Biological aggregations such as insect swarms, bird flocks, and fish schools are arguably some of the most common and least understood patterns in nature. The groups are thought to arise from "social forces" acting on individual organisms, including attraction (for protection and mate choice) and dispersion (for collision avoidance). In this talk, I will discuss recent work on two models investigating characteristics shared by many different aggregations, namely sharp edges and a nearly constant internal population density. The work aims to elucidate the connection between individuals' rules for movement and these macroscopic group properties. In the first model, movement rules of incompressible form provide a mechanism for the formation of vortex-like swarms. In the second model, long-range attraction and short-range dispersal lead to coarsening dynamics and population "clumps". For both models, the mathematical goal is to find localized (compactly supported) solutions of nonlinear partial integrodifferential conservation equations. Time permitting, I will also discuss ongoing work on the modeling of rolling locust swarms.
Audio (MP3 File, Podcast Ready)