Close-to-touching acoustic subwavelength resonators: Eigenfrequency separation and gradient blow-up

Habib Ammari, Bryn Davies, Y. U. Sanghyeon

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1299-1317
Number of pages19
JournalMultiscale Modeling and Simulation
Issue number3
Publication statusPublished - 2020

Bibliographical note

Publisher Copyright:
© by SIAM. Unauthorized reproduction of this article is prohibited.


  • Bispherical coordinates
  • Bubbly media
  • Capacitance coefficients
  • Close-to-touching spheres
  • High-contrast metamaterials
  • Subwavelength resonance

ASJC Scopus subject areas

  • General Chemistry
  • Modelling and Simulation
  • Ecological Modelling
  • General Physics and Astronomy
  • Computer Science Applications


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