{
  "abstract": "Epithelial tissues play a fundamental role in morphogenesis. Mechanically they can be viewed as thin soft materials exhibiting a solid-fluid duality. The Surface Navier-Stokes-Helfrich model accounts for these properties by combining bending and surface hydrodynamics. In order to account for varying cell thickness we incorporate a thickness field in the spirit of a shallow-water equation, but defined on the (self-)evolving surface. This replaces the inextensibility constraint of the two-dimensional fluid and with it the conservation of surface area by an incompressibility constraint of the thin film fluid allowing for changes in surface area. We develop a numerical scheme based on surface finite elements, perform convergence tests, demonstrate the impact on shape evolution of closed surfaces with a constant enclosed volume and discuss implications on modeling morphogenesis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11903",
  "author_total": 2,
  "authors": [
    {
      "name": "Jan Magnus Sischka"
    },
    {
      "name": "Axel Voigt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6wv2bdhv98xx5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11903",
  "fulltext_url": null,
  "id": "6wv2bdhv98xx5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11903",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.soft"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7221197388",
  "pdf_url": "https://arxiv.org/pdf/2610.11903",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6wv2bdhv98xx5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.11903",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11903"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Fluid deformable surfaces with variable thickness - a Surface Shallow-Water-Helfrich model",
  "title_text": "Fluid deformable surfaces with variable thickness - a Surface Shallow-Water-Helfrich model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/6wv2bdhv98xx5",
  "venue": "arXiv",
  "versions": []
}