论文标题
接近接近的声学亚波长谐振器：特征频率分离和梯度爆炸
Close-to-touching acoustic subwavelength resonators: eigenfrequency separation and gradient blow-up
论文作者
论文摘要
在本文中，我们研究了两个高对比度的声音谐振器靠近时，耦合的亚波长谐振模式的行为。我们考虑球形谐振器的情况，并使用双球坐标来得出电容系数的显式表示，我们显示，我们显示，在领先顺序上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，它们的频率具有不同的前阶渐近行为。我们也得出了估计的估计值，因为将谐振器汇集在一起时，散射压力波的梯度会吹动。
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.
