Motion by Mean Curvature from Glauber–Kawasaki Dynamics

Tadahisa Funaki, Kenkichi Tsunoda

Research output: Contribution to journalArticlepeer-review

Abstract

We study the hydrodynamic scaling limit for the Glauber–Kawasaki dynamics. It is known that, if the Kawasaki part is speeded up in a diffusive space-time scaling, one can derive the Allen–Cahn equation which is a kind of the reaction–diffusion equation in the limit. This paper concerns the scaling that the Glauber part, which governs the creation and annihilation of particles, is also speeded up but slower than the Kawasaki part. Under such scaling, we derive directly from the particle system the motion by mean curvature for the interfaces separating sparse and dense regions of particles as a combination of the hydrodynamic and sharp interface limits.

Original languageEnglish
Pages (from-to)183-208
Number of pages26
JournalJournal of Statistical Physics
Volume177
Issue number2
DOIs
Publication statusPublished - 2019 Oct 1

Keywords

  • Allen–Cahn equation
  • Glauber–Kawasaki dynamics
  • Hydrodynamic limit
  • Motion by mean curvature
  • Sharp interface limit

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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