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

초록

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 t(beta) at the beginning and becomes saturated at L-alpha for t >> L-z, where L is the system size. We obtain beta = 0.27 +/- 0.01, alpha = 0.92 +/- 0.02, and the dynamic exponent z approximate to 3.4 for a Sierpinski gasket substrate. A scaling relation z + alpha = 2z(rw) is well satisfied, where z(rw) is the random walk exponent of the fractal substrate. Also, they are in good agreement with the predicted values of a suggested Langevin equation.

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