Illinois Mobile App Master Calendar

Title: Reversible vacuum formation in a 2D swarming model

Abstract:

One way of modeling swarming phenomena is through attraction and repulsion between individuals. We study the continuum limit of the motion of agents in the plane, driven by competing short-range repulsion and long-range attractive forces. At a critical parameter value, we find destabilization of uniformly distributed solutions and analyze bifurcating steady-states. Curiously, the bifurcating branch is vertical, leading to a reversible, non-hysteretic phase transition— an arbitrarily small change in the parameter leads to a reversible O(1) change in solutions. Previous to the bifurcation point, solutions are uniform; past the bifurcation point, solutions are clustered and form vacuum regions. We demonstrate scaling laws near onset for the size of vacuum regions, which can form fissures or bubbles. We also study the effect of small noise, and investigate stability of fissures vs. bubbles. Lastly, we give numerical simulations showing that the continuum bifurcations are good predictors of the dynamics in the finite population case.