Subwavelength phononic bandgap opening in bubbly media

Habib Ammari, Brian Fitzpatrick, Hyundae Lee, Sanghyeon Yu, Hai Zhang

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


The aim of this paper is to show both analytically and numerically the existence of a subwavelength phononic bandgap in bubble phononic crystals. The key result is an original formula for the quasi-periodic Minnaert resonance frequencies of an arbitrarily shaped bubble. The main findings in this paper are illustrated with a variety of numerical experiments.

Original languageEnglish
Pages (from-to)5610-5629
Number of pages20
JournalJournal of Differential Equations
Issue number9
Publication statusPublished - 2017 Nov 5
Externally publishedYes

Bibliographical note

Funding Information:
Hyundae Lee was supported by NRF-2015R1D1A1A01059357 grant. Hai Zhang was supported by HK RGC grant ECS 26301016 and startup fund R9355 from HKUST.

Publisher Copyright:
© 2017 Elsevier Inc.


  • Acoustic waves
  • Bubble
  • Layer potentials
  • Minnaert resonance
  • Phononic band gap

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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