The Dynamical Systems seminar is held on Monday afternoons at
4:00 PM in MCS 148. Tea
beforehand is at 3:45 PM in MCS 144.
September 11; José Antonio Carrillo
(Imperial College London)
Title: Swarming, Interaction Energies and PDEs
Abstract: I will present a survey of the main results about first and second
order models of swarming where repulsion and attraction are modeled
through pairwise potentials. We will mainly focus on the stability of
the fascinating patterns that you get by random particle simulations,
flocks and mills, and their qualitative behavior. Qualitative properties
of local minimizers of the interaction energies are crucial in order to
understand these complex behaviors. Compactly supported global
minimizers determine the flock patterns whose existence is related to
the classical H-stability in statistical mechanics and the classical
obstacle problem for differential operators.