| Abstract: |
| We deal with the time-domain acoustic wave propagation in the presence of subwavelength resonators given by small scaled bubbles enjoying high contrasting mass density and bulk modulus. It is well known that such bubbles generate a single subwavelength resonance called Minnaert resonance. We derive the point-approximation expansion of the wave field in terms of the contrasting scales. The dominant part is a sum of two terms. The first one, i.e. the primary wave, is the one generated in the absence of the bubble. The second one, i.e. the resonant wave, is generated by the interaction between the bubble and the background.
1. We estimate the birth-time of the resonant wave. This is nothing but the travel time
needed by any wave to reach the location of the bubble.
2. We show that the life-time of the resonant wave is inversely proportional to the imaginary part of the resonance.
3. In addition, the period of the resonant wave is characterized by the real part of this resonance.
The birth time, life-time and period have signatures of the background where the bubble is located. They have important applications in inverse problems for imaging modalities using contrast agents. |
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