{
  "id": "1503.02749",
  "version": "v1",
  "published": "2015-03-10T01:59:51.000Z",
  "updated": "2015-03-10T01:59:51.000Z",
  "title": "Aggregation Driven by a Localized Source",
  "authors": [
    "P. L. Krapivsky"
  ],
  "comment": "9 pages",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "We study aggregation driven by a localized source of monomers. The densities become stationary and have algebraic tails far away from the source. We show that in a model with mass-independent reaction rates and diffusion coefficients, the density of monomers decays as $r^{-\\beta(d)}$ in $d$ dimensions. The decay exponent has irrational values in physically relevant dimensions: $\\beta(3)=(\\sqrt{17}+1)/2$ and $\\beta(2)=\\sqrt{8}$. We also study Brownian coagulation with a localized source and establish the behavior of the total cluster density and the total number of of clusters in the system. The latter quantity exhibits a logarithmic growth with time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-10T01:59:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "localized source",
      "algebraic tails far away",
      "study brownian coagulation",
      "study aggregation driven",
      "mass-independent reaction rates"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/48/24/245002",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2015,
      "month": "Jun",
      "volume": 48,
      "number": 24,
      "pages": 245002
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JPhA...48x5002K"
    }
  }
}