{
  "abstract": "We establish convergence of minimizers for a minimal one dimensional atomic-scale model for relaxation in moiré materials to those of a one-dimensional continuum limit functional analogous to those commonly used in practice to model relaxation. The atomic-scale model consists of two periodic chains containing $N$ and $N+1$ atoms per common cell and is exactly moiré-periodic at the atomic scale. Its energy combines harmonic nearest-neighbor intralayer interactions with nonlocal interlayer interactions generated by an even $C^2$ pair potential with polynomial decay. The associated continuum energy couples linear elasticity to a periodic misfit potential, obtained by periodizing the pair potential, which penalizes unfavorable local stackings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37943",
  "author_total": 4,
  "authors": [
    {
      "name": "Hao Lan"
    },
    {
      "name": "Michael Hott"
    },
    {
      "name": "Jeff Calder"
    },
    {
      "name": "Alexander B. Watson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fj2v3wa7x46fx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37943",
  "fulltext_url": null,
  "id": "fj2v3wa7x46fx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37943",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "1703|Advanced Mathematical Modeling in Engineering"
    ]
  ],
  "openalex": "W7214895968",
  "pdf_url": "https://arxiv.org/pdf/2609.37943",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fj2v3wa7x46fx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37943",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37943"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Continuum Limit for One-Dimensional Moiré Relaxation",
  "title_text": "Continuum Limit for One-Dimensional Moiré Relaxation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/fj2v3wa7x46fx",
  "venue": "arXiv",
  "versions": []
}