Larger curvature model on a Sierpinski gasket substrate

Abstract

We consider a larger curvature model on a Sierpinski gasket substrate, where a dropped particle is deposited on a larger curvature site. The interface width W of the model grows as t (beta) at early time t and becomes saturated at L (alpha) for t a parts per thousand << L (z) in a finite system of lateral size L. We obtain beta a parts per thousand 0.331, alpha a parts per thousand 1.59, and the dynamic exponent z a parts per thousand 4.80 for the fractal substrate. These values are consistent with the estimates , and z = 2z (rw) , where z (rw) and d (f) are the random walk exponent and the fractal dimension of the fractal substrate, respectively. A related fractional Langevin equation is also discussed.