{
  "id": "cond-mat/0106443",
  "version": "v1",
  "published": "2001-06-21T14:50:57.000Z",
  "updated": "2001-06-21T14:50:57.000Z",
  "title": "Transition from random to ordered fractals in fragmentation of particles in an open system",
  "authors": [
    "M. K. Hassan",
    "J. Kurths"
  ],
  "comment": "5 pages, latex, No figure",
  "journal": "Phys. Rev. E 64, 016119 (2001)",
  "doi": "10.1103/PhysRevE.64.016119",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\\theta$, whose exact numerical values are given for which $x^{-\\theta}$ or $t^{\\theta z}$ has the dimension of particle size distribution function $\\psi(x,t)$, where $z$ is the kinetic exponent. We obtained conditions for which the scaling and fragmentation process altogether break down and give explicit scaling solution for special case. Finally, we identify a new class of fractals ranging from random to non-random and show that the fractal dimension increases with increasing order and a transition to strictly self-similar pattern occurs when randomness completely ceases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-06-21T14:50:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open system",
      "ordered fractals",
      "transition",
      "fragmentation process altogether break",
      "particle size distribution function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}