Mathematical Sciences: Problems in Crystal Growth and Equilibrium Shapes

数学科学：晶体生长和平衡形状问题

• 批准号: 9305929
• 负责人: Jean Taylor
• 金额: $ 11.4万
• 依托单位: Rutgers University New Brunswick
• 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=9305929&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Crystal; Growth

Crystal equilibrium and growth problems involving anisotropic surface energy and/or mobility will be investigated, with and without diffusion. New theoretical frameworks for considering such problems will be developed, as will new algorithms and computer programs for computing their solutions. In particular, the crystalline approach will be further developed and applied to new problems. In this context, variational problems often become finite dimensional, and parabolic partial differential equations for surface motion become systems of ordinary differential equations. The general context for this work is geometric measure theory.

将研究涉及各向异性表面能和/或迁移率的晶体平衡和生长问题，有或没有扩散。 将开发考虑此类问题的新理论框架，以及用于计算其解决方案的新算法和计算机程序。 特别是，结晶方法将得到进一步发展并应用于新问题。 在这种情况下，变分问题通常变成有限维，表面运动的抛物型偏微分方程变成常微分方程组。 这项工作的一般背景是几何测度论。