Interface-Shifted Minnaert Resonances
Abstract
We develop a unified asymptotic theory for Minnaert resonances generated by a small bubble Dε placed near an interface Γ of material discontinuity in an acoustic background. The bubble has characteristic size ε>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 Θε := dist(Dε,Γ)/ε, and covers the three natural regimes Θε→+∞, Θε→Θ*∈(0,∞), Θε→0: 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 dist(Dε,Γ) = o(ε). 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.
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BibTeX
@misc{diao2026interfaceshifted,
title = {{Interface-Shifted Minnaert Resonances}},
author = {Huaian Diao and Long Li and Mourad Sini},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37423},
eprint = {2609.37423},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37423},
}
RIS
TY - UNPB
TI - Interface-Shifted Minnaert Resonances
AU - Huaian Diao
AU - Long Li
AU - Mourad Sini
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37423
UR - https://arxiv.org/abs/2609.37423
AB - We develop a unified asymptotic theory for Minnaert resonances generated by a small bubble D_ε placed near an interface Γ of material discontinuity in an acoustic background. The bubble has characteristic size ε>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_ε := dist(D_ε,Γ)/ε, and covers the three natural regimes Θ_ε→+∞, Θ_ε→Θ_*∈(0,∞), Θ_ε→0: 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 dist(D_ε,Γ) = o(ε). 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.
ER -