Close-to-touching acoustic subwavelength resonators: eigenfrequency separation and gradient blow-up
dc.contributor.author
Ammari, Habib
dc.contributor.author
Davies, Bryn
dc.contributor.author
Yu, Sanghyeon
dc.date.accessioned
2022-09-21T06:54:04Z
dc.date.available
2020-08-04T09:25:44Z
dc.date.available
2020-08-07T08:31:25Z
dc.date.available
2022-09-21T06:54:04Z
dc.date.issued
2020-01
dc.identifier.uri
http://hdl.handle.net/20.500.11850/429912
dc.description.abstract
In this paper, we study the behaviour 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 behaviour at leading order. We prove that the pair of resonators has two subwavelength resonant modes whose frequencies have different leading-order asymptotic behaviour. We, also, derive estimates for the rate at which the gradient of the scattered pressure wave blows up as the resonators are brought together.
en_US
dc.language.iso
en
en_US
dc.publisher
Seminar for Applied Mathematics, ETH Zurich
en_US
dc.subject
Subwavelength resonance
en_US
dc.subject
High-contrast metamaterials
en_US
dc.subject
Bubbly media
en_US
dc.subject
Bispherical coordinates
en_US
dc.subject
Close-to-touching spheres
en_US
dc.subject
Capacitance coefficients
en_US
dc.title
Close-to-touching acoustic subwavelength resonators: eigenfrequency separation and gradient blow-up
en_US
dc.type
Report
ethz.journal.title
SAM Research Report
ethz.journal.volume
2020-03
en_US
ethz.size
20 p.
en_US
ethz.publication.place
Zurich
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
en_US
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
en_US
ethz.identifier.url
https://math.ethz.ch/sam/research/reports.html?id=876
ethz.relation.isPreviousVersionOf
20.500.11850/447159
ethz.date.deposited
2020-08-04T09:25:53Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-08-07T08:31:39Z
ethz.rosetta.lastUpdated
2023-02-07T06:27:00Z
ethz.rosetta.versionExported
true
ethz.COinS
ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.atitle=Close-to-touching%20acoustic%20subwavelength%20resonators:%20eigenfrequency%20separation%20and%20gradient%20blow-up&rft.jtitle=SAM%20Research%20Report&rft.date=2020-01&rft.volume=2020-03&rft.au=Ammari,%20Habib&Davies,%20Bryn&Yu,%20Sanghyeon&rft.genre=report&
Files in this item
Files | Size | Format | Open in viewer |
---|---|---|---|
There are no files associated with this item. |
Publication type
-
Report [6866]