# Colloquium: Particle system models for two-dimensional grain boundary coarsening, Joe Klobusicky (RPI).

### Event Description:

Title: Particle system models for two-dimensional grain boundary coarsening.

Abstract: We construct a family of particle systems which model the coarsening of two-dimensional networks whose edges evolve by mean curvature. The limiting kinetic equations of these models, describing distributions of grain areas and topologies, are shown to be well-posed. Evidence for the exponential convergence of the empirical densities of the particle system to solutions of the kinetic equations is provided through several minimal models. The framework for the particle system is general enough to allow for various assumptions suggested in the 1980's and 1990's concerning facet exchange and first order neighbor correlations. Multiple particle system models are compared against a level set method.