{
  "id": "1009.2884",
  "version": "v3",
  "published": "2010-09-15T10:02:39.000Z",
  "updated": "2011-07-25T17:02:49.000Z",
  "title": "Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature",
  "authors": [
    "Pierre-Henri Chavanis",
    "Clément Sire"
  ],
  "journal": "Phys. Rev. E 83, 031131 (2011)",
  "doi": "10.1103/PhysRevE.83.031131",
  "categories": [
    "cond-mat.stat-mech",
    "q-bio.QM"
  ],
  "abstract": "We provide an exact analytical solution of the collapse dynamics of self-gravitating Brownian particles and bacterial populations at zero temperature. These systems are described by the Smoluchowski-Poisson system or Keller-Segel model in which the diffusion term is neglected. As a result, the dynamics is purely deterministic. A cold system undergoes a gravitational collapse leading to a finite time singularity: the central density increases and becomes infinite in a finite time t_coll. The evolution continues in the post collapse regime. A Dirac peak emerges, grows and finally captures all the mass in a finite time t_end, while the central density excluding the Dirac peak progressively decreases. Close to the collapse time, the pre and post collapse evolution is self-similar. Interestingly, if one starts from a parabolic density profile, one obtains an exact analytical solution that describes the whole collapse dynamics, from the initial time to the end, and accounts for non self-similar corrections that were neglected in previous works. Our results have possible application in different areas including astrophysics, chemotaxis, colloids and nanoscience.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-07-25T17:02:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.90.+m",
      "05.40.-a",
      "47.20.-k",
      "05.70.-a"
    ],
    "keywords": [
      "exact analytical solution",
      "self-gravitating brownian particles",
      "bacterial populations",
      "zero temperature",
      "finite time"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2011,
      "month": "Mar",
      "volume": 83,
      "number": 3,
      "pages": "031131"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvE..83c1131C"
    }
  }
}