自引力Brownian粒子与细菌群体的类比
摘要
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.
引用
@article{arxiv.cond-mat/0407386,
title = {On the analogy between self-gravitating Brownian particles and bacterial populations},
author = {P. H. Chavanis and M. Ribot and C. Rosier and C. Sire},
journal= {arXiv preprint arXiv:cond-mat/0407386},
year = {2007}
}