University of Utah
Department of Mathematics
epshteyn@math.utah.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--appropriate for a desired set of material properties. Here we
discuss the role of energy in texture development, measured by a character
distribution. We derive an entropy based theory based on a mass transport and
a Kantorovich-Rubinstein-Wasserstein metric to suggest that, to first
approximation, this distribution behaves like the solution to a
Fökker-Planck Equation.
This is joint work with Katayun Barmak, Eva Eggeling, Maria Emelianenko, David Kinderlehrer, Richard Sharp and Shlomo Ta'asan.