A Mathematical and Numerical Framework for Bubble Meta-Screens

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

doi:10.1137/16m1090235

Cited by 34 publications

(36 citation statements)

References 30 publications

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“…Related to this bubbles model, other results were derived very recently. In particular, in the case β = 2 and ω close to the resonance ω M , we find in [6] a mathematical framework for modeling metasurfaces with bubbles, in [7] a justification of the superfocusing of acoustic waves in the presence of gas bubbles and in [8] a justification of the bandgap opening due to periodically distributed bubbles.…”

Section: Introductionmentioning

confidence: 84%

The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies

Ammari

Challa

Choudhury

et al. 2019

Journal of Differential Equations

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We deal with the linearized model of the acoustic wave propagation generated by small bubbles in the harmonic regime. We estimate the waves generated by a cluster of M small bubbles, distributed in a bounded domain Ω, with relative densities having contrasts of the order a β , β > 0, where a models their relative maximum diameter, a ≪ 1. We provide useful and natural conditions on the number M , the minimum distance and the contrasts parameter β of the small bubbles under which the point interaction approximation (called also the Foldy-Lax approximation) is valid.With the regimes allowed by our conditions, we can deal with a general class of such materials. Applications of these expansions in material sciences and imaging are immediate. For instance, they are enough to derive and justify the effective media of the cluster of the bubbles for a class of gases with densities having contrasts of the order a β , β ∈ ( 3 2 , 2) and in this case we can handle any fixed frequency. In the particular and important case β = 2, we can handle any fixed frequency far or close (but distinct) from the corresponding Minnaert resonance. The cluster of the bubbles can be distributed to generate volumetric metamaterials but also low dimensional ones as metascreens and metawires.2010 Mathematics Subject Classification. 35R30, 35C20.

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Section: Introductionmentioning

confidence: 84%

The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies

Ammari

Challa

Choudhury

et al. 2019

Journal of Differential Equations

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“…In this equation, recall that c = ψ 0 , φ 0 . Assume now that u (1) has the form u (1) = y1ψ0 0 . Theñ…”

Section: Computation Of ψ and φmentioning

confidence: 99%

Subwavelength resonances of encapsulated bubbles

Ammari

Fitzpatrick

Hiltunen

et al. 2019

Journal of Differential Equations

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The aim of this paper is to derive a formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance frequency, as a perturbation away from the resonance of the uncoated bubble, in terms of the thickness of the coating. The formula is numerically verified in the case of circular bubbles, where the resonance can be efficiently computed using the multipole method.Mathematics Subject Classification (MSC2000). 35R30, 35C20.

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“…Formal derivation of the effective medium in 3 D domains are derived in [13] and a justification is provided in [3] for frequencies near the Minnaert resonance. In [5], the effective medium corresponding to a periodic distribution of the bubbles in a flat and infinite 2 D surface (a plane) is studied for frequencies near the Minnaert resonance. Compared to these results, here we deal with general shaped (open or closed) surfaces (where no periodicity is needed) and for any fixed frequency.…”

Section: Introductionmentioning

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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A Mathematical and Numerical Framework for Bubble Meta-Screens

Cited by 34 publications

References 30 publications

The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies

The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies

Subwavelength resonances of encapsulated bubbles

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

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