{
  "abstract": "We develop a unified asymptotic theory for Minnaert resonances generated by a small bubble $D_\\varepsilon$ placed near an interface $Γ$ of material discontinuity in an acoustic background. The bubble has characteristic size $\\varepsilon>0$, with its density and bulk modulus depending on the same small parameter through the Minnaert high-contrast scaling. The analysis is organized by the scaled separation \\[ Θ_\\varepsilon := \\frac{\\operatorname{dist}(D_\\varepsilon,Γ)}{\\varepsilon}, \\] and covers the three natural regimes \\[ Θ_\\varepsilon\\to+\\infty, \\qquad Θ_\\varepsilon\\toΘ_*\\in(0,\\infty), \\qquad Θ_\\varepsilon\\to0: \\] 1) In the far-separation regime, the interface is invisible at leading order and the classical full-space Minnaert law is recovered. 2) In the critical regime, the rescaled geometry retains both the bubble and the interface at finite separation, and the Newtonian capacitance is replaced by a flat-interface capacitance determined by the limiting tangent transmission problem. 3) In the near-contact regime, this family converges to a contact-limiting capacitance, yielding the same leading-order Minnaert resonance for all gap scalings satisfying $\\operatorname{dist}(D_\\varepsilon,Γ) = o(\\varepsilon)$. These three regimes provide a unified description of how the resonance frequency changes as the bubble approaches the interface, from the classical isolated-bubble limit to the contact limit. The analysis relies on a uniform reduction of the resonance problem to a scalar equation and on a variational characterization of the interface-dependent capacitances; in particular, Mosco convergence of the associated transmission energies yields convergence of the capacitary potentials and minimum energies up to the singular contact configuration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37423",
  "author_total": 3,
  "authors": [
    {
      "name": "Huaian Diao"
    },
    {
      "name": "Long Li"
    },
    {
      "name": "Mourad Sini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5d61kf9hzfjfq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37423",
  "fulltext_url": null,
  "id": "5d61kf9hzfjfq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37423",
  "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.AP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214973741",
  "pdf_url": "https://arxiv.org/pdf/2609.37423",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5d61kf9hzfjfq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37423",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37423"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Interface-Shifted Minnaert Resonances",
  "title_text": "Interface-Shifted Minnaert Resonances",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/5d61kf9hzfjfq",
  "venue": "arXiv",
  "versions": []
}