{
  "id": "cond-mat/0402227",
  "version": "v1",
  "published": "2004-02-08T18:22:15.000Z",
  "updated": "2004-02-08T18:22:15.000Z",
  "title": "Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations",
  "authors": [
    "Pierre-Henri Chavanis",
    "Clement Sire"
  ],
  "journal": "Phys. Rev. E, 70, 026115 (2004)",
  "doi": "10.1103/PhysRevE.70.026115",
  "categories": [
    "cond-mat.stat-mech",
    "astro-ph"
  ],
  "abstract": "We determine an asymptotic expression of the blow-up time t_coll for self-gravitating Brownian particles or bacterial populations (chemotaxis) close to the critical point. We show that t_coll=t_{*}(eta-eta_c)^{-1/2} with t_{*}=0.91767702..., where eta represents the inverse temperature (for Brownian particles) or the mass (for bacterial colonies), and eta_c is the critical value of eta above which the system blows up. This result is in perfect agreement with the numerical solution of the Smoluchowski-Poisson system. We also determine the asymptotic expression of the relaxation time close but above the critical temperature and derive a large time asymptotic expansion for the density profile exactly at the critical point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-08T18:22:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-gravitating brownian particles",
      "bacterial populations",
      "large time asymptotic expansion",
      "asymptotic expression",
      "critical point"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 668980
    }
  }
}