Acoustic chaos

Moreover, the behavior of a bubble cloud obeys the laws of deterministic chaos, i.e., acoustic chaos or turbulence. Although the analysis of such a system is beyond the scope of this book, it must be emphasized that on the basis of experimental data, Lauterborn and Holzfuss determined that a bubble field experiences some self-organization. The reader interested in a full presentation of... 

Berggren, K.-F., and A.F. Sadreev. Chaos in quantum billiards and similarities with pure-tone random models in acoustics, microwave cavities and electric networks. Mathematical modelling in physics, engineering and cognitive sciences. Proc. of the conf. Mathematical Modelling of Wave Phenomena , 7 229, 2002. 

Similar to energy transfer between different shapes of a liquid droplet, coupling between the volume oscillation and different shape oscillations occur for bubbles in acoustic fields [43]. Interaction between modes can lead to chaotic response of the bubble to the external forcing. For a large enough bubble, the spectrum of distortion modes is dense, and several distortion modes attribute to the shape. Development of chaos depends on the number of excited shape modes. 

K.T. Tang, DJ. Yao, C.M. Yang, H.C. Hao, J.S. Chao, C.H. Li, P.S.Gu, A Portable Electronic Nose Based on Bio-Chemical Surface Acoustic Wave (SAW) Array with Multiplexed Oscillator and Readout Electronics. (ISOEN, Brescia, 2009)... 

The main advantages of hydrophones are (1) the relative ease of use, (2) the fact that FFT analysis can be carried out, a feature which gives information on the type of cavitation (transient vs stable, access to chaos via a cascade of period doubling in the acoustic emissions from pulsating bubbles), (3) the topology of the reactors, (4) the shape of a pulsed signal in pulsed ultrasound, etc. ... 

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