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

P. H. Chavanis; M. Ribot; C. Rosier; C. Sire

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

P. H. Chavanis·M. Ribot·C. Rosier·C. Sire

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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.

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P. H. Chavanis, M. Ribot, C. Rosier, C. Sire. 2004-07-15. On the analogy between self-gravitating Brownian particles and bacterial populations. https://arxiv.org/abs/cond-mat/0407386

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