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Journal Articles Banach Center Publications Year : 2004

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

Abstract

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.

Dates and versions

hal-00004880 , version 1 (09-05-2005)

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Pierre-Henri Chavanis, Magali Ribot, C. Rosier, Clément Sire. On the analogy between self-gravitating Brownian particles and bacterial populations. Banach Center Publications, 2004, 66, pp.103. ⟨hal-00004880⟩
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