Surface morphology coarsening in a nonlocal system

TL;DR

This paper compares the steady-state and coarsening behavior of a surface in local and nonlocal systems, revealing that the long-range interaction radius significantly influences surface morphology evolution.

Contribution

It introduces a nonlocal generalization of a surface evolution model and analyzes how the interaction radius affects steady states and coarsening dynamics.

Findings

Steady-state amplitude is sensitive to the interaction radius.

Coarsening rate increases as the interaction radius decreases.

Nonlocal effects significantly alter surface morphology evolution.

Abstract

Direct comparison is made of the steady-sates and coarsening dynamics in a local system and its nonlocal generalization. The example system is the surface of a solid film in a strong electric field; the morphological evolution of the surface is described, in the long-wavelength approximation, by the amplitude PDE for the film height function. It is shown that the amplitude of the steady-state and the coarsening rate of the surface structure are very sensitive to the radius of the long-range interaction, and that both quantities increase as the radius decreases.