Interplay of instabilities in mounded surface growth

TL;DR

This paper investigates how competing linear and nonlinear instabilities influence mound formation in one-dimensional surface growth, revealing a phase transition and different coarsening behaviors depending on dominant instability.

Contribution

It introduces a numerical study of a conserved growth model showing a phase transition between two mounded states with distinct coarsening dynamics.

Findings

Identification of a non-equilibrium phase transition between two mounded states

Dependence of steady-state configuration on dominant instability

Detailed analysis of coarsening behavior in different phases

Abstract

We numerically study a one-dimensional conserved growth equation with competing linear (Ehrlich-Schwoebel) and nonlinear instabilities. As a control parameter is varied, this model exhibits a non-equilibrium phase transition between two mounded states, one of which exhibits slope selection and the other does not. The coarsening behavior of mounds in these two phases is studied in detail. In the absence of noise the steady-state configuration depends crucially on which of the two instabilities dominates the early time behavior.