{
  "id": "1603.06823",
  "version": "v1",
  "published": "2016-03-22T15:15:26.000Z",
  "updated": "2016-03-22T15:15:26.000Z",
  "title": "Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry",
  "authors": [
    "Raffaele Marino",
    "Erik Aurell"
  ],
  "comment": "20 pages, 4 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider coupled diffusions in $n$-dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a solvability conditions in a multi-scale analysis. As an example we consider coupled diffusions in $3$-dimensional space and on the group manifold $SO(3)$ of proper rotations, generalizing results obtained by H. Brenner (1981). We show in detail how the analysis can be conveniently be carried out using local charts and invariance arguments. As a further example we consider coupled diffusions in $2$-dimensional complex space and on the group manifold $SU(2)$. We show that although the local operators may be the same as for $SO(3)$, due to the global nature of the solvability conditions the resulting diffusion will be different, and generally more isotropic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-22T15:15:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large scales",
      "advective-diffusive motion",
      "small-scale dynamics",
      "internal symmetry",
      "coupled diffusions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160306823M"
    }
  }
}