{
  "id": "1809.04172",
  "version": "v1",
  "published": "2018-09-11T21:19:36.000Z",
  "updated": "2018-09-11T21:19:36.000Z",
  "title": "Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework",
  "authors": [
    "Agata Fronczak",
    "Michał Łepek",
    "Paweł Kukliński",
    "Piotr Fronczak"
  ],
  "comment": "9 pages, 3 figures - in preliminary version, the 3rd one to be done. This is original work",
  "categories": [
    "cond-mat.stat-mech",
    "physics.chem-ph"
  ],
  "abstract": "The time evolution of a system of coagulating particles under the product kernel and arbitrary initial conditions is studied. Using the improved Marcus-Lushnikov approach, the master equation is solved for the probability $W(Q,t)$ to find the system in a given mass spectrum $Q=\\{n_1,n_2,\\dots,n_g\\dots\\}$, with $n_g$ being the number of particles of size $g$. The exact expression for the average number of particles, $\\langle n_g(t)\\rangle$, at arbitrary time $t$ is derived and its validity is confirmed in numerical simulations of several selected initial mass spectra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-11T21:19:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary initial conditions",
      "product kernel",
      "exact kinetics",
      "marcus-lushnikov framework",
      "mass spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}