So the slope oflog < r2 > /t versus logt goes to-1 and dw →.The intersection time from normal to crowded diffusion is the crossover time tCR.