A fractal langevin equation describing the kinetic roughening growth on fractal lattices

Abstract

rw rw (z rw is the random walk exponent on the lattice) is proposed to describe the kinetic roughening growth on fractal substrates. The scaling relation α + = z z rw can be obtained. Kinetic Monte Carlo simulations are carried out for Restricted Solid-on-solid model and Etching model growing on various fractal substrates, and the results prove this scaling relation.

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

“…Recently various growth models on fractal substrates have been studied in connection with the related Langevin equations [14][15][16][17][18][19][20][21][22][23][24]. As shown in figure 1, Sierpinski gasket is composed of the three corner sites and the inner sites.…”

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].…”