Publication 08-CNA-025

Geometric Growth and Character Development in Large Metastable Networks

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

Eva Eggeling
Fraunhofer Austria Research GmbH
Visual Computing
A-8010 Graz, Austria
eva.eggeling@fraunhofer.at

Maria Emelianenko
Department of Mathematical Sciences
George Mason University
Fairfax, VA 22030
memelian@gmu.edu

Yekaterina Epshteyn
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
rina10@andrew.cmu.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: Cellular networks are ubiquitous in nature. They exhibit behavior on many different length and time scales and are generally metastable. Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries. The energetics and connectivity of the grain boundary network plays a crucial role in determining the properties of a material across a wide range of scales. A central problem in materials science is to develop technologies capable of producing an arrangement of grains-a texture-that provides for a desired set of material properties.

Here we discuss briefly the role of energy in texture development, measured by a character distribution, and how this is different from the evolution of geometric features, which we term geometric coarsening. For this purpose we present a critical event model to deepen our understanding of the topological recongurations that occur during the growth process.

Get the paper in its entirety as  08-CNA-025.pdf

---

«   Back to CNA Publications