Mathematical Sciences: Space-Time and Transport Phenomena inExtended Systems

数学科学：扩展系统中的时空和输运现象

• 批准号: 9303769
• 负责人: Leonid Bunimovich
• 金额: $ 11.01万
• 依托单位: Georgia Tech Research Corporation
• 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: 1993-06-15 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303769&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Space; Time; Transport

Bunimovich will study mechanisms of space-time chaos and elucidate some convenient and widely used but vague notions of coherent structures, patterns and intermittency. To do this, he will study the behavior of some classes of coupled map lattices that demonstrate most purely these types of motion. He will consider also the related problem of transport in extended systems by investigating the thermodynamic limit of the first examples of systems of arbitrary number of interacting particles recently proven to be ergodic. 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.

布尼莫维奇将研究时空混沌机制，并阐明一些方便且广泛使用但模糊的相干结构、模式和间歇性概念。 为此，他将研究某些类型的耦合地图晶格的行为，这些晶格最纯粹地演示了这些类型的运动。 他还将通过研究最近被证明是遍历的任意数量相互作用粒子系统的第一个例子的热力学极限来考虑扩展系统中输运的相关问题。 该项目涉及遍历理论的研究。 一般来说，遍历理论涉及理解系统的平均行为，这些系统的动力学过于复杂或混乱，无法在微观细节中遵循。 在“动力学”标题下，可以放置关于抽象变换组如何作用于平滑空间的现代理论。通过这种方式，遍历理论在寻求对同质空间上的流进行分类的过程中与几何学建立了联系。