{
  "abstract": "Networks of interfaces in materials and living systems evolve through motion and rearrangement of interfaces and junctions. Local equilibrium at a junction requires interfacial force balance. We show that in three dimensions the classical Herring condition for triple lines is necessary but insufficient: four triple lines meeting at a quadruple node may each satisfy Herring equilibrium, while the four conditions remain mutually incompatible. Such a frustrated node has no admissible local equilibrium geometry. In the semi-isotropic limit, the six interfacial energies must form the edge lengths of a non-degenerate tetrahedron, with constructibility determined by the Cayley-Menger determinant. This hidden compatibility constraint arises from three-dimensional geometry and applies broadly to foams, polycrystals, tissues and other interfacial networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29030",
  "author_total": 4,
  "authors": [
    {
      "name": "Håkan Hallberg"
    },
    {
      "name": "Vasily V. Bulatov"
    },
    {
      "name": "Bryan W. Reed"
    },
    {
      "name": "Mukul Kumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hqesf7b2h0ta.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29030",
  "fulltext_url": null,
  "id": "6hqesf7b2h0ta",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29030",
  "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.mtrl-sci"
    ],
    [
      "openalex",
      "2505|Solidification and crystal growth phenomena"
    ]
  ],
  "openalex": "W7214348667",
  "pdf_url": "https://arxiv.org/pdf/2609.29030",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hqesf7b2h0ta.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.29030",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29030"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Frustrated junctions in interfacial networks",
  "title_text": "Frustrated junctions in interfacial networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/6hqesf7b2h0ta",
  "venue": "arXiv",
  "versions": []
}