Mathematical Sciences: Singularities in Vortical Flows and Dispersive Systems

数学科学：涡流和色散系统中的奇点

• 批准号: 9623087
• 负责人: Russel Caflisch
• 金额: $ 13.8万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623087&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Singularities; Vortical; Flows

9623087 Caflisch This proposal is for development of analytical and computational methods for describing singularities in the solutions of partial differential equations (PDEs), and for application of those methods to problems of fluid mechanics and other physical systems. The key step in the analysis is transformation of the variables of the PDE to obtain an "unfolded" system, the solutions of which are non-singular. This will be used for vortex sheets, swirling flow, magnetohydrodynamics and crystal patterns. For these problems we will attempt to find singular solutions and to classify their generic type. This proposal is for research on "singularities" in physics and engineering problems. Singularities are points at which the measurable quantities in the system change abruptly or become very large. An important example, which is a main focus of this project is the development of very large rotational velocity in a fluid such as air or liquid. These singularities are believed to be a primary cause of turbulence, an important but poorly understood phenomena in many applications. The goals of this research project are to find these singularities, classify their possible behavior and use them to gain understanding of turbulence and other problems.

9623087 CAFLISCH该建议是用于开发分析和计算方法，用于描述部分微分方程（PDE）解决方案中的奇异性，以及将这些方法应用于流体力学和其他物理系统的问题。分析的关键步骤是对PDE变量的转换，以获得“展开”系统，其解决方案是非单星的。这将用于涡流板，旋转流，磁流失动力学和晶体图案。 对于这些问题，我们将尝试找到单一的解决方案并对其通用类型进行分类。 该建议是针对物理和工程问题中“奇异性”的研究。 奇点是系统中可测量数量突然变化或变得非常大的点。 一个重要的例子，是该项目的主要重点是在空气或液体等流体中发展非常大的旋转速度。 这些奇异性被认为是湍流的主要原因，在许多应用中，这是一种重要但知之甚少的现象。 该研究项目的目标是找到这些奇异性，对其可能的行为进行分类，并利用它们来了解湍流和其他问题。