Workshop

A kinetic model for 2D grain boundary coarsening

  • Govind Menon (Brown University)
Felix-Klein-Hörsaal Universität Leipzig (Leipzig)

Abstract

A fundamental aspect of 2D cellular networks with isotropic line tension is the Mullins-von Neumann n6 rule: the rate of change of the area of a (topological) n-gon is proportional to n6. As a consequence, cells with fewer than 6 sides vanish in finite time, and the network coarsens. Numerical and physical experiments have revealed a form of statistical self-similarity in the long time dynamics.

We propose a kinetic description for the evolution of such networks. The ingredients in our model are an elementary N particle system that mimics essential features of the von Neumann rule, and a hydrodynamic limit theorem for population densities when N. This model is compared with a set of models derived in the physics and materials science communities, as well as extensive numerical simulations by applied mathematicians.

This is joint work with Joe Klobusicky (Brown University and Geisinger Health Systems) and Bob Pego (Carnegie Mellon University).

Valeria Hünniger

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Katja Heid

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Irene Fonseca

Carnegie Mellon University

Richard James

University of Minnesota

Stephan Luckhaus

Universität Leipzig

Felix Otto

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Peter Smereka

University of Michigan