A special seminar on “OPTIMAL CONTROL AND FEEDBACK CONTROL PROBLEMS OF INFLUENZA MODELS” by Hee-Dae Kwon, and “MATHEMATICAL ANALYSIS OF BUBBLY MEDIA” by Hyundae Lee from Inha University, Incheon, South Korea. The seminar is scheduled on January 13, 2020 from 10.00 – 12.00 a.m. at M building, venue room M307.
It is known that a single bubble in the water possesses a quasi-static resonance which is called the Minneart resonance.
Our analysis shows that near and below the Minneart resonant frequency, the effective media has high refractive index, which explains the super-focusing phenomenon observed in the experiment while near and above the Minneart resonant frequency, the effective media is dissipative.
We also present some works on bubbly meta-surface which is a homogenization theory for a thin layer of periodically arranged bubbles mounted on a perfect reflection surface.
Finally, we prove 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.
We also show the existence of a Dirac dispersion cone in a honeycomb crystal comprised of bubbles of arbitrary shape.