Intrinsic geometry approach to surface kinetic roughening

TL;DR

This paper introduces an intrinsic geometry model for surface kinetic roughening that avoids common approximations, revealing KPZ scaling behavior in complex interface morphologies through advanced numerical simulations.

Contribution

It presents a novel intrinsic geometry framework for modeling surface roughening, capable of handling large slopes and overhangs, and explores its implications on KPZ universality.

Findings

KPZ scaling observed for large system sizes and noise levels

Model supports interfaces with large slopes and overhangs

Family-Vicsek scaling confirmed in simulations

Abstract

A model for kinetic roughening of one-dimensional interfaces is presented within an intrinsic geometry framework that is free from the standard small-slope and no-overhang approximations. The model is meant to probe the consequences of the latter on the Kardar-Parisi-Zhang (KPZ) description of non-conserved, irreversible growth. Thus, growth always occurs along the local normal direction to the interface, with a rate that is subject to fluctuations and depends on the local curvature. Adaptive numerical techniques have been designed that are specially suited to the study of fractal morphologies and can support interfaces with large slopes and overhangs. Interface self-intersections are detected, and the ensuing cavities removed. After appropriate generalization of observables such as the global and local surface roughness functions, the interface scaling is seen in our simulations to be of the Family-Vicsek type for arbitrary curvature dependence of the growth rate, KPZ scaling appearing for large sytems sizes and sufficiently large noise amplitudes.