{
  "abstract": "Predicting the highest packing fraction that disordered packing of bidisperse discs can achieve, $ϕ_{max}$, is an important unresolved problem. Such a predictive theory is hindered by the density dependence on the packing protocol and by ensuring disorder. In bidisperse packings, this is more complicated because $ϕ_{max}$ is not a number but a function of the disc species size ratio, $D$, and one of the disc species concentration, $p$. These difficulties have been overcome in monodisperse disc packings by using the cell order distribution (COD)~\\cite{Bl21}. Focusing on size ratios that prohibit rattlers, a COD-based theory is constructed here. It introduces bidisperse statistical closure equations, which combine an explicit disorder criterion with consistent cell and edge statistics, and yields $ϕ_{max}(p,D)$ and structural predictions. The a-priori disorder-guaranteeing criterion proposed here ensures fast exponential a decay of the occurrence probability of ordered clusters with size. Using a constrained maximum-entropy analysis to ensure maximum disorder, the occurrence probabilities of all the possible cell and edge configurations are derived in terms of $p$ and $D$ and they are found to be binomial. All the results are assembled to yield an exact prediction of $ϕ_{max}(p,D)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02805",
  "author_total": 1,
  "authors": [
    {
      "name": "Raphael Blumenfeld"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/45pyx3776fqph.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02805",
  "fulltext_url": null,
  "id": "45pyx3776fqph",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02805",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.soft"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02805",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/45pyx3776fqph.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02805",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02805"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "The maximum packing fraction of disordered bidisperse discs: theory and predictions",
  "title_text": "The maximum packing fraction of disordered bidisperse discs: theory and predictions",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/45pyx3776fqph",
  "venue": "arXiv",
  "versions": []
}