{
  "abstract": "We report improved global-minimum configurations for the classical Thomson problem of $N=60$, $61$, $92$, and $99$ repulsive Coulomb charges confined to a disk. By combining the quenched molecular dynamics (QMD) method with the fixed-border heuristic introduced by Amore and Zarate, we systematically obtain configurations with energies $E_{\\mathrm{QMD}}(60)=2159.3584240930$, $E_{\\mathrm{QMD}}(61)=2237.19264190$, $E_{\\mathrm{QMD}}(92)=5358.35353314$, and $E_{\\mathrm{QMD}}(99)=6254.83029083$, which improve upon the previously best-known values. For $N=60$, the Voronoi diagram of our configuration differs from the one reported earlier. The symmetries for $N=61$ $(C_{2})$ and $N=99$ $(D_{1})$ are confirmed and are consistent with the known symmetry patterns for these configurations. For $N=92$, whereas the previously reported Voronoi diagram has lower symmetry, our solution exhibits a clear $D_{1}$ (axial) symmetry of defects. The results are highly reproducible across multiple independent runs, providing strong evidence that these configurations are robust global-minimum candidates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20777",
  "author_total": 2,
  "authors": [
    {
      "name": "Georgiy K. Lavrov"
    },
    {
      "name": "Eduard G. Nikonov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dx67jf4mtcjhq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20777",
  "fulltext_url": null,
  "id": "dx67jf4mtcjhq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20777",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "physics.class-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2612|Mathematical Approximation and Integration"
    ]
  ],
  "openalex": "W7213580375",
  "pdf_url": "https://arxiv.org/pdf/2609.20777",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dx67jf4mtcjhq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.20777",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20777"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Global Minima of the Thomson Problem in a Disk: A Molecular Dynamics Approach with Fixed Border Charges",
  "title_text": "Global Minima of the Thomson Problem in a Disk: A Molecular Dynamics Approach with Fixed Border Charges",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/dx67jf4mtcjhq",
  "venue": "arXiv",
  "versions": []
}