{
  "id": "cond-mat/0203092",
  "version": "v1",
  "published": "2002-03-05T14:09:58.000Z",
  "updated": "2002-03-05T14:09:58.000Z",
  "title": "Fractal Behavior of the Shortest Path Between Two Lines in Percolation Systems",
  "authors": [
    "Gerald Paul",
    "Shlomo Havlin",
    "H. Eugene Stanley"
  ],
  "comment": "Figures are low resolution and are best viewed when printed",
  "doi": "10.1103/PhysRevE.65.066105",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Using Monte-Carlo simulations, we determine the scaling form for the probability distribution of the shortest path, $\\ell$, between two lines in a 3-dimensional percolation system at criticality; the two lines can have arbitrary positions, orientations and lengths. We find that the probability distributions can exhibit up to four distinct power law regimes (separated by cross-over regimes) with exponents depending on the relative orientations of the lines. We explain this rich fractal behavior with scaling arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-03-05T14:09:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shortest path",
      "percolation system",
      "probability distribution",
      "distinct power law regimes",
      "rich fractal behavior"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}