{
  "id": "0711.4487",
  "version": "v1",
  "published": "2007-11-28T12:37:54.000Z",
  "updated": "2007-11-28T12:37:54.000Z",
  "title": "Generalized Diffusion",
  "authors": [
    "James F. Lutsko",
    "Jean Pierre Boon"
  ],
  "comment": "29 pages, 8 figures",
  "journal": "PHYSICAL REVIEW E 77, 051103 2008",
  "doi": "10.1103/PhysRevE.77.051103",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.mtrl-sci",
    "cond-mat.soft"
  ],
  "abstract": "The Fokker-Planck equation for the probability $f(r,t)$ to find a random walker at position $r$ at time $t$ is derived for the case that the the probability to make jumps depends nonlinearly on $f(r,t)$. The result is a generalized form of the classical Fokker-Planck equation where the effects of drift, due to a violation of detailed balance, and of external fields are also considered. It is shown that in the absence of drift and external fields a scaling solution, describing anomalous diffusion, is only possible if the nonlinearity in the jump probability is of the power law type ($\\sim f^{\\eta }(r,t)$), in which case the generalized Fokker-Planck equation reduces to the well-known Porous Media equation. Monte-Carlo simulations are shown to confirm the theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-28T12:37:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.40.Fb",
      "05.60.-k",
      "05.10.Gg"
    ],
    "keywords": [
      "generalized diffusion",
      "external fields",
      "power law type",
      "generalized fokker-planck equation reduces",
      "well-known porous media equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2008,
      "month": "May",
      "volume": 77,
      "number": 5,
      "pages": "051103"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvE..77e1103L"
    }
  }
}