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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-7,
author = {Pierre-Henri Chavanis and Magali Ribot and Carole Rosier and Cl\'ement Sire},
title = {On the analogy between self-gravitating Brownian particles and bacterial populations},
journal = {Banach Center Publications},
volume = {65},
year = {2004},
pages = {103-126},
zbl = {1055.92005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-7}
}
Pierre-Henri Chavanis; Magali Ribot; Carole Rosier; Clément Sire. On the analogy between self-gravitating Brownian particles and bacterial populations. Banach Center Publications, Tome 65 (2004) pp. 103-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-7/