Characterizing Spatio-Temporal Patterns of Swarms

这个项目的目的是调查以蜂拥而至为代表的大群个体代理的集体行为。除了其内在的科学价值外，了解在自然界中观察到的集体行为(如在鸟群和鱼群中观察到的)预计将促进以纳米颗粒运送药物或执行组装和进行搜索的微型机器人的形式控制技术群的能力。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它们与实验观测的相关性的研究。该项目在不同的数学工具之间建立了一座桥梁，用于描述蜂拥而至的行为，并在从生物学到机器人以及从营销到意见形成的应用领域中对此类行为进行实验相关的测量。对于许多常见的数学模型，群的特征是基本的(例如，群集或碾磨)，并且基于简单的全局量(即平均速度或角动量)。相比之下，这个项目专注于更复杂的观测，揭示了蜂群和蜂群模型的关键属性。例如，信息传播的速度对于蜂群避开障碍物或捕食者至关重要，可以通过对不同类型的行波的分析来表征信息的传播速度。同样，与边界和其他群体的相互作用会产生驻波形式的内部激发。将蜂群行为和可观察性联系起来，需要对微观和宏观两个尺度进行研究。因此，本项目将把信息论和统计物理学的工具(微观模型)与偏微分方程式的分析(宏观模型)结合起来。

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).