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 tβ at early time t and becomes saturated at Lα for t ≫ Lz in a finite system of lateral size L. We obtain β ≈ 0.331, α ≈ 1.59, and the dynamic exponent z ≈ 4.80 for the fractal substrate. These values are consistent with the estimates \( \alpha = z_{rw} - \frac{{d_f }} {2} \), and z = 2zrw, where zrw and df are the random walk exponent and the fractal dimension of the fractal substrate, respectively. A related fractional Langevin equation is also discussed.