THE INTERACTION BETWEEN TWO CLOSE-TO-TOUCHING CONVEX ACOUSTIC SUBWAVELENGTH RESONATORS.

The Minneart resonance is a low frequency resonance in which the wavelength is much larger than the size of the resonators. It is interesting to study the interaction between two adjacent bubbles when they are brought close together. Because the bubbles are usually compressible, in this paper we mainly investigate resonant modes of two general convex resonators with arbitrary shapes to extend the results of Ammari, Davies, and Yu in [Multiscale Model. Simul., 18 (2020), pp. 1299--1317], where a pair of spherical resonators are considered by using bispherical coordinates. We combine the layer potential method for the Helmholtz equation in [Ammari, Davies, and Yu, Multiscale Model. Simul., 18 (2020), pp. 1299--1317, Ammari et al., Proc. A, 473 (2017), 20170469] and the elliptic theory for gradient estimates in [Li, SIAM J. Math. Anal., 52 (2020), pp. 3350--3375, Li, Li, and Yang, Multiscale Model. Simul., 17 (2019), pp. 899--925], to calculate the capacitance coefficients for the coupled C2,α resonators, and then show the leading-order asymptotic behaviors of two different resonant modes and reveal the dependence of the resonant frequencies on their geometric properties, such as convexity, volumes, and curvatures. By the way, the blow-up rates of gradient of the scattered pressure are also presented. [ABSTRACT FROM AUTHOR]