Motion by Mean Curvature from Glauber-Kawasaki Dynamics with Speed Change

Tadahisa Funaki, Patrick van Meurs, Sunder Sethuraman, Kenkichi Tsunoda

    Research output: Contribution to journalArticlepeer-review


    We derive a continuum mean-curvature flow as a certain hydrodynamic scaling limit of Glauber-Kawasaki dynamics with speed change. The Kawasaki part describes the movement of particles through particle interactions. It is speeded up in a diffusive space-time scaling. The Glauber part governs the creation and annihilation of particles. The Glauber part is set to favor two levels of particle density. It is also speeded up in time, but at a lesser rate than the Kawasaki part. Under this scaling, a mean-curvature interface flow emerges, with a homogenized ‘surface tension-mobility’ parameter reflecting microscopic rates. The interface separates the two levels of particle density. Similar hydrodynamic limits have been derived in two recent papers; one where the Kawasaki part describes simple nearest neighbor interactions, and one where the Kawasaki part is replaced by a zero-range process. We extend the main results of these two papers beyond nearest-neighbor interactions. The main novelty of our proof is the derivation of a ‘Boltzmann-Gibbs’ principle which covers a class of local particle interactions.

    Original languageEnglish
    Article number45
    JournalJournal of Statistical Physics
    Issue number3
    Publication statusPublished - Mar 2023

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Mathematical Physics


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