Many Particles' Systems: Theory and Applications
多粒子系统:理论与应用
基本信息
- 批准号:1312142
- 负责人:
- 金额:$ 34.13万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2013
- 资助国家:美国
- 起止时间:2013-08-01 至 2017-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The proposal investigates, theoretically and numerically, a wide spectrum of particle's systems found in various applications. The dimension of those systems is proportional to the number of particles involved which can be quite large, up to 10^{25} in some settings. This makes them too complex to analyze and too costly to solve numerically. However a key feature of those large systems is their multiscale nature: It makes the dynamics extremely complex at the microscopic level of an individual particle. But it can also lead to a drastic reduction in the complexity of the system by approximating it at the mesoscopic or macroscopic level with PDE's in lower dimensions; the main difficulty in that case is the study and control of the correlations between particles. A classical example is the usual mean field limit problem for kinetic equations in statistical physics for which the investigator will develop novel techniques in order to handle singular potentials. New extensions will be investigated as well in order to push beyond the classical framework, including bacterial suspensions, mean field games models and applications to social sciences (consensus formation...). The bacterial suspensions under study have a relatively high number density with hence non negligible correlations between the particles or bacteria. The investigator and collaborators introduce a new numerical scheme to calculate those correlations. In the case of mean field games, in addition of "classical" interactions between the particles or agents, a control on the dynamics is optimized by a central agent. The usual techniques, propagation of chaos on the joint law for instance, are no more applicable and we develop a new approach, based on the minimization of N and 1 agent energies. Systems with a very large number of particles are ubiquitous in science and engineering. Indeed depending on the context and the model, the term "particle" may represent very different objects; in the scope of this project, a particle could for instance be as "simple" as an electron or ion (particles in a plasma), or more complex like a bacteria, an economical or social agent or even a very large structure like a galaxy (dynamics of clusters in astrophysics). Reducing the complexity of such large systems, for instance by approximating them by Partial Differential Equations, is a critical step to be able to use them (numerical simulations...). The project will contribute to the understanding of this phenomenon for a few important applications: the classical framework of statistical physics, suspensions of bacteria with critical density, multi-agent systems in economy and consensus formation. The project also has a direct impact on the education and future careers of graduate students and will also involve undergraduate students.
该提案从理论上和数值上研究了各种应用中发现的各种粒子系统。这些系统的维度与所涉及的粒子数量成正比,这些粒子数量可能非常大,在某些设置中可达 10^{25}。这使得它们太复杂而无法分析,并且无法进行数值求解成本太高。然而,这些大型系统的一个关键特征是它们的多尺度性质:它使得单个粒子的微观水平上的动力学变得极其复杂。但它也可以通过使用较低维度的偏微分方程在介观或宏观水平上逼近系统,从而大幅降低系统的复杂性;这种情况下的主要困难是粒子之间相关性的研究和控制。一个经典的例子是统计物理学中运动方程的常见平均场极限问题,研究者将为此开发新技术来处理奇异势。为了超越经典框架,还将研究新的扩展,包括细菌悬浮液、平均场博弈模型和社会科学应用(形成共识……)。所研究的细菌悬浮液具有相对较高的数密度,因此颗粒或细菌之间的相关性不可忽略。研究人员和合作者引入了一种新的数值方案来计算这些相关性。在平均场博弈的情况下,除了粒子或代理之间的“经典”相互作用之外,对动力学的控制还由中央代理进行优化。通常的技术,例如联合定律上的混沌传播,不再适用,我们开发了一种基于 N 和 1 代理能量最小化的新方法。具有大量粒子的系统在科学和工程中无处不在。事实上,根据上下文和模型,术语“粒子”可能代表非常不同的对象;在该项目的范围内,粒子可以像电子或离子(等离子体中的粒子)一样“简单”,也可以更复杂,如细菌、经济或社会主体,甚至是像星系这样的非常大的结构(天体物理学中的团簇动力学)。降低此类大型系统的复杂性,例如通过偏微分方程逼近它们,是能够使用它们的关键步骤(数值模拟......)。 该项目将有助于理解这种现象的一些重要应用:统计物理学的经典框架、具有临界密度的细菌悬浮液、经济中的多智能体系统和共识形成。该项目还对研究生的教育和未来职业产生直接影响,也将涉及本科生。
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)
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Pierre-Emmanuel Jabin其他文献
Time-asymptotic convergence rates towards discrete steady states of nonlocal selection-mutation model
非局部选择变异模型离散稳态的时间渐近收敛率
- DOI:
- 发表时间:
2019 - 期刊:
- 影响因子:3.5
- 作者:
Wenli Cai;Pierre-Emmanuel Jabin;Hailiang Liu - 通讯作者:
Hailiang Liu
Pierre-Emmanuel Jabin的其他文献
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{{ truncateString('Pierre-Emmanuel Jabin', 18)}}的其他基金
Charting a New Paradigm for Large Non-Exchangeable Multi-Agent and Many-Particle Systems
为大型不可交换多代理和多粒子系统绘制新范式
- 批准号:
2205694 - 财政年份:2022
- 资助金额:
$ 34.13万 - 项目类别:
Standard Grant
DMS-EPSRC Collaborative Research: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications
DMS-EPSRC 协作研究:跨多尺度应用的非线性偏微分方程的稳定性分析
- 批准号:
2219397 - 财政年份:2022
- 资助金额:
$ 34.13万 - 项目类别:
Standard Grant
Charting a New Paradigm for Large Non-Exchangeable Multi-Agent and Many-Particle Systems
为大型不可交换多代理和多粒子系统绘制新范式
- 批准号:
2205694 - 财政年份:2022
- 资助金额:
$ 34.13万 - 项目类别:
Standard Grant
Quantifying Chaos, Correlations, and Oscillations in Multi-Agent Systems and Advection Equations
量化多智能体系统和平流方程中的混沌、相关性和振荡
- 批准号:
2049020 - 财政年份:2020
- 资助金额:
$ 34.13万 - 项目类别:
Standard Grant
Quantifying Chaos, Correlations, and Oscillations in Multi-Agent Systems and Advection Equations
量化多智能体系统和平流方程中的混沌、相关性和振荡
- 批准号:
1908739 - 财政年份:2019
- 资助金额:
$ 34.13万 - 项目类别:
Standard Grant
A novel paradigm for nonlinear convection models and large systems of particles
非线性对流模型和大型粒子系统的新范例
- 批准号:
1614537 - 财政年份:2016
- 资助金额:
$ 34.13万 - 项目类别:
Standard Grant
A novel paradigm for nonlinear convection models and large systems of particles
非线性对流模型和大型粒子系统的新范例
- 批准号:
1614537 - 财政年份:2016
- 资助金额:
$ 34.13万 - 项目类别:
Standard Grant
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