Minnaert resonances for acoustic waves in bubbly media

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

doi:10.1016/j.anihpc.2018.03.007

Cited by 83 publications

(145 citation statements)

References 36 publications

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“…satisfying the Sommerfeld radiation condition) fundamental solution to the Helmholtz operator ∆ + ω 2 in R 2 [55]. The value of this approach is that solving (2.4) is reduced to finding φ, ψ such that the two transmission conditions on ∂D hold [37,54]. An asymptotic analysis of the resonant frequencies and eigenmodes, based on their layerpotential representations (2.6), was performed in [13].…”

Section: Layer-potential Approachmentioning

confidence: 99%

Mimicking the active cochlea with a fluid-coupled array of subwavelength Hopf resonators

Ammari

Davies

2020

Proc. R. Soc. A.

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We present a design for an acoustic metamaterial that mimics the behaviour of the active cochlea. This material is composed of a size-graded array of cylindrical subwavelength resonators, has similar dimensions to the cochlea and is able to per- form frequency separation of audible frequencies. Nonlinear amplification is introduced to the model in order to replicate the behaviour of the cochlear amplifier. This formulation takes the form of a fluid-coupled array of Hopf resonators. We seek solutions in the form of a modal decomposition, so as to retain the physically derived coupling between resonators.

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Section: Layer-potential Approachmentioning

confidence: 99%

Mimicking the active cochlea with a fluid-coupled array of subwavelength Hopf resonators

Ammari

Davies

2020

Proc. R. Soc. A.

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“…|s−s ′ | ·ν s ′ ds ′ ds and define ω 2 M := 8π k l (ρ l −ρ0)Â l . The constant ω M is an approximation of the real part of the Minnaert resonance created by each bubble, see [2,6]. To simplify the exposition of our results in our ongoing work, all the bubbles are assumed to be identical in shape, and have the same density and bulk modulus.…”

Section: Background and Notationsmentioning

confidence: 99%

The Equivalent Media Generated by Bubbles of High Contrasts: Volumetric Metamaterials and Metasurfaces

Ammari¹,

Challa²,

Choudhury³

et al. 2020

Multiscale Model. Simul.

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We deal with the point-interaction approximations for the acoustic wave fields generated by a cluster of highly contrasted bubbles for a wide range of densities and bulk moduli contrasts. We derive the equivalent fields when the cluster of bubbles is appropriately distributed (but not necessarily periodically) in a bounded domain Ω of R 3 . We handle two situations.(1) In the first one, we distribute the bubbles to occupy a 3 dimensional domain. For this case, we show that the equivalent speed of propagation changes sign when the medium is excited with frequencies smaller or larger than (but not necessarily close to) the Minnaert resonance. As a consequence, this medium behaves as a reflective or absorbing depending on whether the used frequency is smaller or larger than this resonance. In addition, if the used frequency is extremely close to this resonance, for a cluster of bubbles with density above a certain threshold, then the medium behaves as a 'wall', i.e. allowing no incident sound to penetrate.(2) In the second one, we distribute the bubbles to occupy a 2 dimensional (open or closed) surface, not necessarily flat. For this case, we show that the equivalent medium is modeled by a Dirac potential supported on that surface. The sign of the surface potential changes for frequencies smaller or larger than the Minnaert resonance, i.e. it behaves as a smart metasurface reducing or amplifying the transmitted sound across it. As in the 3D case, if the used frequency is extremely close to this resonance, for a cluster of bubbles with density above an appropriate threshold, then the surface allows no incident sound to be transmitted across the surface, i.e. it behaves as a white screen.2010 Mathematics Subject Classification. 35R30, 35C20.

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“…We now recall from e.g. [2,3] the main result that will allow us to understand the leading order behaviour of A in (9).…”

Section: Preliminariesmentioning

confidence: 99%

“…Here, we estimate the appropriate material parameters for the system of subwavelength resonators used in our version of the model from [10]. In particular, using physical values for the cochlea and representations of subwavelength acoustic resonators as harmonic oscillators, we estimate the appropriate value for the bulk modulus contrast µ, defined in (2). In [10] it is shown that a suitable approximation to basilar membrane motion can be achieved by considering an array of masses on springs.…”

Section: A Materials Parametersmentioning

confidence: 99%

A fully coupled subwavelength resonance approach to filtering auditory signals

Ammari

Davies

2019

Proc. R. Soc. A.

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The aim of this paper is to understand the behaviour of a large number of coupled subwavelength resonators. We use layer potential techniques in combination with numerical computations to study the acoustic pressure field due to scattering by a graded array of subwavelength resonators. Using this method, we study a graded-resonance model for the cochlea. We compute the resonant modes of the system and explore the model's ability to decompose incoming signals. We are able to offer mathematical explanations for the cochlea's so-called "travelling wave" behaviour and tonotopic frequency map. Mathematics subject classification: 35R30, 35C20

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Minnaert resonances for acoustic waves in bubbly media

Cited by 83 publications

References 36 publications

Mimicking the active cochlea with a fluid-coupled array of subwavelength Hopf resonators

Mimicking the active cochlea with a fluid-coupled array of subwavelength Hopf resonators

The Equivalent Media Generated by Bubbles of High Contrasts: Volumetric Metamaterials and Metasurfaces

A fully coupled subwavelength resonance approach to filtering auditory signals

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