Resonant Microstructures as Dirac-type Sources for Acoustic Wave Control
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(ε) and the corresponding realization cost is asymptotically unbounded as ε ≪ 1, ε being the maximum radius of the bubbles. Thus the Minnaert resonances convert accessible exterior excitations into robust effective interior controls.
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BibTeX
@misc{mukherjee2026resonant,
title = {{Resonant Microstructures as Dirac-type Sources for Acoustic Wave Control}},
author = {Arpan Mukherjee and Mourad Sini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.25978},
eprint = {2605.25978},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.25978},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Resonant Microstructures as Dirac-type Sources for Acoustic Wave Control
AU - Arpan Mukherjee
AU - Mourad Sini
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2605.25978
UR - https://arxiv.org/abs/2605.25978
AB - 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(ε) and the corresponding realization cost is asymptotically unbounded as ε ≪ 1, ε being the maximum radius of the bubbles. Thus the Minnaert resonances convert accessible exterior excitations into robust effective interior controls.
ER -