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Publication 07-CNA-005

On a Statistic Theory of Critical Events in Microstructural Evolution

Katayun Barmak
Department of Materials Science and Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
katayun@andrew.cmu.edu

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 Mathematical Sciences
The University of Akron
Akron, OH 44325
dmitry@math.uakron.edu

David Kinderlehrer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
davidk@andrew.cmu.edu

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

Abstract: One of the most challenging aspects of the microstructural evolution in polycrystalline materials is to understand the role of topological reconfigurations during coarsening. In this paper, we study these critical events in a one-dimensional grain-boundary system and a stochastic framework for modeling texture evolution. The model is based on a master equation derived from numerically determined statistical properties of the system.

Get the paper in its entirety as 07-CNA-005.pdf

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