{
  "abstract": "We investigate the eigenfrequency asymptotics of a bounded acoustic cavity containing a shrinking high-contrast inclusion. This configuration is motivated by contrast-enhanced ultrasound imaging, in which microbubbles are employed as acoustic contrast agents. We identify dimension-dependent material scalings that keep the inclusion-induced resonance in a fixed order-one frequency regime as the inclusion shrinks. Our main result gives a complete asymptotic description of the spectrum in any prescribed bounded frequency window. Two distinct spectral mechanisms arise: the background Dirichlet eigenfrequencies persist as perturbed eigenvalue clusters, while the singular material contrast creates an additional Minnaert eigenvalue branch. The limiting Minnaert frequency is explicit in both dimensions, with a capacitance-based expression in three dimensions and an area-based expression in two dimensions. Two-dimensional numerical experiments confirm both the perturbation of the background Dirichlet eigenfrequencies and the emergence of the additional Minnaert branch.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30721",
  "author_total": 4,
  "authors": [
    {
      "name": "Huaian Diao"
    },
    {
      "name": "Long Li"
    },
    {
      "name": "Mourad Sini"
    },
    {
      "name": "Qilong Zhai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/688g016vc57jy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30721",
  "fulltext_url": null,
  "id": "688g016vc57jy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30721",
  "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.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7204925025",
  "pdf_url": "https://arxiv.org/pdf/2608.30721",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/688g016vc57jy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30721",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30721"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Eigenvalue Asymptotics in High-Contrast Media",
  "title_text": "Eigenvalue Asymptotics in High-Contrast Media",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/688g016vc57jy",
  "venue": "arXiv",
  "versions": []
}