Differential Equations and Nonlinear Analysis Seminar: Rupert L. Frank, California Institute of Technology, A ‘liquid-solid’ phase transition in a simple model for swarming
ZoomWe consider a non-local optimization problem, which is motivated by a simple model for swarming and other self-assembly/aggregation models, and prove the existence of different phases. In particular, we show that in the large mass regime the ground state density profile is the characteristic function of a round ball. An essential ingredient in our proof…