The relaxation of a family of broken bond crystal surface models

TL;DR

This paper investigates the continuum limits of various crystal surface relaxation models, combining computational and theoretical methods to identify the appropriate PDEs and scaling regimes, and exploring large-scale behaviors.

Contribution

It clarifies the correct PDEs and scaling regimes for a family of crystal surface models, integrating computational experiments with theoretical analysis.

Findings

Derived several PDE limits for the models

Clarified the correct surface tension in PDEs

Explored qualitative large-scale behaviors

Abstract

We study the continuum limit of a family of kinetic Monte Carlo models of crystal surface relaxation that includes both the solid-on-solid and discrete Gaussian models. With computational experiments and theoretical arguments we are able to derive several partial differential equation limits identified (or nearly identified) in previous studies and to clarify the correct choice of surface tension appearing in the PDE and the correct scaling regime giving rise to each PDE. We also provide preliminary computational investigations of a number of interesting qualitative features of the large scale behavior of the models.