Nonuniversal effects in mixing correlated-growth processes with randomness: Interplay between bulk morphology and surface roughening

TL;DR

This paper develops a continuum stochastic growth model for competitive surface growth processes combining random deposition with correlated growth, revealing how bulk morphology influences surface roughening through nonuniversal scaling factors.

Contribution

It introduces the effective probability $p_{eff}$ linking bulk morphology to surface roughening and derives a universal scaling framework for mixed growth processes in (1+1) dimensions.

Findings

Effective probability $p_{eff}$ depends on bulk morphology.

Universal scaling functions collapse data for all $p$ in (0,1].

Model extends to higher dimensions and multiple components.

Abstract

To construct continuum stochastic growth equations for competitive nonequilibrium surface-growth processes of the type RD+X that mixes random deposition (RD) with a correlated-growth process X, we use a simplex decomposition of the height field. A distinction between growth processes X that do and do not create voids in the bulk leads to the definition of the {\it effective probability} $p_{\mathrm{eff}}$ of the process X that is a measurable property of the bulk morphology and depends on the {\it activation probability} $p$ of X in the competitive process RD+X. The bulk morphology is reflected in the surface roughening via {\it nonuniversal} prefactors in the universal scaling of the surface width that scales in $p_{\mathrm{eff}}$. The equation and the resulting scaling are derived for X in either a Kardar-Parisi-Zhang or Edwards-Wilkinson universality class in $(1+1)$ dimensions, and illustrated by an example of X being a ballistic deposition. We obtain full data collapse on its corresponding universal scaling function for all $p \in (0;1]$. We outline the generalizations to $(1+n)$ dimensions and to many-component competitive growth processes.