{
  "id": "cond-mat/0501218",
  "version": "v1",
  "published": "2005-01-10T22:03:52.000Z",
  "updated": "2005-01-10T22:03:52.000Z",
  "title": "Percolation with Multiple Giant Clusters",
  "authors": [
    "E. Ben-Naim",
    "P. L. Krapivsky"
  ],
  "comment": "4 pages, 3 figures",
  "journal": "J. Phys. A 38, L417 (2005)",
  "doi": "10.1088/0305-4470/38/23/L01",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft",
    "math.PR"
  ],
  "abstract": "We study the evolution of percolation with freezing. Specifically, we consider cluster formation via two competing processes: irreversible aggregation and freezing. We find that when the freezing rate exceeds a certain threshold, the percolation transition is suppressed. Below this threshold, the system undergoes a series of percolation transitions with multiple giant clusters (\"gels\") formed. Giant clusters are not self-averaging as their total number and their sizes fluctuate from realization to realization. The size distribution F_k, of frozen clusters of size k, has a universal tail, F_k ~ k^{-3}. We propose freezing as a practical mechanism for controlling the gel size.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-10T22:03:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiple giant clusters",
      "percolation transition",
      "cluster formation",
      "universal tail",
      "frozen clusters"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}