{
  "id": "cond-mat/9910236",
  "version": "v1",
  "published": "1999-10-15T13:46:20.000Z",
  "updated": "1999-10-15T13:46:20.000Z",
  "title": "Dependence of Conductance on Percolation Backbone Mass",
  "authors": [
    "Gerald Paul",
    "Sergey V. Buldyrev",
    "Nikolay V. Dokholyan",
    "Shlomo Havlin",
    "Peter R. King",
    "Youngki Lee",
    "H. Eugene Stanley"
  ],
  "comment": "8 pages, 4 figures",
  "doi": "10.1103/PhysRevE.61.3435",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "On two-dimensional percolation clusters at the percolation threshold, we study $<\\sigma(M_B,r)>$, the average conductance of the backbone, defined by two points separated by Euclidean distance $r$, of mass $M_B$. We find that with increasing $M_B$ and for fixed r, $<\\sigma(M_B,r)>$ asymptotically {\\it decreases} to a constant, in contrast with the behavior of homogeneous sytems and non-random fractals (such as the Sierpinski gasket) in which conductance increases with increasing $M_B$. We explain this behavior by studying the distribution of shortest paths between the two points on clusters with a given $M_B$. We also study the dependence of conductance on $M_B$ slightly above the percolation threshold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-10-15T13:46:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "percolation backbone mass",
      "dependence",
      "percolation threshold",
      "two-dimensional percolation clusters",
      "shortest paths"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}