Avoided crossings in three coupled oscillators as a model system of acoustic bubbles

Details Avoided crossings in three coupled oscillators as a model system of acoustic bubbles Avoided crossings in three coupled oscillators as a model system of acoustic bubbles

2005-06-09

arxiv.org/abs/physics/0506080v3

Phys. Rev. E 72, 036306 (2005)

Physics

Fluid Dynamics

16 pages, 6 figures, REVTeX4; Fig. 3 replaced, present address given

Scientific paper

10.1103/PhysRevE.72.036306

The resonance frequencies and oscillation phases of three acoustically coupled bubbles are examined to show that avoided crossings can appear in a multibubble system. Via a simple coupled oscillator model, we show that if at least three bubbles exist, it is possible for their resonance frequencies as functions of the separation distances between the bubbles to experience an avoided crossing. Furthermore, by focusing our attention on the oscillation phases and based on analysis of the transition frequencies [M. Ida, Phys. Lett. A 297, 210 (2002); M. Ida, J. Phys. Soc. Jpn. 71, 1214 (2002)] of the coupled bubbles, we show that a distinct state exchange takes place between the bubbles at a point in the avoided crossing region, where a resonance frequency of the triple-bubble system crosses with a transition frequency not corresponding to the resonance frequencies.

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