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Article
The role of multiple microscopic mechanisms in cluster interface evolution
JOURNAL OF DIFFERENTIAL EQUATIONS
  • G Karali
  • MA Katsoulakis, University of Massachusetts - Amherst
Publication Date
2007
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=μσκ, 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.
Pages
418-438
Citation Information
G Karali and MA Katsoulakis. "The role of multiple microscopic mechanisms in cluster interface evolution" JOURNAL OF DIFFERENTIAL EQUATIONS Vol. 235 Iss. 2 (2007)
Available at: http://works.bepress.com/markos_katsoulakis/27/