CAREER: Emerging Challenges in Wave Turbulence Theory
职业:波浪湍流理论中的新挑战
基本信息
- 批准号:2044626
- 负责人:
- 金额:$ 43万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2021
- 资助国家:美国
- 起止时间:2021-09-01 至 2022-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Wave turbulence (WT) is a general physical phenomenon describing the nonlinear dynamical interactions of waves far from thermal equilibrium. Examples of wave turbulence occur in classical surface water waves and also in quantum dynamical systems involving a Bose-Einstein condensate (BEC). Even though wave fields describing the processes of random wave interactions in nature are enormously diverse, there is a common mathematical framework that models and describes the dynamics of spectral energy transfer through probability densities associated with weakly non-linear interactions in quantum or classical wave systems. The probability densities are solutions of wave kinetic (WK) equations, whose nonlocal interaction operators are of kinetic type. This project aims to tackle open challenges in the theory of nonlinear waves via the study of the associated wave turbulence theory. An integral part of the project is its educational component and the opportunities to involve students from all levels in the research. To this end, the principal investigator will organize summer schools for underrepresented and disabled K-12 students, design graduate courses on Partial Differential Equations, Wave Turbulence and Statistical Physics, and organize an undergraduate and graduate research internship program of excellence and a mathematics-physics conference for young researchers. In addition, the principal investigator will participate in the NSF RTG SMU summer undergraduate research program, with participants from both SMU and Texas Rio Grande Valley University (a Hispanic-serving institution) as well as the SMU Hamilton Undergraduate Research Scholars and the SMU Undergraduate Research Assistant Programs. This project concentrates on three main topics in WT theory. The first topic is to study the rigorous justification of 3-wave kinetic equations, by the Feynman diagrammatic approach. The second topic is to establish a mathematical foundation for the Garrett-Munk spectrum of the ocean, using the renormalization group method. The third topic is the proof of the finite time formation of singularities of solutions to the finite temperature BEC system, with the addition of a new, previously missing, collision operator derived by Yves Pomeau and the principal investigator. Several ideas from kinetic theory, dispersive equations, oceanography, and quantum mechanics will be combined to study the proposed problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
波浪湍流是描述远离热平衡的波浪之间非线性动力相互作用的一种普遍物理现象。波湍流的例子发生在经典的表面水波中,也发生在涉及玻色-爱因斯坦凝聚(BEC)的量子动力学系统中。尽管描述自然界中随机波相互作用过程的波场非常多样,但有一个共同的数学框架,通过与量子或经典波系统中弱非线性相互作用相关的概率密度来建模和描述谱能量转移的动力学。概率密度是波动方程(WK)的解,其非局部相互作用算子是动力学型的。该项目旨在通过研究相关的波浪湍流理论来解决非线性波浪理论中的公开挑战。该项目的一个组成部分是其教育部分和让各级学生参与研究的机会。为此,首席研究员将为代表性不足和残疾的K-12学生组织暑期学校,设计偏微分方程,波浪湍流和统计物理学的研究生课程,并为年轻研究人员组织本科生和研究生卓越的研究实习计划和南极物理学会议。此外,首席研究员将参加NSF RTG SMU夏季本科研究项目,参与者来自SMU和德克萨斯州格兰德河谷大学(一所西班牙裔服务机构)以及SMU汉密尔顿本科研究学者和SMU本科研究助理计划。这个项目集中在WT理论的三个主要主题。第一个主题是研究三波动力学方程的严格证明,用费曼图解法。 第二个主题是使用重整化群方法建立海洋Garrett-Munk谱的数学基础。第三个主题是有限温度BEC系统的解决方案的奇点的有限时间形成的证明,增加了一个新的,以前失踪,碰撞运营商得出的Yves Pomeau和首席研究员。该奖项反映了NSF的法定使命,并通过使用基金会的智力价值和更广泛的影响审查标准进行评估,被认为值得支持。
项目成果
期刊论文数量(4)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Wave turbulence and collective behavior models for wave equations with short- and long-range interactions
- DOI:10.23952/cot.2022.2
- 发表时间:2021-10
- 期刊:
- 影响因子:0
- 作者:A. Aceves;R. Alonso;Minh-Binh Tran
- 通讯作者:A. Aceves;R. Alonso;Minh-Binh Tran
On a thermal cloud—Bose–Einstein condensate coupling system
在热云上——玻色——爱因斯坦凝聚耦合系统
- DOI:10.1140/epjp/s13360-021-01510-z
- 发表时间:2021
- 期刊:
- 影响因子:0
- 作者:Tran, Minh-Binh;Pomeau, Yves
- 通讯作者:Pomeau, Yves
A deep learning approximation of non-stationary solutions to wave kinetic equations
波动动力学方程非平稳解的深度学习近似
- DOI:10.1016/j.apnum.2022.12.010
- 发表时间:2022
- 期刊:
- 影响因子:2.8
- 作者:Walton, Steven;Tran, Minh-Binh;Bensoussan, Alain
- 通讯作者:Bensoussan, Alain
A reaction network approach to the convergence to equilibrium of quantum Boltzmann equations for Bose gases
- DOI:10.1051/cocv/2021079
- 发表时间:2016-08
- 期刊:
- 影响因子:0
- 作者:G. Craciun;Minh-Binh Tran
- 通讯作者:G. Craciun;Minh-Binh Tran
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Minh-Binh Tran其他文献
On the dynamics of finite temperature trapped Bose gases
- DOI:
10.1016/j.aim.2017.12.007 - 发表时间:
2018-02-05 - 期刊:
- 影响因子:1.7
- 作者:
Soffer, Avy;Minh-Binh Tran - 通讯作者:
Minh-Binh Tran
A structure preserving scheme for the Kolmogorov–Fokker–Planck equation
- DOI:
10.1016/j.jcp.2016.11.009 - 发表时间:
2017-02-01 - 期刊:
- 影响因子:
- 作者:
Erich L. Foster;Jérôme Lohéac;Minh-Binh Tran - 通讯作者:
Minh-Binh Tran
On the wave turbulence theory: ergodicity for the elastic beam wave equation
- DOI:
10.1007/s00209-025-03734-6 - 发表时间:
2025-04-05 - 期刊:
- 影响因子:1.000
- 作者:
Benno Rumpf;Avy Soffer;Minh-Binh Tran - 通讯作者:
Minh-Binh Tran
Parallel Schwarz Waveform Relaxation Algorithm for an N-Dimensional Semilinear Heat Equation
- DOI:
10.1051/m2an/2013121 - 发表时间:
2010-06 - 期刊:
- 影响因子:0
- 作者:
Minh-Binh Tran - 通讯作者:
Minh-Binh Tran
Controlling the rates of a chain of harmonic oscillators with a point Langevin thermostat
用点朗之万热浴控制一系列谐波振荡器的速率
- DOI:
10.1016/j.jde.2025.01.054 - 发表时间:
2025-05-05 - 期刊:
- 影响因子:2.300
- 作者:
Amirali Hannani;Minh-Nhat Phung;Minh-Binh Tran;Emmanuel Trélat - 通讯作者:
Emmanuel Trélat
Minh-Binh Tran的其他文献
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{{ truncateString('Minh-Binh Tran', 18)}}的其他基金
Collaborative Research: On New Directions for the Derivation of Wave Kinetic Equations
合作研究:波动力学方程推导的新方向
- 批准号:
2306379 - 财政年份:2024
- 资助金额:
$ 43万 - 项目类别:
Standard Grant
Questions in Wave Turbulence and Quantum Kinetic Theories
波湍流和量子动力学理论中的问题
- 批准号:
2305523 - 财政年份:2022
- 资助金额:
$ 43万 - 项目类别:
Standard Grant
CAREER: Emerging Challenges in Wave Turbulence Theory
职业:波浪湍流理论中的新挑战
- 批准号:
2303146 - 财政年份:2022
- 资助金额:
$ 43万 - 项目类别:
Continuing Grant
Questions in Wave Turbulence and Quantum Kinetic Theories
波湍流和量子动力学理论中的问题
- 批准号:
1854453 - 财政年份:2018
- 资助金额:
$ 43万 - 项目类别:
Standard Grant
Questions in Wave Turbulence and Quantum Kinetic Theories
波湍流和量子动力学理论中的问题
- 批准号:
1814149 - 财政年份:2018
- 资助金额:
$ 43万 - 项目类别:
Standard Grant
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