Mathematical Sciences: Studies in Composite Media and Turbulent Transport

数学科学：复合介质和湍流传输研究

• 批准号: 9005799
• 负责人: Marco Avellaneda
• 金额: $ 4.93万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9005799&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Composite; Media

This project concerns two problems involving the averaging of partial differential equations with important applications go Physics. The first one consists of studying the response tensor, i.e. the tensor of effective properties of a composite material in which different processes are coupled, such as thermoelectric or thermoelastic media. The second is to study the long time, large-scale asymptotics of diffusion-advection equations in which the velocity is a random, incompressible field, with a continuum of excited space and time scales. This equation is known to exhibit interesting crossover phenomena, which are not well understood in the multidimensional case. The principal investigator hopes to develop new mathematical insight to such problems, based on the theory of homogenization. In particular, the advection-diffusion problem involves understanding renormalization of equations with random coefficient outside the regime in which mean-field theory is valid.

这个项目涉及两个问题， 有重要应用的偏微分方程 物理学 第一个是研究 张量，即复合材料有效性质的张量 不同工艺耦合的材料，例如 热电或热弹性介质。 二是研究 扩散-平流的长时间大尺度渐近性 方程中的速度是随机的，不可压缩的 场，具有连续的激发空间和时间尺度。 这 已知方程表现出有趣的交叉现象， 这在多维情况下不是很好理解。 首席研究员希望开发新的数学 基于均质化理论，对这类问题进行了深入的研究。 特别地，对流扩散问题涉及 理解带有随机变量的方程的重正化 系数以外的制度，其中平均场理论是 有效的.