{
  "id": "1211.1093",
  "version": "v1",
  "published": "2012-11-06T02:44:08.000Z",
  "updated": "2012-11-06T02:44:08.000Z",
  "title": "First passage times in homogeneous nucleation and self-assembly",
  "authors": [
    "Romain Yvinec",
    "Maria R. D'Orsogna",
    "Tom Chou"
  ],
  "comment": "18 pages, 9 Figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.mes-hall",
    "q-bio.QM"
  ],
  "abstract": "Motivated by nucleation and molecular aggregation in physical, chemical and biological settings, we present a thorough analysis of the general problem of stochastic self-assembly of a fixed number of identical particles in a finite volume. We derive the Backward Kolmogorov equation (BKE) for the cluster probability distribution. From the BKE we study the distribution of times it takes for a single maximal cluster to be completed, starting from any initial particle configuration. In the limits of slow and fast self-assembly, we develop analytical approaches to calculate the mean cluster formation time and to estimate the first assembly time distribution. We find, both analytically and numerically, that faster detachment can lead to a shorter mean time to first completion of a maximum-sized cluster. This unexpected effect arises from a redistribution of trajectory weights such that upon increasing the detachment rate, paths that take a shorter time to complete a cluster become more likely.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-06T02:44:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "36.20.Hb",
      "02.50.Cw",
      "36.20.Ey",
      "36.20.Fz"
    ],
    "keywords": [
      "first passage times",
      "homogeneous nucleation",
      "self-assembly",
      "mean cluster formation time",
      "initial particle configuration"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.4772598",
      "journal": "Journal of Chemical Physics",
      "year": 2012,
      "month": "Dec",
      "volume": 137,
      "number": 24,
      "pages": 4107
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JChPh.137x4107Y"
    }
  }
}