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
• 负责人: Pierre-Emmanuel Jabin
• 金额: $ 38.3万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-15 至 2020-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1908739&HistoricalAwards=false
• 关键词: Quantifying; Chaos; Correlations; Oscillations; Multi

The project studies transport and advection equations with applications in the Biosciences, Statistical Physics and Fluid Mechanics. A first guiding example for the research includes large systems of interacting "agents" or "particles" that have long been employed in Physics: in Astrophysics to predict the evolution in time of galaxies or galaxy clusters to try to understand how they are formed, in plasmas to describe the dynamics of ions and electrons in plasmas, to model the behavior of air bubbles in water or other small objects in a fluid. In addition, such large systems are now widely used in Biology to model the motion of micro-organisms ("particles" can then be cells in the human body), in Finance and Economics, and other Social Sciences. A second guiding set of examples is composed of various fluid models (liquid or gas) which can exhibit complex compressive effects commonly found in geophysical (oceans or atmosphere) or biological settings. The project aims at deriving and validating effective models: By reducing the complexity of large systems of agents/particles through the so-called mean-field limit, or by controlling the behavior of effective state laws in Fluid Mechanics that are a priori unstable.The models investigated in this research all employ transport equations: non-linear convection systems in low dimension for compressible fluids, the linear Liouville equation in very large dimension for simple multi-agent systems but more also more complex non-linear equations (such as Hamilton-Jacobi-Bellman) for systems with control. The project focuses in particular on systems that are unstable or singular and are expected to create or amplify correlations and oscillations. A key unifying question in the research is to identify the critical scale in the models to quantify how those correlations or oscillations may develop. For large systems of particles, the project makes use of explicit estimates involving the rescaled relative entropy, renormalized to include the comparisons between the Gibbs equilibria. For convective models, the project introduces new semi-norms which precisely track the possible oscillations in the density at the critical log or log log scales.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.

该项目研究了在生物科学，统计物理学和流体力学中应用的运输和对流方程。该研究的第一个指导示例包括长期以来在物理学中使用的大量相互作用的“剂”或“颗粒”系统：在天体物理学中预测星系或星系簇时间的演变，以试图在等离子体中理解它们在等离子体中的形成方式，以描述在等离子和电子中的动态，以形成空气中的流动或其他小对象或其他小对象。 此外，现在如此大的系统在生物学中被广泛用于模拟微生物的运动（然后可以是人体中的细胞），在金融和经济学以及其他社会科学中。第二组引导示例由各种流体模型（液体或气体）组成，这些模型可能表现出在地球物理（海洋或大气）或生物环境中常见的复杂压缩效果。该项目旨在通过所谓的均值场限制来降低大型试剂/颗粒系统/颗粒的复杂性，或通过控制有效的状态法律在流体机制中的行为，这些模型在本研究中进行了调查。对于具有控制的系统，也更复杂的非线性方程（例如汉密尔顿 - 雅各布 - 贝尔曼）。该项目尤其着重于不稳定或奇异的系统，并有望创建或放大相关性和振荡。研究中的一个关键统一问题是确定模型中的临界量表，以量化这些相关性或振荡的发展方式。对于大型粒子系统，该项目利用涉及重新验证的相对熵的明确估计值，重新归一化以包括吉布斯平衡之间的比较。对于对流模型，该项目引入了新的半符号，这些半符号可以准确地跟踪关键日志或日志尺度上的密度振荡。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响审查标准来评估的支持。

项目成果

Global weak solutions to the relativistic BGK equation

• DOI: 10.1080/03605302.2019.1669642
• 发表时间: 2019-02
• 期刊: Communications in Partial Differential Equations
• 影响因子: 1.9
• 作者: J. Calvo;P. Jabin;J. Soler

Analysis of Hyperspectral Data by Means of Transport Models and Machine Learning

• DOI: 10.1109/igarss39084.2020.9323215
• 发表时间: 2020-09
• 期刊: IGARSS 2020 - 2020 IEEE International Geoscience and Remote Sensing Symposium
• 作者: W. Czaja;Dong Dong-Dong;P. Jabin;Franck Olivier Ndjakou Njeunje

Local regularity result for an optimal transportation problem with rough measures in the plane.

局部规律性导致了平面上粗略措施的最优运输问题。

• 发表时间: 2021
• 期刊: Annals of functional analysis
• 影响因子: 1
• 作者: Jabin, P.-E.;Mellet, A.;Molina-Fructuoso, M.
• 通讯作者: Molina-Fructuoso, M.