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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2008

Critical dynamics of self-gravitating Langevin particles and bacterial populations

Résumé

We study the critical dynamics of the generalized Smoluchowski-Poisson system (for self-gravitating Langevin particles) or generalized Keller-Segel model (for the chemotaxis of bacterial populations). These models [Chavanis & Sire, PRE, 69, 016116 (2004)] are based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations with index $n$ similar to polytropic stars in astrophysics. At the critical index $n_{3}=d/(d-2)$ (where $d\ge 2$ is the dimension of space), there exists a critical temperature $\Theta_{c}$ (for a given mass) or a critical mass $M_{c}$ (for a given temperature). For $\Theta>\Theta_{c}$ or $MM_{c}$ the system collapses and forms, in a finite time, a Dirac peak containing a finite fraction $M_c$ of the total mass surrounded by a halo. This study extends the critical dynamics of the ordinary Smoluchowski-Poisson system and Keller-Segel model in $d=2$ corresponding to isothermal configurations with $n_{3}\to +\infty$. We also stress the analogy between the limiting mass of white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial populations in the generalized Keller-Segel model of chemotaxis.

Dates et versions

hal-00318716 , version 1 (04-09-2008)

Identifiants

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Clément Sire, Pierre-Henri Chavanis. Critical dynamics of self-gravitating Langevin particles and bacterial populations. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 78, pp.061111. ⟨10.1103/PhysRevE.78.061111⟩. ⟨hal-00318716⟩
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