Most technologically useful materials arise as polycrystalline microstructures, composed of a myriad of small crystallites, grains, separated by interfaces, grain boundaries. The energetics and connectivity of the network of boundaries are implicated in many properties across all scales of use, for example, functional properties, like conductivity in microprocessor wires, and lifetime properties, like fracture toughness in structures. Engineering a microstructure to achieve a desired set of performance characteristics is a major focus in materials science. In , a framework for modeling critical events in microstructure evolution was proposed and applied to a simplified one-dimensional system. By regarding a system of grain boundaries as a collection of interacting particles, one can then utilize the machinery of statistical mechanics, in particular, Boltzmann kinetics. The results obtained were found to compare favorably with numerical simulations as well as experimental data in both the distributions of grain boundary lengths and orientations.
In my research, I have utilized an analogous approach to extend prior work to a more realistic two-dimensional model. The extension to two dimensions is non-trivial in that topological reconfigurations (critical events) such as neighbor switching, absent in one dimension, must now be treated. The resulting model is a partial integro-differential equation describing the evolution of the distribution of misorientations in a two-dimensional grain boundary network, a distribution which is of great importance to materials scientists and engineers. Currently, I am exploring numerical methods of solution including the method of finite differences and Direct Simulation Monte Carlo. The plausibility of the derived model will require numerical validation by means of comparison with results gathered from numerical simulations and experimental data. Next summer I am applying for an NSF funded REU out of Harvard’s Materials Science and Engineering Center and I believe that having participated in the EXTREEMS-QED program and having done research in the field of materials science will greatly increase my chances of being selected. The work I am doing is also topical in that in 2011, under the Obama administration, the Materials Genome Initiative was launched, a multi-agency initiative designed to create a new era of policy, resources, and infrastructure that support U.S. institutions in the effort to discover, manufacture, and deploy advanced materials twice as fast, at a fraction of the cost.
 Barmak, K., et al. "A new perspective on texture evolution." International Journal on Numerical Analysis and Modeling 5 (2008): 93-108.