David Kinderlehrer

David Kinderlehrer's recent activity is in applied mathematics and in analysis, in particular partial differential equations. The work in applied mathematics, joint with Shlomo Ta'asan, colleagues in the Materials Science and Engineering Department, and his extraordinary postdocs is directed toward understanding evolution of material microstructure. Nearly all technologically useful materials are polycrystalline microstructures composed of a myriad of small crystallites or grains separated by grain boundaries, and comprise cellular networks. A central problem in materials is to develop technologies capable of producing an arrangement, or ordering, of the grains in terms of geometry and crystallographic texture that provides desired properties for a given function. The order, if indeed it is present at all, must be conferred by the network grain boundaries or interfaces, because they are what changes during the coarsening process. Using new experimental techniques and especially developed large scale simulation, Kinderlehrer's team has discovered the grain boundary character distribution (GBCD), a statistic which details texture evolution. In the simplest situation, it is a Boltzmann distribution related to the interface energy density.