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Accueil du site > Publications > Publications 2004 > On the analogy between self-gravitating Brownian particles and bacterial populations

On the analogy between self-gravitating Brownian particles and bacterial populations

P.H. Chavanis, M. Ribot, C. Rosier, and C. Sire

par Clément Sire - 11 avril 2006

We develop the analogy between self-gravitating Brownian particles and bacterial populations. In the high friction limit, the self-gravitating Brownian gas is described by the Smoluchowski-Poisson system. These equations can develop a self-similar collapse leading to a finite time singularity. Coincidentally, the Smoluchowski-Poisson system corresponds to a simplified version of the Keller-Segel model of bacterial populations. In this biological context, it describes the chemotactic aggregation of the bacterial colonies. We extend these classical models by introducing a small-scale regularization. In the gravitational context, we consider a gas of self-gravitating Brownian fermions and in the biological context we consider finite size effects. In that case, the collapse stops when the system feels the influence of the small-scale regularization. A phenomenon of “explosion”, reverse to the collapse, is also possible.

Preprint cond-mat/0407386