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

Pierre-Henri Chavanis; Magali Ribot; Carole Rosier; Clément Sire

Banach Center Publications (2004)

- Volume: 66, Issue: 1, page 103-126
- ISSN: 0137-6934

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topPierre-Henri Chavanis, et al. "On the analogy between self-gravitating Brownian particles and bacterial populations." Banach Center Publications 66.1 (2004): 103-126. <http://eudml.org/doc/282071>.

@article{Pierre2004,

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.},

author = {Pierre-Henri Chavanis, Magali Ribot, Carole Rosier, Clément Sire},

journal = {Banach Center Publications},

language = {eng},

number = {1},

pages = {103-126},

title = {On the analogy between self-gravitating Brownian particles and bacterial populations},

url = {http://eudml.org/doc/282071},

volume = {66},

year = {2004},

}

TY - JOUR

AU - Pierre-Henri Chavanis

AU - Magali Ribot

AU - Carole Rosier

AU - Clément Sire

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

JO - Banach Center Publications

PY - 2004

VL - 66

IS - 1

SP - 103

EP - 126

AB - 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.

LA - eng

UR - http://eudml.org/doc/282071

ER -

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