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On a mean-curvature interface limit from a system of interacting particles

Mathematics Colloquium

On a mean-curvature interface limit from a system of interacting particles
Series: Mathematics Colloquium
Location: MATH 501
Presenter: Sunder Sethuraman, University of Arizona
We discuss a derivation of a continuum mean-curvature flow as a scaling limit of a class of particle systems.  We consider zero-range + Glauber interacting particle systems, where the zero-range part moves particles while preserving particle numbers, and the Glauber part allows creation and annihilation of particles, while favoring two levels of particle density.  When the two parts are simultaneously seen in certain (different) time-scales, and the Glauber part is `bi-stable', a mean-curvature interface flow, between the two levels of particle density, can be captured directly as a limit of the mass empirical density. 
Such a `direct' limit might be compared with a `two-stage' approach:  When the zero-range part is diffusively scaled but the Glauber part is not scaled, the hydrodynamic limit is a non-linear Allen-Cahn reaction-diffusion PDE for the continuum space-time mass density. It is understood in such PDEs, when the `bi-stable' reaction term is now scaled, that the limit of the solutions takes on stable values across an interface moving by a mean-curvature flow.  This is joint work-in-progress with Perla El Kettani, Tadahisa Funaki, Danielle Hilhorst, and Hyunjoon Park.
(Refreshments will be served in the Math Commons Room at 3:30 PM)