{
  "id": "1002.4976",
  "version": "v1",
  "published": "2010-02-26T12:30:32.000Z",
  "updated": "2010-02-26T12:30:32.000Z",
  "title": "Analytical And Numerical Approximation of Effective Diffusivities in The Cytoplasm of Biological Cells",
  "authors": [
    "Michael Hanke",
    "Marry-Chriz Cabauatan-Villanueva"
  ],
  "comment": "21 pages, 6 figures",
  "categories": [
    "math.NA",
    "cond-mat.soft",
    "q-bio.QM"
  ],
  "abstract": "The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard discretization techniques. In the present paper we propose a homogenization technique for computing effective diffusion constants. This is accomplished by using a two-step strategy. The first step consists of an analytic homogenization from the smallest to an intermediate scale. The homogenization error is estimated by comparing the analytic diffusion constant with a numerical estimate obtained by using real cell geometries. The second step consists of a random homogenization. Since no analytical solution is known to this homogenization problem, a numerical approximation algorithm is proposed. Although rather expensive this algorithm provides a reasonable estimate of the homogenized diffusion constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-26T12:30:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "92C37",
      "65C05",
      "92C40"
    ],
    "keywords": [
      "numerical approximation",
      "biological cells",
      "effective diffusivities",
      "homogenization",
      "standard discretization techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.4976H"
    }
  }
}