Mathematical Sciences: The Mathematical Physics of Crystals

数学科学：晶体的数学物理

• 批准号: 9304269
• 负责人: Charles Radin
• 金额: $ 12.15万
• 依托单位: University of Texas at Austin
• 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: 1993-06-01 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9304269&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Physics; Crystals

Radin will study mathematical problems relating the causes of crystalline symmetry in low temperature matter and classification of the dynamical systems associated with uniquely ergodic tilings of Euclidean space. The methods to be used are a combination of traditional ergodic theory and new techniques from aperiodic tilings. It is expected that the recent results on rotation symmetric tilings will open significant new research in the study of material structure and in the classification of dynamical systems. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.

雷丁将研究与低温物质中晶体对称性的原因有关的数学问题，以及与欧几里德空间的唯一遍历瓦片有关的动力系统的分类。将使用的方法是传统遍历理论和来自非周期平铺的新技术的组合。预计最近关于旋转对称瓦片的结果将在物质结构的研究和动力系统的分类方面开启重要的新研究。这个项目涉及对遍历理论的研究。一般说来，遍历理论涉及理解系统的平均行为，这些系统的动力学太复杂或太混乱，以至于无法在微观细节上进行跟踪。在标题“动力学可以被放在现代理论如何抽象变换如何作用于光滑空间。这样，遍历理论与几何联系起来，寻求在均匀空间上对流动进行分类。