{
  "id": "2402.05069",
  "version": "v1",
  "published": "2024-02-07T18:20:04.000Z",
  "updated": "2024-02-07T18:20:04.000Z",
  "title": "Mathematical analysis of a mesoscale model for multiphase membranes",
  "authors": [
    "Jakob Fuchs",
    "Matthias Röger"
  ],
  "comment": "18 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author [Arch. Ration. Mech. Anal. 193, 2009] for the one-phase case. We present a mathematical analysis of the asymptotic reduction to the macroscale when a key length parameter becomes arbitrarily small. We identify two main contributions in the energy: one that can be connected to bending of the overall structure and a second that describes the cost of the internal phase separations. We prove the $\\Gamma$-convergence towards a perimeter functional for the phase separation energy and construct, in two dimensions, recovery sequences for the convergence of the full energy towards a 2D reduction of the J\\\"ulicher-Lipowksy bending energy with a line tension contribution for phase separated hypersurfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-07T18:20:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74K15",
      "49J45",
      "49Q20",
      "74L15",
      "74Q05"
    ],
    "keywords": [
      "mathematical analysis",
      "mesoscale model",
      "multiphase membranes",
      "phase separation energy",
      "model extends work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}