{
  "id": "0804.3517",
  "version": "v2",
  "published": "2008-04-22T12:37:01.000Z",
  "updated": "2009-01-16T13:41:54.000Z",
  "title": "Critical dynamics of self-gravitating Langevin particles and bacterial populations",
  "authors": [
    "Clement Sire",
    "Pierre-Henri Chavanis"
  ],
  "journal": "Phys. Rev. E, 78, 061111 (2008)",
  "doi": "10.1103/PhysRevE.78.061111",
  "categories": [
    "cond-mat.stat-mech",
    "q-bio.PE",
    "q-bio.QM"
  ],
  "abstract": "We study the critical dynamics of the generalized Smoluchowski-Poisson system (for self-gravitating Langevin particles) or generalized Keller-Segel model (for the chemotaxis of bacterial populations). These models [Chavanis & Sire, PRE, 69, 016116 (2004)] are based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations with index $n$ similar to polytropic stars in astrophysics. At the critical index $n_{3}=d/(d-2)$ (where $d\\ge 2$ is the dimension of space), there exists a critical temperature $\\Theta_{c}$ (for a given mass) or a critical mass $M_{c}$ (for a given temperature). For $\\Theta>\\Theta_{c}$ or $M<M_{c}$ the system tends to an incomplete polytrope confined by the box (in a bounded domain) or evaporates (in an unbounded domain). For $\\Theta<\\Theta_{c}$ or $M>M_{c}$ the system collapses and forms, in a finite time, a Dirac peak containing a finite fraction $M_c$ of the total mass surrounded by a halo. This study extends the critical dynamics of the ordinary Smoluchowski-Poisson system and Keller-Segel model in $d=2$ corresponding to isothermal configurations with $n_{3}\\to +\\infty$. We also stress the analogy between the limiting mass of white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial populations in the generalized Keller-Segel model of chemotaxis.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-16T13:41:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.90.+m",
      "05.40.-a",
      "47.20.-k",
      "05.70.-a"
    ],
    "keywords": [
      "self-gravitating langevin particles",
      "bacterial populations",
      "critical dynamics",
      "generalized keller-segel model",
      "white dwarf stars"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2008,
      "month": "Dec",
      "volume": 78,
      "number": 6,
      "pages": "061111"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvE..78f1111S"
    }
  }
}