Mathematical Sciences: Geometric Measure Theory and the Calculus of Variations

数学科学：几何测度论和变分法

• 批准号: 9006955
• 负责人: Frederick Almgren
• 金额: $ 21.84万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006955&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Measure; Theory

The principal investigator will continue an ongoing project in the geometric calculus of variations and its applications. This will include an investigation into the geometric structure of surfaces minimizing integrals with geometric integrands such as area. Additionally, he will study the evolution of surfaces towards minimization and analyze the algorithms for their computation. And he will begin a theoretical study of general evolution processes such as would model the growth of a crystal as it freezes from its melt. Geometric measure theory provides the mathematical setting for these analyses and their applications in continuum mechanics. This project involves a variety of applications of geometric measure theory as well as extensions of the theory itself. Crystal growth and soap films are two physical phenomena to which this theory has already been applied. The principal investigator will study both the theoretical aspects of geometric measure theory and ways of developing software for its use in computer graphics.

首席研究员将继续一个正在进行的项目 在几何变分法及其应用中。 这将包括对几何结构的调查 最小化具有几何被积函数的积分的曲面， 作为地区。 此外，他还将研究表面的演变 最小化，并分析其算法 计算 他将开始一个理论研究的一般 演化过程，例如模拟晶体的生长 因为它从融化中冻结。 几何测度理论提供了 这些分析的数学设置及其 在连续介质力学中的应用 该项目涉及几何的各种应用 这是理论本身的延伸，也是理论本身的延伸。 晶体生长和肥皂膜是两种物理现象， 这一理论已经得到应用。 主要研究者 我将研究几何测量的理论方面， 计算机软件开发理论与方法 graphics-遗漏广西快乐