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Swarming, Interaction Energies and PDEs

Hold Date 2017-04-13 16:30~2017-04-13 17:30

Place IMI Auditorium (W1-D-413), West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Jose Carrillo (Imperial College London)

Date: Thursday, April 13, 2017
        16:00 - 16:30 (teatime in the Information Study Room(W1-A-812), 8F, West Zone 1)
        16:30 - 17:30 (IMI Auditorium W1-D-413)

Speaker: Jose Carrillo (Imperial College London)

Title: Swarming, Interaction Energies and PDEs

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.