Dynamics and Variational Problems

动力学和变分问题

• 批准号: 0600037
• 负责人: Michael Loss
• 金额: --
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600037&HistoricalAwards=false
• 关键词: Dynamics; Variational; Problems

Dynamics and Variational ProblemsAbstract of Proposed ResearchMichael Loss and Eric A. Carlen This project will support research on some mathematical problems that are motivated by questions arising from issues about the behavior of complex physical systems. We shall develop analytic and probabilistic tools to study a number of problems in statistical mechanics. These include proving results about Cercignani's conjecture, deriving optimal geometric correlation inequalities, studying certain variational principles that arise in the study of phase transitions and also some topics in Quantum electrodynamics. Many of these results center on the proof of physically motivated inequalities. The investigators have had considerable success in recent years in discovering some sharp geometrical and analytic inequalities using techniques from the calculus of variations.

动力学和变分问题拟议研究摘要michael Loss和Eric A. Carlen这个项目将支持一些数学问题的研究，这些问题是由复杂物理系统的行为问题引起的。我们将发展分析和概率工具来研究统计力学中的一些问题。这些包括证明Cercignani猜想的结果，推导最优几何相关不等式，研究相变研究中出现的某些变分原理以及量子电动力学中的一些主题。这些结果中的许多都是基于对生理上的不平等的证明。近年来，研究人员利用变分法的技术，在发现一些尖锐的几何不等式和解析不等式方面取得了相当大的成功。