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Rupert L. Frank, California Institute of Technology, A ‘liquid-solid’ phase transition in a simple model for swarming
September 23, 2020 | 3:00 pm - 4:00 pm EDT
We 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 is a strict rearrangement inequality with a quantitative error estimate. We formulate several open problems which might be amenable to PDE techniques.
(Zoom meeting: Link pass: 1234)