Close-to-touching acoustic subwavelength resonators: Eigenfrequency separation and gradient blow-up

Habib Ammari; Bryn Davies; Y. U. Sanghyeon

doi:10.1137/20M1313350

Close-to-touching acoustic subwavelength resonators: Eigenfrequency separation and gradient blow-up

Habib Ammari, Bryn Davies, Y. U. Sanghyeon

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

In this paper, we study the behavior of the coupled subwavelength resonant modes when two high-contrast acoustic resonators are brought close together. We consider the case of spherical resonators and use bispherical coordinates to derive explicit representations for the capacitance coefficients which, we show, capture the system's resonant behavior at leading order. We prove that the pair of resonators has two subwavelength resonant modes whose frequencies have different leading-order asymptotic behavior. We also derive estimates for the rate at which the gradient of the scattered pressure wave blows up as the resonators are brought together.

Original language	English
Pages (from-to)	1299-1317
Number of pages	19
Journal	Multiscale Modeling and Simulation
Volume	18
Issue number	3
DOIs	https://doi.org/10.1137/20M1313350
Publication status	Published - 2020

Bibliographical note

Publisher Copyright:
© by SIAM. Unauthorized reproduction of this article is prohibited.

Keywords

Bispherical coordinates
Bubbly media
Capacitance coefficients
Close-to-touching spheres
High-contrast metamaterials
Subwavelength resonance

ASJC Scopus subject areas

General Chemistry
Modelling and Simulation
Ecological Modelling
General Physics and Astronomy
Computer Science Applications

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10.1137/20M1313350

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abstract = "In this paper, we study the behavior of the coupled subwavelength resonant modes when two high-contrast acoustic resonators are brought close together. We consider the case of spherical resonators and use bispherical coordinates to derive explicit representations for the capacitance coefficients which, we show, capture the system's resonant behavior at leading order. We prove that the pair of resonators has two subwavelength resonant modes whose frequencies have different leading-order asymptotic behavior. We also derive estimates for the rate at which the gradient of the scattered pressure wave blows up as the resonators are brought together.",

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AU - Ammari, Habib

AU - Davies, Bryn

AU - Sanghyeon, Y. U.

N1 - Publisher Copyright: © by SIAM. Unauthorized reproduction of this article is prohibited.

PY - 2020

Y1 - 2020

N2 - In this paper, we study the behavior of the coupled subwavelength resonant modes when two high-contrast acoustic resonators are brought close together. We consider the case of spherical resonators and use bispherical coordinates to derive explicit representations for the capacitance coefficients which, we show, capture the system's resonant behavior at leading order. We prove that the pair of resonators has two subwavelength resonant modes whose frequencies have different leading-order asymptotic behavior. We also derive estimates for the rate at which the gradient of the scattered pressure wave blows up as the resonators are brought together.

AB - In this paper, we study the behavior of the coupled subwavelength resonant modes when two high-contrast acoustic resonators are brought close together. We consider the case of spherical resonators and use bispherical coordinates to derive explicit representations for the capacitance coefficients which, we show, capture the system's resonant behavior at leading order. We prove that the pair of resonators has two subwavelength resonant modes whose frequencies have different leading-order asymptotic behavior. We also derive estimates for the rate at which the gradient of the scattered pressure wave blows up as the resonators are brought together.

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KW - Bubbly media

KW - Capacitance coefficients

KW - Close-to-touching spheres

KW - High-contrast metamaterials

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Close-to-touching acoustic subwavelength resonators: Eigenfrequency separation and gradient blow-up

Abstract

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