title: Postcollapse dynamics of self-gravitating Brownian particles and bacterial populations.
abstract: We address the postcollapse dynamics of a self-gravitating gas of Brownian particles in D dimensions in both canonical and microcanonical ensembles. In the canonical ensemble, the postcollapse evolution is marked by the formation of a Dirac peak with increasing mass. The density profile outside the peak evolves self-similarly with decreasing central density and increasing core radius. In the microcanonical ensemble, the postcollapse regime is marked by the formation of a "binarylike" structure surrounded by an almost uniform halo with high temperature. These results are consistent with thermodynamical predictions in astrophysics. We also show that the Smoluchowski-Poisson system describing the collapse of self-gravitating Brownian particles in a strong-friction limit is isomorphic to a simplified version of the Keller-Segel equations describing the chemotactic aggregation of bacterial populations. Therefore, our study has direct applications in this biological context.
authors.affiliation: Laboratoire de Physique Théorique (FRE 2603 du CNRS), Université Paul Sabatier, 118, route de Narbonne,31062 Toulouse Cedex 4, France. Clement.Sire@irsaamc.ups-tlse.fr
authors.forename: Clément
authors.initials: C
authors.lastname: Sire
authors.forename: Pierre-Henri
authors.initials: PH
authors.lastname: Chavanis