FRG: Collaborative Research: Singularity Formation for the Three-Dimensional Euler Equations and Related Problems
FRG:协作研究:三维欧拉方程的奇异性形成及相关问题
基本信息
- 批准号:0354560
- 负责人:
- 金额:$ 25.35万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2004
- 资助国家:美国
- 起止时间:2004-07-01 至 2008-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The question of singularity formation for the three-dimensional Euler equations of incompressible inviscid fluid flow is a celebrated open problem in mathematics and physics. The existence of Euler singularities is likely to have substantial implications for physical fluid dynamics, in particular a role in the onset and structure of turbulence. This research will utilize a combination of numerical and analytical methods to study Euler singularity formation, as well as examine the significance of these singularities for fluid dynamic turbulence. A centerpiece of the project is a new method for constructing singular Euler solutions, starting from a semi-analytic approach using complex space-time and singularities in the complex plane. The results should be amenable to rigorous analysis and direct numerical validation. A full numerical and analytic validation of the singularity construction forms a main component of this proposal. Several related projects involving singularity formation in interfacial internal waves, and in incompressible nondissipative magnetohydrodynamics will also be undertaken. The incompressible Euler equations are a system of partial differential equations that describe the flow of inviscid fluids. Although these equations have been known for nearly 250 years, basic mathematical questions concerning the nature of solutions are still open. In particular, it is still not known whether solutions of the three dimensional Euler equations can form a singularity, that is, an infinite value in a flow quantity such as the velocity or vorticity (which measures circulation) in finite time. Due to its implications in turbulence theory, the question of Euler singularities has received intense attention over the last 20 years. Successful construction of Euler singularities would solve a major problem of mathematics and would establish a new method for addressing singularity formation. A fluid dynamic understanding of these singularities could lead to important insights on the structure of turbulence, one of the major open problems of classical physics. This in turn could lead to important new methods for understanding and simulating turbulent flows, essential in a wide range of engineering applications, including the design of aircraft and watercraft.
不可压缩无粘流体流动的三维欧拉方程的奇性形成问题是数学和物理学中的一个著名的公开问题。欧拉奇点的存在可能对物理流体动力学有重大影响,特别是在湍流的开始和结构中起作用。这项研究将利用数值和分析方法相结合的方法来研究欧拉奇点的形成,以及检验这些奇点对流体动力湍流的意义。该项目的核心是一种构造奇异欧拉解的新方法,该方法从使用复时空和复平面中的奇点的半解析方法开始。结果应该服从严格的分析和直接的数值验证。对奇点结构进行充分的数值和分析验证构成了这一提议的主要组成部分。还将开展几个涉及界面内波奇点形成和不可压缩非耗散磁流体力学的相关项目。不可压缩欧拉方程是一组描述无粘流体流动的偏微分方程组。虽然这些方程已经知道了近250年,但关于解的性质的基本数学问题仍然是悬而未决的。特别是,三维欧拉方程的解是否能在有限时间内形成奇点,即速度或涡量等流量的无穷值,目前尚不清楚。由于欧拉奇点在湍流理论中的意义,在过去的20年里,欧拉奇点问题受到了极大的关注。欧拉奇点的成功构建将解决一个重大的数学问题,并将建立一种解决奇点形成的新方法。对这些奇点的流体动力学理解可能导致对湍流结构的重要洞察,湍流结构是经典物理学的主要开放问题之一。这反过来可能导致理解和模拟湍流的重要新方法,这在广泛的工程应用中是必不可少的,包括飞机和船舶的设计。
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 }}
Michael Siegel其他文献
Motion of a disk embedded in a nearly inviscid Langmuir film. Part 1. Translation
嵌入几乎无粘性朗缪尔薄膜中的圆盘的运动。
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:3.7
- 作者:
E. Yariv;Rodolfo Brandão;Michael Siegel;H. A. Stone - 通讯作者:
H. A. Stone
Highlights from the Field of Pediatric Dermatology Research from the 2023 PeDRA Annual Conference
2023 年小儿皮肤科研究领域亮点来自于小儿皮肤科研究协会年会
- DOI:
10.1016/j.jid.2024.09.014 - 发表时间:
2025-04-01 - 期刊:
- 影响因子:5.700
- 作者:
Hannah R. Chang;Morgan Dykman;Leslie Castelo-Soccio;Colleen H. Cotton;Carrie C. Coughlin;Elena B. Hawryluk;Leslie Lawley;Lara Wine Lee;Kalyani Marathe;Dawn H. Siegel;JiaDe Yu;PeDRA Focused Study Group Leads;Michael Siegel;Esteban Fernández Faith;Lisa Arkin - 通讯作者:
Lisa Arkin
Tu1662: COMPARISON OF QUALITY PERFORMANCE METRICS IN SCREENING AND SURVEILLANCE COLONOSCOPY: A SINGLE-CENTER EXPERIENCE
- DOI:
10.1016/s0016-5085(22)62444-2 - 发表时间:
2022-05-01 - 期刊:
- 影响因子:
- 作者:
James S. Love;Meredith Yellen;Jeffrey Rebhun;Michael Siegel;Asim Shuja - 通讯作者:
Asim Shuja
Effective Partnering in Conducting Benefit-Risk Patient Preference Studies: Perspectives From a Patient Advocacy Organization, a Pharmaceutical Company, and Academic Stated-Preference Researchers
- DOI:
10.1177/2168479017746404 - 发表时间:
2018-12-30 - 期刊:
- 影响因子:1.900
- 作者:
Anne M. Wolka;Angelyn O. Fairchild;Shelby D. Reed;Greg Anglin;F. Reed Johnson;Michael Siegel;Rebecca Noel - 通讯作者:
Rebecca Noel
Capturing the Dynamic Nature of Cyber Risk: Evidence from an Explorative Case Study
捕捉网络风险的动态本质:探索性案例研究的证据
- DOI:
10.24251/hicss.2023.738 - 发表时间:
2023 - 期刊:
- 影响因子:29.3
- 作者:
S. Zeijlemaker;Michael Siegel - 通讯作者:
Michael Siegel
Michael Siegel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('Michael Siegel', 18)}}的其他基金
Conference: Conference on Frontiers in Applied and Computational Mathematics (FACM 2023): New trends in computational wave propagation and imaging
会议:应用与计算数学前沿会议(FACM 2023):计算波传播和成像的新趋势
- 批准号:
2246813 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Standard Grant
Numerical Methods and Analysis for Interfacial Flow with Ionic Fluids and Surfactants
离子流体和表面活性剂界面流动的数值方法与分析
- 批准号:
1909407 - 财政年份:2019
- 资助金额:
$ 25.35万 - 项目类别:
Standard Grant
Conferences on Frontiers in Applied and Computational Mathematics: 2015-2017
应用与计算数学前沿会议:2015-2017
- 批准号:
1517152 - 财政年份:2015
- 资助金额:
$ 25.35万 - 项目类别:
Standard Grant
Numerical Methods and Analysis for Induced-Charge Electrokinetic Flow with Deformable Interfaces
可变形界面感应电荷动电流的数值方法与分析
- 批准号:
1412789 - 财政年份:2014
- 资助金额:
$ 25.35万 - 项目类别:
Standard Grant
Conference on Frontiers in Applied and Computational Mathematics 2014, May 22 - 23, 2014
2014年应用与计算数学前沿会议,2014年5月22日至23日
- 批准号:
1444295 - 财政年份:2014
- 资助金额:
$ 25.35万 - 项目类别:
Standard Grant
EXTREEMS-QED: Research and training in computational and data-enabled science and engineering for undergraduates in the mathematical sciences at NJIT
EXTREEMS-QED:为 NJIT 数学科学本科生提供计算和数据支持的科学与工程方面的研究和培训
- 批准号:
1331010 - 财政年份:2013
- 资助金额:
$ 25.35万 - 项目类别:
Continuing Grant
Numerical methods and analysis for interfacial fluid flow with soluble surfactant
可溶性表面活性剂界面流体流动的数值方法与分析
- 批准号:
1009105 - 财政年份:2010
- 资助金额:
$ 25.35万 - 项目类别:
Continuing Grant
Collaborative Research: Efficient surface-based numerical methods for 3D interfacial flow with surface tension
合作研究:基于表面的高效数值方法,用于具有表面张力的 3D 界面流动
- 批准号:
1016406 - 财政年份:2010
- 资助金额:
$ 25.35万 - 项目类别:
Continuing Grant
Collaborative Research: Numerics and Analysis of Singularities for the Euler Equations
合作研究:欧拉方程的数值和奇异性分析
- 批准号:
0707263 - 财政年份:2007
- 资助金额:
$ 25.35万 - 项目类别:
Standard Grant
Analysis and numerical computations of free boundaries in fluid dynamics: surfactant solubility and elastic fibers
流体动力学中自由边界的分析和数值计算:表面活性剂溶解度和弹性纤维
- 批准号:
0708977 - 财政年份:2007
- 资助金额:
$ 25.35万 - 项目类别:
Continuing Grant
相似海外基金
FRG: Collaborative Research: New birational invariants
FRG:协作研究:新的双有理不变量
- 批准号:
2244978 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2245017 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245111 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245077 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2244879 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Standard Grant
FRG: Collaborative Research: New Birational Invariants
FRG:合作研究:新的双理性不变量
- 批准号:
2245171 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2403764 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2245021 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245097 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245147 - 财政年份:2023
- 资助金额:
$ 25.35万 - 项目类别:
Continuing Grant














{{item.name}}会员




