The role of multiple microscopic mechanisms in cluster interface evolution

17Citations
Citations of this article
7Readers
Mendeley users who have this article in their library.

Abstract

In this paper we discuss mesoscopic models describing pattern formation mechanisms for a prototypical model of surface processes that involves multiple microscopic mechanisms. We focus on a mean field partial differential equation, which contains qualitatively microscopic information on particle-particle interactions and multiple particle dynamics, and we rigorously derive the macroscopic cluster evolution laws and transport structure. We show that the motion by mean curvature is given by V = μ σ κ, where k is the mean curvature, σ is the surface tension and μ is an effective mobility that depends on the presence of the multiple mechanisms and speeds up the cluster evolution. This is in contrast with the Allen-Cahn equation where V = κ. © 2007 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Karali, G., & Katsoulakis, M. A. (2007). The role of multiple microscopic mechanisms in cluster interface evolution. Journal of Differential Equations, 235(2), 418–438. https://doi.org/10.1016/j.jde.2006.12.021

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free