Short-range stationary patterns and long-range disorder in an evolution equation for one-dimensional interfaces

TL;DR

This paper introduces a new local evolution equation for one-dimensional interfaces affected by ion beam sputtering, revealing a coexistence of short-range order and long-range disorder with analytical insights.

Contribution

It presents a novel evolution equation and numerical analysis showing unique pattern formation behaviors not previously observed in surface dynamics.

Findings

Development of a new local evolution equation for interfaces.

Observation of interrupted coarsening with stable patterns.

Analytical estimates for pattern wavelength and growth velocity.

Abstract

A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell pattern develops with constant wavelength and amplitude at intermediate distances, while the profile is disordered and rough at larger distances. Moreover, for a wide range of parameters the lateral extent of ordered domains ranges up to tens of cells. This behavior is new in the context of dynamics of surfaces or interfaces with morphological instabilities. We also provide analytical estimates for the stationary pattern wavelength and mean growth velocity.