Chavanis, Pierre-Henri; Ribot, Magali; Rosier, Carole; Sire, Clément On the analogy between self-gravitating Brownian particles and bacterial populations. (English) Zbl 1055.92005 Biler, Piotr (ed.) et al., Nonlocal elliptic and parabolic problems. Papers of the conference, Bȩdlewo, Poland, September 12–15, 2003. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 66, 103-126 (2004). Summary: 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.For the entire collection see [Zbl 1052.35002]. Cited in 5 Documents MSC: 92C17 Cell movement (chemotaxis, etc.) 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) PDFBibTeX XMLCite \textit{P.-H. Chavanis} et al., Banach Cent. Publ. 66, 103--126 (2004; Zbl 1055.92005) Full Text: arXiv