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The Equivalent Media Generated by Bubbles of High Contrasts: Volumetric Metamaterials and Metasurfaces
Multiscale Modeling and Simulation ( IF 1.6 ) Pub Date : 2020-02-19 , DOI: 10.1137/19m1237259 Habib Ammari , Durga Prasad Challa , Anupam Pal Choudhury , Mourad Sini
Multiscale Modeling and Simulation ( IF 1.6 ) Pub Date : 2020-02-19 , DOI: 10.1137/19m1237259 Habib Ammari , Durga Prasad Challa , Anupam Pal Choudhury , Mourad Sini
Multiscale Modeling &Simulation, Volume 18, Issue 1, Page 240-293, January 2020.
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 $\Omega$ of $\mathbb{R}^3$. We handle two situations. (1) In the first one, we distribute the bubbles to occupy a three 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 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 two 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 three dimensional 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.
中文翻译：
高对比度气泡产生的等效介质：体积超材料和超表面
2020年1月，《多尺度建模与仿真》，第18卷，第1期，第240-293页。
我们处理由一系列高对比度的气泡簇产生的声波场的点相互作用近似，这些气泡在广泛的密度和体积模量对比范围内。当气泡簇在$ mathbb {R} ^ 3 $的有界域$ \ Omega $中适当分布（但不一定周期性）时，我们得出等效字段。我们处理两种情况。（1）在第一个中，我们分布气泡以占据三维域。对于这种情况，我们表明当介质以小于或大于（但不一定接近）Minnaert共振的频率激发时，等效传播速度会改变符号。结果，取决于所使用的频率是小于还是大于该共振，该介质表现为反射或吸收。此外，如果所使用的频率非常接近该共振，则对于密度高于某个阈值的一簇气泡，该介质将充当“墙”，即不允许任何入射声穿透。（2）在第二个中，我们将气泡分布为占据二维（开放或封闭）表面，不一定是平坦的表面。对于这种情况，我们表明等效介质是由该表面上支撑的Dirac势建模的。对于小于或大于Minnaert共振的频率，表面电势的符号会发生变化，即，它表现为智能超颖表面，可减少或放大通过它的传输声音。与三维情况一样，如果使用的频率非常接近该共振，则对于密度高于适当阈值的气泡簇，
更新日期：2020-02-19
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 $\Omega$ of $\mathbb{R}^3$. We handle two situations. (1) In the first one, we distribute the bubbles to occupy a three 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 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 two 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 three dimensional 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.
中文翻译：
高对比度气泡产生的等效介质：体积超材料和超表面
2020年1月，《多尺度建模与仿真》，第18卷，第1期，第240-293页。
我们处理由一系列高对比度的气泡簇产生的声波场的点相互作用近似，这些气泡在广泛的密度和体积模量对比范围内。当气泡簇在$ mathbb {R} ^ 3 $的有界域$ \ Omega $中适当分布（但不一定周期性）时，我们得出等效字段。我们处理两种情况。（1）在第一个中，我们分布气泡以占据三维域。对于这种情况，我们表明当介质以小于或大于（但不一定接近）Minnaert共振的频率激发时，等效传播速度会改变符号。结果，取决于所使用的频率是小于还是大于该共振，该介质表现为反射或吸收。此外，如果所使用的频率非常接近该共振，则对于密度高于某个阈值的一簇气泡，该介质将充当“墙”，即不允许任何入射声穿透。（2）在第二个中，我们将气泡分布为占据二维（开放或封闭）表面，不一定是平坦的表面。对于这种情况，我们表明等效介质是由该表面上支撑的Dirac势建模的。对于小于或大于Minnaert共振的频率，表面电势的符号会发生变化，即，它表现为智能超颖表面，可减少或放大通过它的传输声音。与三维情况一样，如果使用的频率非常接近该共振，则对于密度高于适当阈值的气泡簇，
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