{
  "id": "cond-mat/9910281",
  "version": "v1",
  "published": "1999-10-19T01:40:29.000Z",
  "updated": "1999-10-19T01:40:29.000Z",
  "title": "Scale Invariance and Lack of Self-Averaging in Fragmentation",
  "authors": [
    "P. L. Krapivsky",
    "I. Grosse",
    "E. Ben-Naim"
  ],
  "comment": "4 pages, revtex",
  "journal": "Phys. Rev. E 61, R993 (2000)",
  "doi": "10.1103/PhysRevE.61.R993",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We derive exact statistical properties of a class of recursive fragmentation processes. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution in one dimension, P(x) ~ x^{-2p}. In d dimensions, the volume distribution diverges algebraically in the small fragment limit, P(V)\\sim V^{-\\gamma} with \\gamma=2p^{1/d}. Hence, the entire range of exponents allowed by mass conservation is realized. We demonstrate that this fragmentation process is non-self-averaging. Specifically, the moments Y_\\alpha=\\sum_i x_i^{\\alpha} exhibit significant fluctuations even in the thermodynamic limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-10-19T01:40:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scale invariance",
      "small fragment limit",
      "derive exact statistical properties",
      "mass conservation",
      "entire range"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}