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Publication 07-CNA-05

On a Stastical Theory of Critical Events in Microstructural Evolution

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

M. Emelianenko
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
Current address:
George Mason University
Fairfax, VA 22030
memelian@gmu edu

D. Golovaty
Department of Theoretical and Applied Mathematical Sciences
The University of Akron
Akron, OH 44325
dmitry@math.uakron.edu

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

and

S. 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.

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