Mathematical Sciences: Motion of Curves and Surfaces in Crystalline Materials

数学科学：晶体材料中曲线和曲面的运动

• 批准号: 9626147
• 负责人: Jean Taylor
• 金额: $ 5万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626147&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Motion; Curves; Surfaces

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.

9626147 泰勒 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率函数的平衡和生长问题。她正在开发新的理论框架来考虑此类问题，并创建新的算法和程序来计算其解决方案。将使用结晶方法：该方法背后的总体思想是表面由平面片段组成，具有固定的法线方向和固定的邻接，但距原点的距离可变，并且这些片段的运动由距离的常微分方程组。该方法可以被认为是有限元方法的变体，其中法线高斯图被离散化。 预计这项研究将增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深入了解。这将部分通过应用结晶方法来解释观察到的材料中的微面和其他行为来实现。