Minnaert resonances for acoustic waves in bubbly media

Habib Ammari; Brian Fitzpatrick; David Gontier; Hyundae Lee; Hai Zhang

doi:10.1016/j.anihpc.2018.03.007

Minnaert resonances for acoustic waves in bubbly media

Habib Ammari
, Brian Fitzpatrick
, David Gontier
, Hyundae Lee
, Hai Zhang

Department of Mathematics
ETH Zurich
Department of Mathematics
Inha University
Department of Mathematics
The Hong Kong University of Science and Technology

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

101 Citations (Scopus)

Abstract

Through the application of layer potential techniques and Gohberg–Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions.

Original language	English
Pages (from-to)	1975-1998
Number of pages	24
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	35
Issue number	7
DOIs	https://doi.org/10.1016/j.anihpc.2018.03.007
Publication status	Published - 1 Nov 2018
Externally published	Yes

Keywords

Acoustic waves
Bubble
Layer potentials
Minnaert resonance
Monopole approximation

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10.1016/j.anihpc.2018.03.007

Cite this

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abstract = "Through the application of layer potential techniques and Gohberg{\textendash}Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions.",

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author = "Habib Ammari and Brian Fitzpatrick and David Gontier and Hyundae Lee and Hai Zhang",

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AU - Fitzpatrick, Brian

AU - Gontier, David

AU - Lee, Hyundae

AU - Zhang, Hai

PY - 2018/11/1

Y1 - 2018/11/1

N2 - Through the application of layer potential techniques and Gohberg–Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions.

AB - Through the application of layer potential techniques and Gohberg–Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions.

KW - Acoustic waves

KW - Bubble

KW - Layer potentials

KW - Minnaert resonance

KW - Monopole approximation

UR - https://www.scopus.com/pages/publications/85045085286

U2 - 10.1016/j.anihpc.2018.03.007

DO - 10.1016/j.anihpc.2018.03.007

M3 - Article

AN - SCOPUS:85045085286

SN - 0294-1449

VL - 35

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EP - 1998

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 7

ER -

Minnaert resonances for acoustic waves in bubbly media

Abstract

Keywords

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