{
  "abstract": "A diblock copolymer is a soft-matter composed of two chemically distinct block of repeating monomers covalently bonded together at an end-to-end junction to form a single polymer chain. In this paper, we establish the existence of infinitely many smooth periodic unbounded domain patterns of Delaunay-type in $\\mathbb{R}^3$ that optimize the energy distribution in diblock copolymer melts. We emphasize that pattern domains at the equilibrium correspond to stationary sets of the screened Ohta--Kawasaki free energy functional \\begin{align*} \\mathcal{P}_γ(Ω) := |\\partialΩ| + γ\\int_Ω\\int_Ω G_κ(|x-y|) \\,\\mathrm{d}x\\mathrm{d}y, \\end{align*} where $γ>0$, $κ>0$ and $G_κ(r)=\\frac{1}{r} e^{-κr}$ is the repulisive Yukawa potential. Equivalently, these equilibria satisfy the corresponding Euler--Lagrange equation \\begin{align*} \\mathcal{H}_Ω(x):= H_{\\partialΩ}(x) + γ\\int_Ω G_κ(|x-y|) \\mathrm{d}y = \\textrm{Const} \\quad \\text{on } \\partialΩ, \\end{align*} where $H_{\\partialΩ}$ denotes the mean curvature of the surface $\\partialΩ$. By analyzing the linearization of $Ω\\mapsto \\mathcal{H}_Ω$ around flat cylinders and applying the Crandall--Rabinowitz bifurcation theorem, for any $κ> 0$ and sufficiently small $γ> 0$, we prove the existence of non-trivial, $2π$-periodic Delaunay-type equilibrium cylinder interfaces with shapes close to a Delaunay unduloid surface of constant mean curvature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01333",
  "author_total": 2,
  "authors": [
    {
      "name": "Guy Foghem"
    },
    {
      "name": "Mouhamed Moustapha Fall"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4btwz741gzdw7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01333",
  "fulltext_url": null,
  "id": "4btwz741gzdw7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01333",
  "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"
    ],
    [
      "openalex",
      "2505|Block Copolymer Self-Assembly"
    ]
  ],
  "openalex": "W7206189449",
  "pdf_url": "https://arxiv.org/pdf/2609.01333",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4btwz741gzdw7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01333",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01333"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Delaunay-type interface in a screened model of diblock copolymer melts",
  "title_text": "Delaunay-type interface in a screened model of diblock copolymer melts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/4btwz741gzdw7",
  "venue": "arXiv",
  "versions": []
}