Discrete restricted curvature model with diffusion on a fractal substrate

Abstract

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 β early on, with β ≈ 0.221(8) and becomes saturated at L α with α ≈ 1.54(2), where L is the system size. They satisfy a scaling relation 2α + 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.

Dynamic scaling behaviors of linear fractal Langevin-type equation driven by nonconserved and conserved noise

“…(iii) For m = 3, there exists the scaling relations 2α + d f = 2z rw and z = 3z rw , which are supported by the numerical data of Ref. [23].…”

Surface growth on diluted lattices using a restricted curvature model

“…where d is the substrate dimension. Recently, there have been eorts to understand the growth dynamics on fractal substrates [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The linear continuum equations on various fractal substrates were modified by replacing ∇ h n 2 with ∇ h nz rw , and the fractional Langevin equations were proposed [18,23].…”