Characterizing Spatio-Temporal Patterns of Swarms

该项目旨在研究以蜂群为代表的大型个体主体群体的集体行为。除了其内在的科学价值外，理解自然界中观察到的集体行为（如鸟群和鱼群）有望促进以纳米颗粒输送药物或微型机器人进行组装和搜索的形式控制技术群体的能力。有各种各样的模型提供表面上相似的输出，也就是说，它们都产生某种集体运动。然而，缺乏区分蜂群模型并确定其与实验观察的相关性的研究。该项目在不同的数学工具之间建立了一座桥梁，用于描述群体行为，并在从生物学到机器人技术，从市场营销到舆论形成等应用领域对这种行为进行实验相关测量。对于许多常见的数学模型，群体的特征是基本的（例如，群集或铣削），并且基于简单的全局量（即平均速度或角动量）。相比之下，该项目侧重于更复杂的可观察对象，揭示了群体和群体模型的关键属性。例如，信息传播的速度对于蜂群躲避障碍物或捕食者至关重要，并且可以通过分析不同类型的行波来表征。同样，与边界和其他群的相互作用产生驻波形式的内部激励。将群体行为和可观察到的事物联系起来需要研究微观和宏观尺度。因此，本项目将信息论和统计物理（微观模型）的工具与偏微分方程（宏观模型）的分析相结合。

This project is aimed at investigation of collective behavior of large groups of individual agents that is typified by swarming. In addition to its intrinsic scientific value, understanding collective behavior observed in nature (such as in flocks of birds and schools of fish) is expected to facilitate the ability to control technological swarms in the form of nanoparticles delivering drugs or micro-robots performing assemblies and conducting searches. There is a variety of models that provide superficially similar output, that is, they all generate some sort of collective motion. However, there is a lack of studies that distinguish among swarming models and determine their relevance with respect to experimental observations. This project develops a bridge between different mathematical tools to describe swarming behavior and experimentally relevant measures of such behavior in application fields ranging from biology to robotics and from marketing to opinion formation. For many common mathematical models, characterizations of swarms are elementary (for example, flocking or milling) and are based on simple global quantities (that is, average velocity or angular momentum). In contrast, this project focuses on more complex observables unveiling key attributes of swarms and swarming models. For instance, the speed of information propagation is crucial in swarming to avoid obstacles or predators and can be characterized through the analysis of different types of traveling waves. Similarly, interaction with boundaries and other swarms generate internal excitations in the form of standing waves. Connecting swarming behavior and observables requires investigating both micro- and macro-scales. Therefore, this project will combine tools from information theory and statistical physics (micro-models) with the analysis of partial differential equations (macro-models).