{
  "id": "1908.01197",
  "version": "v1",
  "published": "2019-08-03T16:23:48.000Z",
  "updated": "2019-08-03T16:23:48.000Z",
  "title": "Murray's law for discrete and continuum models of biological networks",
  "authors": [
    "Jan Haskovec",
    "Peter Markowich",
    "Giulia Pilli"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We demonstrate the validity of Murray's law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with general metabolic coefficient and multiple branching nodes and derive a generalization of the classical 3/4-law. Next we prove an analogue of the discrete Murray's law for the continuum system obtained in the continuum limit of the discrete model on a rectangular mesh. Finally, we consider a continuum model derived from phenomenological considerations and show the validity of the Murray's law for its linearly stable steady states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-03T16:23:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "92C35",
      "05C21",
      "76S05"
    ],
    "keywords": [
      "continuum model",
      "biological networks",
      "discrete murrays law",
      "general metabolic coefficient",
      "branch conductivities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}