{
  "abstract": "We consider a geometric mechanochemical model of vesicles which couples the Helfrich flow for the shape of a lipid bilayer vesicle membrane $X$ with a reaction-diffusion equations for a single ``morphogen'' $ϕ$ on $X$. The Helfrich flow is the $L^2$ gradient flow of the elastic bending energy $E(X)=\\int_X (H-c_0)^2 dS$ of $X$, typically supplemented by area or volume constraints, or both. The morphogen $ϕ$ adsorbs/desorbs at places of high/low mean curvature $H$, i.e., the kinetics of $ϕ$ depend on $H$, and conversely $ϕ$ modifies the spontaneous curvature $c_0$ on $X$. The flow is no longer gradient, and hence allows for more complicated dynamics, including time periodic orbits, e.g., ``breathing and moving'' vesicle shapes. We show how to compute bifurcation diagrams for such solution branches via numerical continuation and bifurcation methods. We mostly focus on ``planar'' vesicles (1D closed curves) but also give an outlook on 3D vesicles (2D closed membranes).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09360",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexander Meiners"
    },
    {
      "name": "Hannes Uecker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dffxe287a5mpk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09360",
  "fulltext_url": null,
  "id": "dffxe287a5mpk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09360",
  "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",
      "math.AP"
    ],
    [
      "arxiv",
      "nlin.AO"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212116178",
  "pdf_url": "https://arxiv.org/pdf/2609.09360",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dffxe287a5mpk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.09360",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09360"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.AO",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Breathing and moving vesicles in a geometric mechanochemical model",
  "title_text": "Breathing and moving vesicles in a geometric mechanochemical model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/dffxe287a5mpk",
  "venue": "arXiv",
  "versions": []
}