Hydrodynamics of Collective Phenomena and Applications

集体现象的流体动力学及其应用

基本信息

批准号：
2107956
负责人：
Roman Shvydkoy
金额：
$ 33万
依托单位：
University of Illinois at Chicago
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-06-01 至 2024-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2107956&HistoricalAwards=false
关键词：
Hydrodynamics Collective Phenomena Applications

项目摘要

Among the various collective phenomena observed in nature there are many that resemble the motion of a fluid. Such examples are abundant in biology, for example, a large flock of birds swinging constantly changing shape or a school of fish swirling in a milling pattern. Other examples include crowd dynamics and social networking, for example the formation of friend-clusters on social media, or dynamics of opinions among a large group of individuals. Examples also arise in technology, such as the coordinated fight of an escort of unmanned aerial vehicles or satellite navigation. All of these large systems are governed by models similar to those we use to study motion of a liquid, like water or gas. A set of new ideas on how to study this analogy recently developed into a new mathematical subject, called Hydrodynamics of Collective Behavior. This project will analyze hydrodynamic collective models both from the point of view of their mathematical properties and with a view towards their applications to self-organized dynamics and emergent phenomena.Central to the project will be analysis of the so-called Euler Alignment Systems (EAS for short). Particular focus will be placed on justification of a class of isentropic EASs via the hydrodynamic limit from a noisy kinetic Fokker-Plank model. In the framework of systems with singular communication introduced in PI’s earlier works, the project sets forth a program of research on understanding topological interactions prevalent in many biological systems. Such interactions enrich the models with a possibility of more diverse collective outcomes and, from theoretical perspective, endow them with a fractional parabolic structure. The regularity theory exploiting this parabolic structure will be developed in the context of unidirectional flocks. Applications of this research will be made to several fields of mathematics including the so-called opinion mean-field games and finding their Nash equilibria, alignment of interfacial profile in two-fluid porous media problem, and modeling turbulent energy cascade in 2D inviscid fluid flows.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.

在自然界观察到的各种集体现象中，有许多类似于流体的运动。这样的例子在生物学中很丰富，例如，大批鸟类不断变化的形状或以磨坊模式旋转的鱼类。其他示例包括人群动态和社交网络，例如在社交媒体上形成朋友群体，或大量个人观点的动态。技术也出现了例子，例如无人驾驶汽车或卫星导航的伴游的协调战斗。所有这些大型系统都受模型的控制，类似于我们用于研究液体运动（如水或气体）的模型。关于如何研究这种类比的一系列新想法最近发展成为一个新的数学主题，称为集体行为的流体动力学。该项目将从其数学特性的角度来分析流体动力集体模型，并以特殊的重点放在通过从嘈杂的动力学fokker plank模型中的流体动力学限制的一类等质EAS的理由上。在PI较早作品中引入的具有单一沟通的系统的框架中，该项目阐述了一项有关理解许多生物系统中普遍存在的拓扑相互作用的研究计划。这种相互作用丰富了模型，具有更多样化的集体结果，从理论的角度来看，它们具有分数的抛物线结构。利用这种抛物线结构的规律性理论将在单向羊群的背景下发展。这项研究的应用将在几个数学领域中进行，包括所谓的意见均值游戏，并在两流体多孔的媒体问题中找到其NASH等效，对界面概况的一致性，并在2D Inviscid Flic中对动荡的能量级联建模，这些奖项通过评估NSF的智力传统，并反映了NSF的Intection Merit。标准。