{
  "id": "cond-mat/0511237",
  "version": "v1",
  "published": "2005-11-09T18:06:24.000Z",
  "updated": "2005-11-09T18:06:24.000Z",
  "title": "Probability distribution of residence times of grains in models of ricepiles",
  "authors": [
    "Punyabrata Pradhan",
    "Deepak Dhar"
  ],
  "comment": "13 pages, 23 figures, Submitted to Phys. Rev. E",
  "journal": "Phys. Rev. E 73, 021303 (2006).",
  "doi": "10.1103/PhysRevE.73.021303",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "We study the probability distribution of residence time of a grain at a site, and its total residence time inside a pile, in different ricepile models. The tails of these distributions are dominated by the grains that get deeply buried in the pile. We show that, for a pile of size $L$, the probabilities that the residence time at a site or the total residence time is greater than $t$, both decay as $1/t(\\ln t)^x$ for $L^{\\omega} \\ll t \\ll \\exp(L^{\\gamma})$ where $\\gamma$ is an exponent $ \\ge 1$, and values of $x$ and $\\omega$ in the two cases are different. In the Oslo ricepile model we find that the probability that the residence time $T_i$ at a site $i$ being greater than or equal to $t$, is a non-monotonic function of $L$ for a fixed $t$ and does not obey simple scaling. For model in $d$ dimensions, we show that the probability of minimum slope configuration in the steady state, for large $L$, varies as $\\exp(-\\kappa L^{d+2})$ where $\\kappa$ is a constant, and hence $ \\gamma = d+2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-09T18:06:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability distribution",
      "total residence time inside",
      "minimum slope configuration",
      "oslo ricepile model",
      "non-monotonic function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}