New Tools in the Study of Wave Propagation: Dynamical Systems for Kinetic Equations, Inviscid Limits for Modulated Periodic Waves, and Rigorous Numerical Stability Analysis
波传播研究的新工具:运动方程的动力系统、调制周期波的无粘极限以及严格的数值稳定性分析
基本信息
- 批准号:1700279
- 负责人:
- 金额:$ 20.8万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2017
- 资助国家:美国
- 起止时间:2017-07-01 至 2022-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The PI will study a selection of key open problems in the theory of wave propagation arising in a variety of settings including thin film flow, pattern formation, detonation, and the kinetic theory of gases. The problems considered share the features of computational complexity, multiple length/time scales, and genuine physical interest in applications. Many concern questions that current numerics and experiment are not adequate to resolve. Several of the planned subprojects involve numerically assisted proof using scientific computation with guaranteed error bounds, up to and including rigorous numerical proof. An integral part of the project is the simultaneous development of a user-friendly numerical platform, STABLAB, for numerical stability investigation, and the systematic exploration with this platform of physical behavior in gas and fluid dynamics in the delicate situations of reacting or ionized flow. The problems addressed involve issues in dynamical systems, singular perturbation theory, spectral theory of linear operators, nonlinear partial differential equations, and rigorous scientific computation, and should result in the development of new mathematical tools of general application. In particular, development of dynamical systems tools for kinetic shock and boundary layer problems would unify and extend results obtained for Boltzmann phenomena by the "Kyoto School" of Sone et al using a variety of formal and analytic methods. Likewise, the introduction of new inviscid stability criteria for roll waves and of Kreiss symmetrizer techniques for analysis of modulated fronts open new directions in the study of periodic modulation. The problem on galloping detonations, if solved, will answer a longstanding question, while associated rigorous Wensel,Kramers, and Brillouin method developments will be of wide general use. Determination of simple stability criteria for roll waves in shallow water flow are of practical interest in hydraulic engineering. Finally, the development of rigorous numerical proof and error estimate techniques is potentially transformative, having broader implications for standards in scientific computing.
PI将研究在各种环境下产生的波传播理论中的一些关键开放问题,包括薄膜流动、图案形成、爆轰和气体动力学理论。所考虑的问题具有计算复杂性、多个长度/时间尺度以及对应用程序真正的物理兴趣的特征。许多令人担忧的问题,目前的数值和实验都不足以解决。计划中的几个子项目涉及使用科学计算进行数值辅助证明,并保证误差范围,达到并包括严格的数值证明。该项目的一个组成部分是同时开发一个用户友好的数值平台STABLAB,用于数值稳定性研究,并利用该平台系统地探索在反应或电离流动的微妙情况下气体和流体动力学中的物理行为。所解决的问题涉及动力系统、奇异摄动理论、线性算子的谱理论、非线性偏微分方程和严格的科学计算,并应导致新的普遍应用的数学工具的发展。特别是,动力学激波和边界层问题动力系统工具的开发将统一和扩展Sone等人的“京都学派”使用各种形式和分析方法对Boltzmann现象所取得的结果。同样,新的横波无粘稳定性准则的引入和Kreiss对称化技术的引入也为周期调制的研究开辟了新的方向。关于飞驰爆炸的问题如果得到解决,将回答一个长期存在的问题,而相关的严格的文塞尔、克拉默斯和布里渊方法的发展将具有广泛的普遍用途。确定浅水水流中横浪的简单稳定性判据在水利工程中具有重要的实用价值。最后,严格的数值证明和误差估计技术的发展具有潜在的变革性,对科学计算中的标准具有更广泛的影响。
项目成果
期刊论文数量(24)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves
守恒定律抛物线系统中的图灵模式和周期波的数值观测稳定性
- DOI:10.1016/j.physd.2017.12.003
- 发表时间:2018
- 期刊:
- 影响因子:0
- 作者:Barker, Blake;Jung, Soyeun;Zumbrun, Kevin
- 通讯作者:Zumbrun, Kevin
Multidimensional Stability of Large-Amplitude Navier–Stokes Shocks
- DOI:10.1007/s00205-017-1147-7
- 发表时间:2017-07
- 期刊:
- 影响因子:2.5
- 作者:J. Humpherys;Gregory Lyng;K. Zumbrun
- 通讯作者:J. Humpherys;Gregory Lyng;K. Zumbrun
A calculus proof of the Cramér–Wold theorem
CraméräWold 定理的微积分证明
- DOI:10.1090/proc/13794
- 发表时间:2018
- 期刊:
- 影响因子:1
- 作者:Lyons, Russell;Zumbrun, Kevin
- 通讯作者:Zumbrun, Kevin
Recent Results on Stability of Planar Detonations
- DOI:10.1007/978-3-319-52042-1_11
- 发表时间:2016-08
- 期刊:
- 影响因子:0
- 作者:K. Zumbrun
- 通讯作者:K. Zumbrun
Stable manifolds for a class of singular evolution equations and exponential decay of kinetic shocks
一类奇异演化方程的稳定流形和运动激波的指数衰减
- DOI:10.3934/krm.2019001
- 发表时间:2019
- 期刊:
- 影响因子:1
- 作者:Pogan, Alin;Zumbrun, Kevin
- 通讯作者:Zumbrun, Kevin
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Kevin Zumbrun其他文献
Pointwise Estimates and Stability for Dispersive–Diffusive Shock Waves
- DOI:
10.1007/s002050000110 - 发表时间:
2000-11-01 - 期刊:
- 影响因子:2.400
- 作者:
Peter Howard;Kevin Zumbrun - 通讯作者:
Kevin Zumbrun
Stability of viscous detonations for Majda’s model
- DOI:
10.1016/j.physd.2013.06.001 - 发表时间:
2013-09-15 - 期刊:
- 影响因子:
- 作者:
Jeffrey Humpherys;Gregory Lyng;Kevin Zumbrun - 通讯作者:
Kevin Zumbrun
Erratum to: Stability and Asymptotic Behavior of Periodic Traveling Wave Solutions of Viscous Conservation Laws in Several Dimensions
- DOI:
10.1007/s00205-010-0291-0 - 发表时间:
2010-01-26 - 期刊:
- 影响因子:2.400
- 作者:
Myunghyun Oh;Kevin Zumbrun - 通讯作者:
Kevin Zumbrun
Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation
- DOI:
10.1007/s00285-010-0379-z - 发表时间:
2010-11-13 - 期刊:
- 影响因子:2.300
- 作者:
Shantia Yarahmadian;Blake Barker;Kevin Zumbrun;Sidney L. Shaw - 通讯作者:
Sidney L. Shaw
Stability of Viscous Weak Detonation Waves for Majda’s Model
- DOI:
10.1007/s10884-015-9440-3 - 发表时间:
2015-03-13 - 期刊:
- 影响因子:1.300
- 作者:
Jeffrey Hendricks;Jeffrey Humpherys;Gregory Lyng;Kevin Zumbrun - 通讯作者:
Kevin Zumbrun
Kevin Zumbrun的其他文献
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{{ truncateString('Kevin Zumbrun', 18)}}的其他基金
Multi-Dimensional and Vorticity Effects in Inclined Shallow Water Flow
倾斜浅水流的多维和涡度效应
- 批准号:
2206105 - 财政年份:2022
- 资助金额:
$ 20.8万 - 项目类别:
Standard Grant
Frontiers in Modulation, Dynamics, and Pattern Formation for Hyperbolic, Kinetic, and Convection-Reaction-Diffusion Systems
双曲、动力学和对流-反应-扩散系统的调制、动力学和图案形成前沿
- 批准号:
2154387 - 财政年份:2022
- 资助金额:
$ 20.8万 - 项目类别:
Standard Grant
New problems in continuum mechanics: asymptotic eigenvalue distributions, rigorous numerical stability analysis and weakly nonlinear asymptotics in periodic thin film flow
连续介质力学的新问题:周期性薄膜流中的渐近特征值分布、严格的数值稳定性分析和弱非线性渐近
- 批准号:
1400555 - 财政年份:2014
- 资助金额:
$ 20.8万 - 项目类别:
Continuing Grant
Stability and dynamics of shock, detonation, and boundary layers
冲击、爆炸和边界层的稳定性和动力学
- 批准号:
0801745 - 财政年份:2008
- 资助金额:
$ 20.8万 - 项目类别:
Continuing Grant
Laser-Matter Interactions and Highly Nonlinear Geometrical Optics; Dynamics of Reacting Flows
激光与物质相互作用和高度非线性几何光学;
- 批准号:
0505780 - 财政年份:2005
- 资助金额:
$ 20.8万 - 项目类别:
Standard Grant
Stability of compressible flow in real media
实际介质中可压缩流的稳定性
- 批准号:
0300487 - 财政年份:2003
- 资助金额:
$ 20.8万 - 项目类别:
Continuing Grant
Hydrodynamic Stability in viscous, compressible flow
粘性可压缩流中的流体动力学稳定性
- 批准号:
0070765 - 财政年份:2000
- 资助金额:
$ 20.8万 - 项目类别:
Continuing Grant
I. Stability of Waves in Viscous Conservation Laws. II. Phase Transitions and Minimal Surfaces
I. 粘性守恒定律中波的稳定性。
- 批准号:
9706842 - 财政年份:1997
- 资助金额:
$ 20.8万 - 项目类别:
Continuing Grant
Mathematical Sciences: Problems in Conservation Laws
数学科学:守恒定律问题
- 批准号:
9404384 - 财政年份:1994
- 资助金额:
$ 20.8万 - 项目类别:
Standard Grant
Mathematical Sciences: Postdoctoral Research Fellowship
数学科学:博士后研究奖学金
- 批准号:
9107990 - 财政年份:1991
- 资助金额:
$ 20.8万 - 项目类别:
Fellowship Award
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