{
  "id": "1708.01604",
  "version": "v1",
  "published": "2017-08-04T17:51:18.000Z",
  "updated": "2017-08-04T17:51:18.000Z",
  "title": "Oscillations in aggregation-shattering processes",
  "authors": [
    "S. A. Matveev",
    "P. L. Krapivsky",
    "A. P. Smirnov",
    "E. E. Tyrtyshnikov",
    "N. V. Brilliantov"
  ],
  "comment": "5+5 pages, 6+1 figures",
  "categories": [
    "cond-mat.stat-mech",
    "physics.chem-ph"
  ],
  "abstract": "We observe never-ending oscillations in systems undergoing aggregation and collision-controlled shattering. Specifically, we investigate aggregation-shattering processes with aggregation kernels K_{i,j} = (i/j)^a+(j/i)^a and shattering kernels F_{i,j}=\\lambda K_{i,j}, where i and j are cluster sizes and parameter \\lambda quantifies the strength of shattering. When 0<a<1/2, there are no oscillations and the system monotonically approaches to a steady state for all values of \\lambda; in this region we obtain an analytical solution for the stationary cluster size distribution. Numerical solutions of the rate equations show that oscillations emerge in the 1/2<a<1 range. When the shattering rate is sufficiently large oscillations decay and eventually disappear, while for \\lambda<\\lambda_c(a) oscillations apparently persist forever. Thus never-ending oscillations can arise in closed aggregation-shattering processes without sinks and sources of particles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-04T17:51:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "aggregation-shattering processes",
      "never-ending oscillations",
      "sufficiently large oscillations decay",
      "stationary cluster size distribution",
      "system monotonically approaches"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}