Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature - Université Toulouse 3 Accéder directement au contenu
Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2011

Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature

Résumé

We provide an exact analytical solution of the collapse dynamics of self-gravitating Brownian particles and bacterial populations at zero temperature. These systems are described by the Smoluchowski-Poisson system or Keller-Segel model in which the diffusion term is neglected. As a result, the dynamics is purely deterministic. A cold system undergoes a gravitational collapse leading to a finite time singularity: the central density increases and becomes infinite in a finite time t_coll. The evolution continues in the post collapse regime. A Dirac peak emerges, grows and finally captures all the mass in a finite time t_end, while the central density excluding the Dirac peak progressively decreases. Close to the collapse time, the pre and post collapse evolution is self-similar. Interestingly, if one starts from a parabolic density profile, one obtains an exact analytical solution that describes the whole collapse dynamics, from the initial time to the end, and accounts for non self-similar corrections that were neglected in previous works. Our results have possible application in different areas including astrophysics, chemotaxis, colloids and nanoscience.

Dates et versions

hal-00526890 , version 1 (16-10-2010)

Identifiants

Citer

Pierre-Henri Chavanis, Clément Sire. Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2011, 83 (3), pp.031131. ⟨10.1103/PhysRevE.83.031131⟩. ⟨hal-00526890⟩
39 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More