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
基本信息
- 批准号:1115277
- 负责人:
- 金额:$ 26.5万
- 依托单位:
- 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:
- 关键词:
项目摘要
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.
本计画将探讨Lorenz系统之复杂奇异性之精确解析形式、三体问题之8字形解,以及由Navier-Stokes边界层所获得之讯号。分析和数值技术都将被使用。研究Lorenz系统的目的是理解Lorenz解在整个复平面上的解析延拓。关于8字形的解决方案,该项目将表明,这个系统的复杂奇点有一个吸引人的简单结构。Navier-Stokes边界层主要是用谱分析技术研究的。我们将在复平面上定位和解释信号解析延拓的奇异点,并获得测量以及理解外部流所施加的时间尺度。首先,我们的目标是获得新的见解纳维尔-斯托克斯边界层,这是非常重要的工程和气象。作为其重要性的一个例子,我们提到汽车的能量摄入的一个主要部分是在边界层耗散。其次,我们将写一本新书,把计算机体系结构放在科学计算的核心。这本书将介绍一种科学计算的风格,它深深地被计算机体系结构的最新进展所告知。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Divakar Viswanath其他文献
The Dynamics of Transition to Turbulence in Plane Couette Flow
平面库埃特流向湍流转变的动力学
- DOI:
- 发表时间:
2007 - 期刊:
- 影响因子:0
- 作者:
Divakar Viswanath - 通讯作者:
Divakar Viswanath
Shuffling cards for blackjack, bridge, and other card games
二十一点、桥牌和其他纸牌游戏的洗牌
- DOI:
- 发表时间:
2006 - 期刊:
- 影响因子:0
- 作者:
Mark A. Conger;Divakar Viswanath - 通讯作者:
Divakar Viswanath
Stable manifolds and the transition to turbulence in pipe flow
稳定流形和管道流向湍流的过渡
- DOI:
10.1017/s0022112009006041 - 发表时间:
2008 - 期刊:
- 影响因子:3.7
- 作者:
Divakar Viswanath;P. Cvitanovic - 通讯作者:
P. Cvitanovic
The critical layer in pipe flow at high Reynolds number
高雷诺数管流的临界层
- DOI:
10.1098/rsta.2008.0225 - 发表时间:
2008 - 期刊:
- 影响因子:0
- 作者:
Divakar Viswanath - 通讯作者:
Divakar Viswanath
Divakar Viswanath的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Divakar Viswanath', 18)}}的其他基金
SCREMS: Scientific Computing and Mathematics at the University of Michigan
SCEMS:密歇根大学的科学计算和数学
- 批准号:
1026317 - 财政年份:2010
- 资助金额:
$ 26.5万 - 项目类别:
Standard Grant
LTB: Accurate Computational Methods for Very Large Dynamical Systems
LTB:超大型动力系统的精确计算方法
- 批准号:
0715510 - 财政年份:2007
- 资助金额:
$ 26.5万 - 项目类别:
Standard Grant
Symbolic Dynamics Methods for Low Dimensional Dynamics
低维动力学的符号动力学方法
- 批准号:
0407110 - 财政年份:2004
- 资助金额:
$ 26.5万 - 项目类别:
Standard Grant
相似海外基金
High-Order Numerical Methods for Convection-Diffusion Equations with Unbounded Singularities
具有无界奇点的对流扩散方程的高阶数值方法
- 批准号:
1818467 - 财政年份:2018
- 资助金额:
$ 26.5万 - 项目类别:
Standard Grant
Theory and Implementation of Novel Numerical Methods for Equations with Singularities
奇异性方程新数值方法的理论与实现
- 批准号:
1418853 - 财政年份:2014
- 资助金额:
$ 26.5万 - 项目类别:
Standard Grant
Numerical Studies of Singularities and Black Holes
奇点和黑洞的数值研究
- 批准号:
1205202 - 财政年份:2012
- 资助金额:
$ 26.5万 - 项目类别:
Continuing Grant
New Development of Numerical Methods for Partial Differential Equations with Singularities
奇异性偏微分方程数值方法的新进展
- 批准号:
24540108 - 财政年份:2012
- 资助金额:
$ 26.5万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Numerical Investigations of Singularities in Higher-Dimensional Space-time
高维时空奇点的数值研究
- 批准号:
22540293 - 财政年份:2010
- 资助金额:
$ 26.5万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Numerical treatment of singularities and the Generalized Finite Element Method: theory, algorithms, and applications
奇点的数值处理和广义有限元方法:理论、算法和应用
- 批准号:
1016556 - 财政年份:2010
- 资助金额:
$ 26.5万 - 项目类别:
Standard Grant
Numerical studies of singularities and black holes
奇点和黑洞的数值研究
- 批准号:
0855532 - 财政年份:2009
- 资助金额:
$ 26.5万 - 项目类别:
Standard Grant
Numerical Methods with Validation for Partial Differential Equations with Singularities
具有奇点的偏微分方程验证的数值方法
- 批准号:
21540106 - 财政年份:2009
- 资助金额:
$ 26.5万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Research Experience in Numerical Methods for Partial Differential Equations with Singularities
奇异性偏微分方程数值方法的研究体会
- 批准号:
0713743 - 财政年份:2007
- 资助金额:
$ 26.5万 - 项目类别:
Standard Grant
Numerical Methods and Numerical Analysis for Partial Differential Equations with Singularities
具有奇异性的偏微分方程的数值方法和数值分析
- 批准号:
18540107 - 财政年份:2006
- 资助金额:
$ 26.5万 - 项目类别:
Grant-in-Aid for Scientific Research (C)