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Route to shrimps: Dissipation driven formation of shrimp-shaped domains

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  • Varga, Roxána
  • Klapcsik, Kálmán
  • Hegedűs, Ferenc

Abstract

In this paper, two scenarios for the formation of shrimp-shaped domains [1] are presented. The employed test model is the Keller–Miksis equation that is a second order, harmonically forced nonlinear oscillator describing the dynamics of a single spherical gas bubble placed in a liquid domain. The results have shown that with an increasing dissipation rate (liquid viscosity), shrimp-shaped domains are evolved within the complex structure of each subharmonic resonances in the amplitude-frequency parameter plane of the external forcing. The mechanism is the coalescence and interaction of two pairs of a period-doubling and a saddle-node codimension-two bifurcation curves.

Suggested Citation

  • Varga, Roxána & Klapcsik, Kálmán & Hegedűs, Ferenc, 2020. "Route to shrimps: Dissipation driven formation of shrimp-shaped domains," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303650
    DOI: 10.1016/j.chaos.2019.109424
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    References listed on IDEAS

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    1. Varga, Roxána & Paál, György, 2015. "Numerical investigation of the strength of collapse of a harmonically excited bubble," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 56-71.
    2. Zhang, Yuning & Zhang, Yuning & Qian, Zhongdong & Ji, Bin & Wu, Yulin, 2016. "A review of microscopic interactions between cavitation bubbles and particles in silt-laden flow," Renewable and Sustainable Energy Reviews, Elsevier, vol. 56(C), pages 303-318.
    3. Medeiros, E.S. & de Souza, S.L.T. & Medrano-T, R.O. & Caldas, I.L., 2011. "Replicate periodic windows in the parameter space of driven oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 982-989.
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    1. da Costa, Diogo Ricardo & Rocha, Julia G.S. & de Paiva, Luam S. & Medrano-T, Rene O., 2021. "Logistic-like and Gauss coupled maps: The born of period-adding cascades," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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