Discrete restricted curvature model with diffusion on a fractal substrate

초록

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 t(beta) early on, with beta approximate to 0.221(8) and becomes saturated at L-alpha with alpha approximate to 1.54(2), where L is the system size. They satisfy a scaling relation 2 alpha + d(f) = 2z(rw) very well, where z(rw) and d(f) are the random walk exponent and the fractal dimension of the substrate, respectively. Also, a possible Langevin equation is introduced to describe the model.

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