Conserved noise restricted-solid-on-solid model on fractal substrates

Abstract

A conserved noise restricted solid-on-solid model on both a Sierpinski gasket substrate and a checkerboard fractal substrate is studied. The interface width W grows as t(β) at early time t and becomes saturated at L(α) for t >> L(z), where L is the system size. We obtain β ≈ 0.0788, α ≈ 0.377 for a Sierpinski gasket, and β ≈ 0.100, α ≈ 0.516 for a checkerboard fractal. The dynamic exponent z ≈ 4.79 for a Sierpinski gasket and z ≈ 5.16 for a checkerboard fractal are obtained by the relation z = α/β. They satisfy the scaling relations 4 α + 2 d(f) = z and z = 2 z(rw), where z(rw) is the random-walk exponent of the fractal substrate. A fractional Langevin equation is introduced to describe the model.

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

“…(ii) For m = 2, our results here are consistent with the theoretical and numerical work of Ref. [22]. (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.…”

Discrete restricted curvature model with diffusion on a fractal substrate

“…Recently, various growth models on fractal substrates have been studied in connection with the related Langevin equations [12][13][14][15][16]. Here, we study the CNRC model on a fractal substrate.…”

Surface growth on diluted lattices using a restricted curvature model

“…Monte Carlo simulations were carried out on various deterministic fractal substrates for the equilibrium RSOS model [18], CNRSOS model [23], and RC model [24], and the results were found to agree well with the predictions for all cases and, based on the results, Kim and Kim conjectured that the power counting predictions might be exact [23]. On the other hand, on random fractal substrates, i.e.…”

“…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]. The main idea for this modification was motivated by the EW equation [18].…”

“…The fractional HM equation for n = 2 with a conserved noise is known to describe growth by the conserved-noise restricted solid-on-solid (CNRSOS) model on fractal substrates [23].…”