Alignment of self-propelled particles : from microscopic to hydrodynamic models.

Amic Frouvelle (CEREMADE, Paris)

Nov 18. 2022, 11:45 — 12:45

In this course, we present some models of alignment of self propelled particles. We start from the microscopic modelling, using systems of large number of interacting particles (either under the form of Ordinary or Stochastic differential equations, or of Piecewise Deterministic Markov Processes). When the number of particles is large, the behavior is well approximated by a kinetic equation, for which we can study phenomena of phase transitions : when the alignment force is low compared to the angular noise, the only steady-state is isotropic, while if the alignment is strong, some non-isotropic states emerge. Thanks to modified entropy methods, we can prove the convergence towards one of these steady states for the space-homogeneous version. For the space-inhomogeneous version, methods of hypocoercivity can be used to prove local stability of the isotropic state. Finally, if time allows, we will describe the large-scale limit of the kinetic equation, under the form of a hydrodynamic model, for which questions of hyperbolicity and well-posedness arise.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Mathematical Methods for the Study of Self-organization in the Biological Sciences (Thematic Programme)
Pierre Degond (IMT)
Marie Doumic (Sorbonne U, Paris)
Anna Kicheva (ISTA, Klosterneuburg)
Sara Merino-Aceituno (U of Vienna)
Christian Schmeiser (U of Vienna)