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dc.contributor.author
Feppon, Florian
dc.contributor.author
Ammari, Habib
dc.date.accessioned
2022-07-18T13:04:06Z
dc.date.available
2022-04-01T03:13:34Z
dc.date.available
2022-06-07T15:24:32Z
dc.date.available
2022-07-18T13:02:23Z
dc.date.available
2022-07-18T13:04:06Z
dc.date.issued
2022-07
dc.identifier.issn
0022-2526
dc.identifier.issn
1467-9590
dc.identifier.other
10.1111/sapm.12493
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/540314
dc.identifier.doi
10.3929/ethz-b-000540314
dc.description.abstract
This paper provides several contributions to the mathematical analysis of subwavelength resonances in a high-contrast medium containing N acoustic obstacles. Our approach is based on an exact decomposition formula which reduces the solution of the sound scattering problem to that of an N dimensional linear system, and characterizes resonant frequencies as the solutions to an N-dimensional nonlinear eigenvalue problem. Under a simplicity assumptions on the eigenvalues of the capacitance matrix, we prove the analyticity of the scattering resonances with respect to the square root of the contrast parameter, and we provide a deterministic algorithm allowing to compute all terms of the corresponding Puiseux series. We then establish a nonlinear modal decomposition formula for the scattered field as well as point scatterer approximations for the far-field pattern of the sound wave scattered by N bodies. As a prerequisite to our analysis, a first part of the work establishes various novel results about the capacitance matrix and its symmetry properties, since qualitative properties of the resonances, such as the leading order of the scattering frequencies or of the corresponding far-field pattern are closely related to its spectral decomposition.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Wiley
en_US
dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject
Capacitance matrix
en_US
dc.subject
High-contrast medium
en_US
dc.subject
Holomorphic integral operators
en_US
dc.subject
Modal decomposition
en_US
dc.subject
Point scatterer approximation
en_US
dc.subject
Subwavelength resonance
en_US
dc.title
Modal decompositions and point scatterer approximations near the Minnaert resonance frequencies
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
dc.date.published
2022-03-24
ethz.journal.title
Studies in Applied Mathematics
ethz.journal.volume
149
en_US
ethz.journal.issue
1
en_US
ethz.journal.abbreviated
Stud. appl. math. (Cambr.)
ethz.pages.start
164
en_US
ethz.pages.end
229
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Oxford
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::09504 - Ammari, Habib / Ammari, Habib
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02500 - Forschungsinstitut für Mathematik / Institute for Mathematical Research
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::09504 - Ammari, Habib / Ammari, Habib
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02500 - Forschungsinstitut für Mathematik / Institute for Mathematical Research
ethz.date.deposited
2022-04-01T03:14:46Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
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ethz.rosetta.installDate
2022-07-18T13:02:30Z
ethz.rosetta.lastUpdated
2023-02-07T04:41:51Z
ethz.rosetta.versionExported
true
ethz.COinS
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