Multiscale Modeling &Simulation, Volume 18, Issue 3, Page 1299-1317, January 2020.
In this paper, we study the behavior 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 behavior at leading order. We prove that the pair of resonators has two subwavelength resonant modes whose frequencies have different leading-order asymptotic behavior. We also derive estimates for the rate at which the gradient of the scattered pressure wave blows up as the resonators are brought together.

中文翻译：

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接近接触的声学亚波长谐振器：特征频率分离和梯度衰减

《多尺度建模与仿真》，第18卷，第3期，第1299-1317页，2020
年1月。在本文中，我们研究了当两个高对比度的声谐振器靠近时耦合的亚波长谐振模的行为。我们考虑了球形谐振器的情况，并使用双球形坐标来导出电容系数的显式表示，我们展示了它们以超前顺序捕获了系统的谐振行为。我们证明这对谐振器具有两个亚波长谐振模式，其频率具有不同的前导渐近行为。我们还导出了当谐振器聚集在一起时散射压力波的梯度爆炸速率的估计值。