Geometric approach to instability phenomena in fluid and mechanical systems

流体和机械系统中不稳定现象的几何方法

• 批准号: 341849-2007
• 负责人: Krechetnikov, Rouslan
• 金额: $ 1.46万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=399647
• 关键词: Geometric; approach; instability; phenomena; fluid

The major goal of the proposed research is to develop an efficient mathematical language for treating instability and singularity phenomena, which occur frequently in physical systems. In view of universal, coordinate-free, character of these phenomena, the methodology will be based on geometric considerations. Of particular focus are fluid systems with complex interfaces and non-holonomic mechanical systems with effects of dissipation, where a number of concrete practical problems will be analyzed using analytical, computational, and experimental methods. At a more general level, geometric treatment of field theories, which include fluid dynamics and many other physical theories, will be pursued. The anticipated impact of these studies will be a development of new geometry-inspired methods, and solving a number of outstanding problems with the help these methods.

该研究的主要目标是开发一种有效的数学语言来处理物理系统中经常发生的不稳定性和奇异现象。鉴于这些现象的普遍性、无坐标性，方法将以几何考虑为基础。特别关注的是具有复杂界面的流体系统和具有耗散效应的非完整力学系统，其中将使用分析，计算和实验方法分析一些具体的实际问题。在更一般的水平上，几何处理的领域理论，其中包括流体动力学和许多其他物理理论，将追求。这些研究的预期影响将是新的几何启发方法的发展，并解决了一些突出的问题的帮助下，这些方法。