Complex Singularities in Numerical Analysis and Nonlinear Dynamics

数值分析和非线性动力学中的复杂奇点

• 批准号: 1115277
• 负责人: Divakar Viswanath
• 金额: $ 26.5万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-15 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1115277&HistoricalAwards=false
• 关键词: Complex; Singularities; Numerical; Analysis; Nonlinear

This project will investigate the precise analytic form of the complex singularities ofthe Lorenz system, the figure-eight solution of the three-body problem, and signals obtainedfrom the Navier-Stokes boundary layer. Both analytic and numerical techniqueswill be used. Research on the Lorenz system has the aim of understanding the analyticcontinuation of the Lorenz solutions to the entire complex plane. With regard to thefigure-eight solution, the project will show that the complex singularities of this systemhave an appealingly simple structure. The Navier-Stokes boundary layer has beenstudied primarily using techniques from spectral analysis. We will locate and elucidatesingularities of the analytic continuation of the signal in the complex plane, and andobtain a measurement as well as an understanding of the time scales imposed by theouter flow.This project endeavors to benefit the public in two respects. Firstly, we aim to obtainnew insights into the Navier-Stokes boundary layer which is of immense importance inengineering and meteorology. As an example of its importance, we mention that amajor part of the energy intake of automobiles is dissipated in the boundary layer.Secondly, we will write a new book that puts computer architecture at the heart ofscientific computing. This book will introduce a style of scientific computing that isdeeply informed by recent progress in computer architecture to a wider audience.

该项目将研究洛伦兹系统（Lorenz System）复杂奇异性的精确分析形式，三体问题的图八解，以及从Navier-Stokes边界层获得的信号。分析技术和数值技术都将使用。关于洛伦兹系统的研究旨在了解洛伦兹溶液对整个复杂平面的分析性关联。关于图八个解决方案，该项目将表明该系统的复杂奇异性是一种吸引人的简单结构。 Navier-Stokes边界层主要使用光谱分析中的技术进行了研究。我们将找到和阐明信号在复杂平面中的分析性延续的延续，并进行测量以及对Theouter流量施加的时间尺度的理解。这项项目努力在两个方面使公众受益。首先，我们旨在获得对Navier-Stokes边界层的见解，该介于Navier-Stokes边界层极为重要的是工程学和气象学。作为其重要性的一个例子，我们提到，在边界层中消散了汽车能量摄入的部分。这本书将介绍一种科学计算的风格，这些计算是通过计算机体系结构的最新进度来了解更多受众的。