{
  "id": "math/0605769",
  "version": "v1",
  "published": "2006-05-30T20:51:10.000Z",
  "updated": "2006-05-30T20:51:10.000Z",
  "title": "The Neumann sieve problem and dimensional reduction: a multiscale approach",
  "authors": [
    "Nadia Ansini",
    "Jean-Francois Babadjian",
    "Caterina Ida Zeppieri"
  ],
  "comment": "43 pages, 4 figures",
  "journal": "Mathematical Models and Methods in Applied Sciences, 17, no. 5 (2007), 681-735",
  "categories": [
    "math.AP"
  ],
  "abstract": "We perform a multiscale analysis for the elastic energy of a $n$-dimensional bilayer thin film of thickness $2\\delta$ whose layers are connected through an $\\epsilon$-periodically distributed contact zone. Describing the contact zone as a union of $(n-1)$-dimensional balls of radius $r\\ll \\epsilon$ (the holes of the sieve) and assuming that $\\delta \\ll \\epsilon$, we show that the asymptotic memory of the sieve (as $\\epsilon \\to 0$) is witnessed by the presence of an extra interfacial energy term. Moreover we find three different limit behaviors (or regimes) depending on the mutual vanishing rate of $\\delta$ and $r$. We also give an explicit nonlinear capacitary-type formula for the interfacial energy density in each regime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-30T20:51:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J45",
      "74K35",
      "74K15",
      "74B20",
      "74G65",
      "35B40"
    ],
    "keywords": [
      "neumann sieve problem",
      "multiscale approach",
      "dimensional reduction",
      "dimensional bilayer thin film",
      "explicit nonlinear capacitary-type formula"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5769A"
    }
  }
}