Characterizing Spatio-Temporal Patterns of Swarms

Arizona State University, Scottsdale AZ

Investigators

Abstract

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).