{
  "id": "cond-mat/0501417",
  "version": "v1",
  "published": "2005-01-18T12:29:02.000Z",
  "updated": "2005-01-18T12:29:02.000Z",
  "title": "Nonextensive statistics in viscous fingering",
  "authors": [
    "Patrick Grosfils",
    "Jean Pierre Boon"
  ],
  "comment": "8 pages including 3 figures; to appear in PHYSICA A",
  "doi": "10.1016/j.physa.2005.09.007",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Measurements in turbulent flows have revealed that the velocity field in nonequilibrium systems exhibits $q$-exponential or power law distributions in agreement with theoretical arguments based on nonextensive statistical mechanics. Here we consider Hele-Shaw flow as simulated by the Lattice Boltzmann method and find similar behavior from the analysis of velocity field measurements. For the transverse velocity, we obtain a spatial $q$-Gaussian profile and a power law velocity distribution over all measured decades. To explain these results, we suggest theoretical arguments based on Darcy's law combined with the non-linear advection-diffusion equation for the concentration field. Power law and $q$-exponential distributions are the signature of nonequilibrium systems with long-range interactions and/or long-time correlations, and therefore provide insight to the mechanism of the onset of fingering processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-18T12:29:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonextensive statistics",
      "viscous fingering",
      "nonequilibrium systems",
      "power law velocity distribution",
      "theoretical arguments"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}