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Publication 06-CNA-10

Grain Boundary Evolution: New Perspectives

Maria Emelianenko
Department of Mathematical Sciences and
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
masha@cmu.edu

Dmitry Golovaty
Department of Theoretical and Applied Mathematics
The University of Akron
Akron, OH 44325
dmitry@math.uakron.edu

David Kinderlehrer
Department of Mathematical Sciences and
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
davidk@cmu.edu

Shlomo Ta'asan
Department of Mathematical Sciences and
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
shlomo@andrew.cmu.edu

Abstract: In this paper, we study mesoscopic behavior of a grain boundary and investigate the possibility of modeling texture evolution. One of the most challenging aspects of this problem is to understand the role of topological reconfigurations during coarsening. To this end, we investigate grain boundary evolutionin a one-dimensional system designed specifically to target critical event evolution in microstructure. We suggest stochastic frameworks that may be used to model this system. We compare the predictions of the models with simulations and discuss their limitations and possible extensions to higher-dimensional cases.

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