Nonequilibrium Interface Dynamics:
Hierarchical Modeling and Multiscale Simulation of Materials Interfaces

CSIC Building (#406), Seminar Room 4122.
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Mesoscale Issues in Microstructural Simulation I

Dr. David Kinderlehrer

Mathematical Science at Carnegie Mellon University

Abstract:   Polycrystalline interfaces play a role in many material properties, for example conductivity and fracture toughness, and across many scales. Preparing arrangements or distributions of boundaries suitable for a given purpose is a central problem in materials. It is, indeed, the central problem of microstructure and has an extensive history dating from prehistory. Grain growth is one of the primary microstructural mechanisms. We may ask many questions, for example as C. S. Smith did, to what extent is grain growth like or unlike the growth of soap bubbles.

Here we exhibit a consistent variational approach to the mesoscale simulation of large systems of grain boundaries subject to Mullins Equation of curvature driven growth. Accuracy and statistical significance are objectives. We introduce this theory and its discretization as a dissipative system in two and three dimensions. We discuss some consequences and challenges, including some ideas about coarse graining the simulation.