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Hamiltonian description of bubble dynamics

  • Statistical, Nonlinear, and Soft Matter Physics
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Abstract

The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.

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Authors and Affiliations

  1. Il’ichev Pacific Oceanological Institute, Far East Division, Russian Academy of Sciences, ul. Baltiĭskaya 43, Vladivostok, 690041, Russia

    A. O. Maksimov

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  1. A. O. Maksimov
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Correspondence to A. O. Maksimov.

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Original Russian Text © A.O. Maksimov, 2008, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 133, No. 2, pp. 412–428.

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Maksimov, A.O. Hamiltonian description of bubble dynamics. J. Exp. Theor. Phys. 106, 355–370 (2008). https://doi.org/10.1134/S1063776108020143

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  • DOI: https://doi.org/10.1134/S1063776108020143

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