We systematically employ the method of matched asymptotic expansions to model Helmholtz resonators, with thermoviscous effects incorporated starting from first principles and with the lumped parameters characterizing the neck and cavity geometries precisely defined and provided explicitly for a wide range of geometries. With an eye towards modeling acoustic metasurfaces, we consider resonators embedded in a rigid surface, each resonator consisting of an arbitrarily shaped cavity connected to the external half-space by a small cylindrical neck. The bulk of the analysis is devoted to the problem where a single resonator is subjected to a normally incident plane wave; the model is then extended using "Foldy's method" to the case of multiple resonators subjected to an arbitrary incident field. As an illustration, we derive critical-coupling conditions for optimal and perfect absorption by a single resonator and a model metasurface, respectively.

中文翻译：

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亥姆霍兹谐振器的渐近建模，包括热粘性效应

我们系统地采用匹配渐近膨胀的方法来模拟亥姆霍兹谐振器，从第一原理开始结合热粘性效应，并使用集中参数来表征颈部和空腔几何形状，并为各种几何形状精确定义和明确提供。着眼于模拟声学超表面，我们考虑嵌入刚性表面的谐振器，每个谐振器由一个任意形状的腔组成，通过一个小的圆柱形颈部连接到外部半空间。大部分分析致力于解决单个谐振器受到垂直入射平面波影响的问题。然后使用“Foldy 方法”将模型扩展到受任意入射场影响的多个谐振器的情况。作为例证，