Mathematical Sciences: Motion of Curves and Surfaces in Crystalline Materials

9626147泰勒在这个项目中，研究人员继续她对平衡和增长问题的研究，包括各向异性表面自由能和迁移率函数。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。将使用结晶法：这种方法背后的一般思想是，曲面由多个平面分段组成，具有固定的法向和固定的邻接，但与原点的距离可变，并且这些分段的运动由关于距离的常微分方程组控制。这种方法可以看作是有限元方法的一种变种，其中法向高斯映射是离散的。预计这项研究将促进对表面自由能和动力学在决定材料表面和界面形状方面的作用的理解，并提供对基本数学的洞察。这将在一定程度上通过应用结晶方法来解释观察到的材料微面和其他行为来实现。

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.