Statement ( Brief Version ) - Yekaterina Epshteyn August 2009 1

• Some of my recent and ongoing work is to understand and to discover a predictive theory for microstructure evolution. 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. In the collaborative work [2] which involves Departments of Mathematical Sciences and Material Sciences at Carnegie Mellon University we have proposed a theory which accounts for the kinetics of network evolution. In [2], we have introduced the grain boundary character distribution, the GBCD, a basic texture measure, and established an entropy based theory for it which suggests that GBCD satisfies Fokker-Planck type kinetics. For this, a simplified critical event model is introduced and studied. Current and Future Goals: In [1], our aim is to use accurate large scale simulation to develop multiscale theory of complex evolving networks, exploit dissipation/entropy method for simplified models, and to establish kinetics of Grain Boundary Character distribution (GBCD) evolution.