Long-Time Dynamics of Acoustic Resonators and Applications in Inverse Problems

Speaker: 李隆博士，Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences

Inviter: 张海文

Title: Long-Time Dynamics of Acoustic Resonators and Applications in Inverse Problems

Language: Chinese

Time & Venue: 2026.3.29 16:30-17:30 南楼N613

Abstract: We discuss the time-domain acoustic wave propagation in the presence of a subwavelength resonator modeling a Microbubble. A uniform point-approximation expansion of the wave field—valid in both space and time—is derived. The leading-order behavior consists of two components:

1.The primary wave, representing the field generated in the absence of the bubble;

2.The resonant wave, arising from the interaction between the bubble and the background medium.

We show that the lifetime of the resonant wave is inversely proportional to the imaginary part of the relevant subwavelength resonance (here, the Minnaert resonance), while its oscillation period is determined by the real part.

As an application, we exploit the resonant wave’s characteristics—particularly its lifetime and period—to recover the mass density or bulk modulus in heterogeneous background media. This approach has significant implications for imaging techniques employing contrast agents.