{
  "id": "cond-mat/0004397",
  "version": "v2",
  "published": "2000-04-24T17:00:27.000Z",
  "updated": "2000-04-27T19:41:18.000Z",
  "title": "Flow Between Two Sites on a Percolation Cluster",
  "authors": [
    "Jos{é} S. Andrade",
    "jr.",
    "Sergey V. Buldyrev",
    "Nikolay V. Dokholyan",
    "Shlomo Havlin",
    "Peter R. King",
    "Youngki Lee",
    "Gerald Paul",
    "H. Eugene Stanley"
  ],
  "comment": "31 pages, 12 Figures",
  "doi": "10.1103/PhysRevE.62.8270",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "We study the flow of fluid in porous media in dimensions $d=2$ and 3. The medium is modeled by bond percolation on a lattice of $L^d$ sites, while the flow front is modeled by tracer particles driven by a pressure difference between two fixed sites (``wells'') separated by Euclidean distance $r$. We investigate the distribution function of the shortest path connecting the two sites, and propose a scaling {\\it Ansatz} that accounts for the dependence of this distribution (i) on the size of the system, $L$, and (ii) on the bond occupancy probability, $p$. We confirm by extensive simulations that the {\\it Ansatz} holds for $d=2$ and 3, and calculate the relevant scaling parameters. We also study two dynamical quantities: the minimal traveling time of a tracer particle between the wells and the length of the path corresponding to the minimal traveling time ``fastest path'', which is not identical to the shortest path. A scaling {\\it Ansatz} for these dynamical quantities also includes the effect of finite system size $L$ and off-critical bond occupation probability $p$. We find that the scaling form for the distribution functions for these dynamical quantities for $d=2$ and 3 is similar to that for the shortest path but with different critical exponents. The scaling form is represented as the product of a power law and three exponential cutoff functions. We summarize our results in a table which contains estimates for all parameters which characterize the scaling form for the shortest path and the minimal traveling time in 2 and 3 dimensions; these parameters are the fractal dimension, the power law exponent, and the constants and exponents that characterize the exponential cutoff functions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-04-27T19:41:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "percolation cluster",
      "shortest path",
      "minimal traveling time",
      "exponential cutoff functions",
      "scaling form"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}