Mathematical Sciences: Studies in Geometric Analysis and Algebra

数学科学：几何分析和代数研究

• 批准号: 9305848
• 负责人: Frederick Almgren
• 金额: $ 24万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9305848&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Geometric; Analysis

This proposal is for investigation of geometric evolution processes such as might model dendritic growth of a crystal freezing from its melt. The mathematical setting is that of geometric measure theory in which crystals are sets of finite perimeter and temperature and concentration fields are functions belonging to appropriate Sobolev spaces. The final evolution is a limit of discrete time approximations in which crystal geometries are determined by solving variational problems and fields evolve by diffusion equations.

这个建议是为了研究几何演化 例如可以模拟晶体的树枝状生长的过程 从融化中冻结。 数学设定是， 几何测量理论，其中晶体是有限的集合 周长、温度和浓度场是函数 属于适当的索博列夫空间。 最后的进化是 离散时间近似的极限，其中晶体 通过求解变分问题来确定几何形状， 场通过扩散方程演化。