Abstract:
Several competing kinetic models for 2D grain boundary networks were proposed by physicists and materials scientists in the 1990s. The essential feature of these models is that they consist of linear transport equations for several "topological species", with a nonlinear boundary coupling. We introduce particle systems for these equations and prove hydrodynamic limit theorems that establish the kinetic equations as laws of large numbers for these particle systems. The key technical tool is a set of exponential concentration estimates. |