Mathematical Sciences: Motion of Curves and Surfaces in Crystalline Materials

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9626147 Taylor In this project the investigator continues her study of equilibrium and growth problems involving anisotropic surface free energy and mobility functions. She is developing new theoretical frameworks for considering such problems as well as creating new algorithms and programs for computing their solutions. The crystalline approach is to be used: the general idea behind this approach is that surfaces are composed of segments of planes, with fixed normal direction and with fixed adjacencies but with variable distance from the origin, and the motion of these segments is governed by a system of ordinary differential equations for the distances. This method may be considered as a variant of finite element method where the normal Gauss map is discretized. It is expected that this research will advance the understanding of the role of surface free energy and kinetics in determining the shapes of surfaces and interfaces in materials as well as provide insight into the underlying mathematics. This will be accomplished in part by applying crystalline methods to explain observed microfaceting and other behavior in materials.