{
  "id": "0705.4366",
  "version": "v2",
  "published": "2007-05-30T11:23:14.000Z",
  "updated": "2008-11-20T17:05:06.000Z",
  "title": "Critical mass of bacterial populations in a generalized Keller-Segel model. Analogy with the Chandrasekhar limiting mass of white dwarf stars",
  "authors": [
    "Pierre-Henri Chavanis",
    "Clement Sire"
  ],
  "journal": "Physica A, 387, 1999 (2008)",
  "doi": "10.1016/j.physa.2007.10.075",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We point out a remarkable analogy between the limiting mass of white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial populations in a generalized Keller-Segel model of chemotaxis [Chavanis & Sire, PRE, 69, 016116 (2004)]. This model is based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations similar to gaseous polytropes in astrophysics. For the critical index n_3=d/(d-2) (where d is the dimension of space), the theory of polytropes leads to a unique value of the mass M_c that we interpret as a limiting mass. In d=3, we find M_c=202.8956... and in d=2, we recover the well-known result M_c=8 pi (in suitable units). For M<M_c, the system evaporates (in an infinite domain) or tends to an equilibrium state (for box-confined configurations). For M>M_c, the system collapses and forms a Dirac peak containing a mass M_c surrounded by a halo. This paper exposes the model and shows, by simple considerations, the origin of the critical mass. A detailed description of the critical dynamics of the generalized Keller-Segel model will be given in a forthcoming paper.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-20T17:05:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized keller-segel model",
      "white dwarf stars",
      "critical mass",
      "chandrasekhar limiting mass",
      "bacterial populations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Physica A Statistical Mechanics and its Applications",
      "year": 2008,
      "month": "Mar",
      "volume": 387,
      "number": "8-9",
      "pages": 1999
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhyA..387.1999C"
    }
  }
}