Periodic orbit theory applied to a chaotically oscillating gas bubble in water

Simon, Gábor; Cvitanović, Predrag; Levinsen, Mogens T.; Csabai, István; Horváth, Áron

doi:10.1088/0951-7715/15/1/302

Cited by 29 publications

(23 citation statements)

References 40 publications

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“…The accumulated knowledge of this nonlinear behavior has been summarized in many reviews [18][19][20] and papers [1,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. The most important findings are the existence of period-doubling cascades in the bifurcation structure [1,21,30,31,35], the appearance of resonance horns in the amplitude-frequency plane of the driving [24,27,34] or the alternation of chaotic and periodic windows [21,23,33]. These structures show similarities with the results obtained on other nonlinear oscillators such as Toda [37], Duffing [38][39][40][41] and others [42], implying that they are universal features of nonlinear systems rather than unique properties of oscillating bubbles.…”

Section: Introductionmentioning

confidence: 99%

Classification of the bifurcation structure of a periodically driven gas bubble

Varga

Hegedűs

2016

Nonlinear Dyn

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The bifurcation structure of a periodically driven spherical gas/vapour bubble is examined by means of methods of nonlinear analysis. The study of Behnia and his coworkers [1] revealed that the bifurcation structures with the pressure amplitude of the excitation as control parameter are structurally similar provided that R E ω is kept constant. In the present paper, this problem is revisited. Analytical and numerical investigations of the bubble oscillator, which is the Keller-Miksis equation, are presented. It is shown that the validity range of Behnia's condition is governed by the viscosity and the surface tension, and holds only for relatively large bubbles. In water, the effect of viscosity is negligible, and the surface tension plays significant role at bubble size lower than approximately 5 µm.

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Section: Introductionmentioning

confidence: 99%

Classification of the bifurcation structure of a periodically driven gas bubble

Varga

Hegedűs

2016

Nonlinear Dyn

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“…In addition, this condition was used to plot the bifurcation diagram of a cavitation bubble in [45,48]. This method continued through increasing the control parameter and the new resulting discrete points were plotted in the bifurcation diagrams versus the altered control parameters.…”

Section: Bifurcation Diagramsmentioning

confidence: 99%

Effect of magnetic field on the radial pulsations of a gas bubble in a non-Newtonian fluid

Behnia

Mobadersani

Yahyavi

et al. 2015

Chaos, Solitons & Fractals

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a b s t r a c tDynamics of acoustically driven bubbles' radial oscillations in viscoelastic fluids are known as complex and uncontrollable phenomenon indicative of highly active nonlinear as well as chaotic behavior. In the present paper, the effect of magnetic fields on the non-linear behavior of bubble growth under the excitation of an acoustic pressure pulse in non-Newtonian fluid domain has been investigated. The constitutive equation [Upper-Convective Maxwell (UCM)] was used for modeling the rheological behaviors of the fluid. Due to the importance of the bubble in the medical applications such as drug, protein or gene delivery, blood is assumed to be the reference fluid. It was found that the magnetic field parameter (B) can be used for controlling the nonlinear radial oscillations of a spherical, acoustically forced gas bubble in nonlinear viscoelastic media. The relevance and importance of this control method to biomedical ultrasound applications were highlighted. We have studied the dynamic behavior of the radial response of the bubble before and after applying the magnetic field using Lyapunov exponent spectra, bifurcation diagrams and time series. A period-doubling bifurcation structure was predicted to occur for certain values of the parameters effects. Results indicated its strong impact on reducing the chaotic radial oscillations to regular ones.

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“…In our analysis the following condition was used: P max R fðR; _ RÞ : _ R ¼ 0g which gives the maximal radius from each acoustic period. Also, this condition was used to plot the bifurcation diagram of a cavitation bubble in [60]. In order to generate the bifurcation points, the equation of the microbubble motion was solved numerically for 900 acoustic cycles of the lower frequency and then a Poincaré section was constructed.…”

Section: Bifurcation Diagramsmentioning

confidence: 99%

Intelligent controlling microbubble radial oscillations by using Slave–Master Feedback control

Behnia

Yahyavi

Mobadersani

2014

Applied Mathematics and Computation

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a b s t r a c tDynamics of acoustically driven microbubbles in ultrasonic fields are known to be complex and uncontrollable phenomena indicative of a highly active nonlinear as well as chaotic behavior. In this paper, a method based on Slave-Master Feedback (SMF) to suppress unstable radial oscillations of contrast agents is presented. In the proposed control process, the encapsulated microbubbles as the slave system is coupled with a dynamical system as the master, so that the output of the coupled system is able to produce a stable oscillation. A great virtue of this control technique is its flexibility. In comparison with existing techniques, the present dynamical chaos control method does not need to know more than one variable. The numerical results show its strong impact on reducing the chaotic oscillations to regular ones.

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Periodic orbit theory applied to a chaotically oscillating gas bubble in water

Cited by 29 publications

References 40 publications

Classification of the bifurcation structure of a periodically driven gas bubble

Classification of the bifurcation structure of a periodically driven gas bubble

Effect of magnetic field on the radial pulsations of a gas bubble in a non-Newtonian fluid

Intelligent controlling microbubble radial oscillations by using Slave–Master Feedback control

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