Collective Behavior: Macroscopic versus Kinetic Descriptions

A Theory and Challenges for Coarsening in Microstructure

Yekaterina Epshteyn

University of Utah

Cellular networks are ubiquitous in nature. Most technologically useful materials arise as polycrystalline microstructures, composed of a myriad of small crystallites, or grains, separated by interfaces, or grain boundaries. The energetics and connectivity of the grain boundaries network plays a crucial role in determining the properties of a material across a wide range of scales. Coarsening, or growth process is influenced mainly by the effort of the system to decrease the interfacial energy subject to spatial constraints. The recently discovered Grain Boundary Character Distribution (GBCD) indicates that the boundary network of a cellular structure, and, more generally, material texture has a natural order. In this talk we will present and discuss a theory for the evolution of this statistic which leads to many interesting questions.

There are several coarsening systems, or models of physical systems which undergo an evolution process where coarsening occurs. These run a gamut from Monte Carlo and Potts models to kinetic theory. A number of these exhibit behavior similar to the one discussed in the talk and hence we think that there can be some interesting universal properties as well.

This is joint work with K. Barmak, E. Eggeling, M. Emelianenko, D.Kinderlehrer, R. Sharp, S. Ta’asan and Patrick Bardsley.