Mathematical Sciences: Motion of Curves and Surfaces in Crystalline Materials

在这个项目中，研究者继续研究涉及各向异性表面自由能和迁移函数的平衡和生长问题。她正在开发新的理论框架来考虑这些问题，并创建新的算法和程序来计算它们的解决方案。晶体方法将被使用：这种方法背后的一般思想是，表面是由平面的片段组成的，具有固定的法线方向和固定的邻接，但与原点的距离是可变的，这些片段的运动由距离的常微分方程系统控制。这种方法可以看作是将法向高斯映射离散化的有限元方法的一种变体。预期这项研究将促进对表面自由能和动力学在确定材料表面和界面形状方面的作用的理解，并提供对基础数学的见解。这将在一定程度上通过应用晶体方法来解释观察到的材料中的微面化和其他行为来实现。

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.