Random walk diffusion model with restricted solid on solid condition on fractal substrates. (24th November 2017) - Kim, Jin Min
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 t β at the beginning and becomes saturated at L α for t ≫ L z, where L is the system size. We obtain β = 0.27 ± 0.01, α = 0.92 ± 0.02, and the dynamic exponent z ≈ 3.4 for a Sierpinski gasket substrate. A scaling relation z + α = 2 z r w 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.