{
  "abstract": "We study finite-time acoustic wave tracking using effective interior Dirac-type actuators generated by clusters of subwavelength resonant bubbles driven from exterior transducers. Starting from a time-domain point-interaction approximation, the full scattering problem is reduced to a finite-dimensional delayed system of interacting retarded monopoles. After localization to a bounded observation domain, we formulate the tracking problem on a prescribed finite-dimensional Dirichlet spectral subspace. At the ideal level, a full-rank spatial coupling condition yields exact tracking of arbitrary sufficiently smooth compatible trajectories in this subspace by interior point sources. These ideal actuators are realized using small, high-contrast bubbles, whose Laplace-domain transfer operator encodes the Minnaert resonances and collective attenuation. The principal mode of each cluster is isolated by the Perron--Frobenius structure and the intra-cluster spectral gap. Clusters tuned to the same band are then treated as a collective resonant block. The selected Dirichlet bands are matched with the corresponding Minnaert bands. For prescribed slowly time-modulated resonant pressure profiles, with sufficiently flat initialization, we construct causal exterior controls and obtain a quantitative tracking estimate on every fixed time interval $[0,T]$. In contrast, on frequency ranges uniformly separated from the Minnaert resonances, the actuator gain is $O(\\varepsilon)$ and the corresponding realization cost is asymptotically unbounded as $\\varepsilon \\ll 1$, $\\varepsilon$ being the maximum radius of the bubbles. Thus the Minnaert resonances convert accessible exterior excitations into robust effective interior controls.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.25978",
  "author_total": 2,
  "authors": [
    {
      "name": "Arpan Mukherjee"
    },
    {
      "name": "Mourad Sini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cwayeyaza7wbj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.25978",
  "fulltext_url": null,
  "id": "cwayeyaza7wbj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.25978",
  "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"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7162439920",
  "pdf_url": "https://arxiv.org/pdf/2605.25978",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cwayeyaza7wbj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2605.25978",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.25978"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Resonant Microstructures as Dirac-type Sources for Acoustic Wave Control",
  "title_text": "Resonant Microstructures as Dirac-type Sources for Acoustic Wave Control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/cwayeyaza7wbj",
  "venue": "arXiv",
  "versions": []
}