{
  "id": "cond-mat/0305425",
  "version": "v2",
  "published": "2003-05-19T05:33:26.000Z",
  "updated": "2003-10-02T02:50:51.000Z",
  "title": "Sandpile on Scale-Free Networks",
  "authors": [
    "K. -I. Goh",
    "D. -S. Lee",
    "B. Kahng",
    "D. Kim"
  ],
  "comment": "4 pages, 3 figures, 1 table, revtex4, final version appeared in PRL",
  "journal": "Phys. Rev. Lett. 91, 148701 (2003)",
  "doi": "10.1103/PhysRevLett.91.148701",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model on scale-free (SF) networks, where threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent $\\tau$. Applying the theory of multiplicative branching process, we obtain the exponent $\\tau$ and the dynamic exponent $z$ as a function of the degree exponent $\\gamma$ of SF networks as $\\tau=\\gamma/(\\gamma-1)$ and $z=(\\gamma-1)/(\\gamma-2)$ in the range $2 < \\gamma < 3$ and the mean field values $\\tau=1.5$ and $z=2.0$ for $\\gamma >3$, with a logarithmic correction at $\\gamma=3$. The analytic solution supports our numerical simulation results. We also consider the case of uniform threshold, finding that the two exponents reduce to the mean field ones.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-10-02T02:50:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scale-free networks",
      "mean field values",
      "analytic solution supports",
      "avalanche size distribution",
      "power law"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}