Random walk diffusion model with restricted solid on solid condition on fractal substrates

Abstract

A random walk diffusion model with a restricted solid-on-solid (RSOS) condition is studied on both Sierpinski gasket and checkerboard fractal substrates. A deposited particle is allowed to hop randomly until finding a site satisfying the RSOS condition. The interface width W of the model grows as at the beginning and becomes saturated at for , where L is the system size. We obtain , , and the dynamic exponent for a Sierpinski gasket substrate. A scaling relation is well satisfied, where zrw is the random walk exponent of the fractal substrate. Also, they are in good agreement with the predicted values of a suggested Langevin equation.