Discrete restricted curvature model with diffusion on a fractal substrate

Abstract

.A restricted curvature model with diffusion on a Sierpinski gasket substrate is studied. A surface particle is allowed to hop to the nearest neighbor site under the restricted curvature condition. The interface width W grows as tβ early on, with β ≈ 0.221(8) and becomes saturated at Lα with α ≈ 1.54(2), where L is the system size. They satisfy a scaling relation 2α + df = 2zrw very well, where zrw and df are the random walk exponent and the fractal dimension of the substrate, respectively. Also, a possible Langevin equation is introduced to describe the model.