State space geometry of the chaotic pilot-wave hydrodynamics

N.B. Budanur, M. Fleury, Chaos: An Interdisciplinary Journal of Nonlinear Science 29 (2019) 013122.

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Journal Article | Published | English
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Abstract
We consider the motion of a droplet bouncing on a vibrating bath of the same fluid in the presence of a central potential. We formulate a rotation symmetry-reduced description of this system, which allows for the straightforward application of dynamical systems theory tools. As an illustration of the utility of the symmetry reduction, we apply it to a model of the pilot-wave system with a central harmonic force. We begin our analysis by identifying local bifurcations and the onset of chaos. We then describe the emergence of chaotic regions and their merging bifurcations, which lead to the formation of a global attractor. In this final regime, the droplet’s angular momentum spontaneously changes its sign as observed in the experiments of Perrard et al.
Publishing Year
Date Published
2019-01-22
Journal Title
Chaos: An Interdisciplinary Journal of Nonlinear Science
Volume
29
Issue
1
Article Number
013122
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eISSN
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Budanur NB, Fleury M. State space geometry of the chaotic pilot-wave hydrodynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2019;29(1):013122. doi:10.1063/1.5058279
Budanur, N. B., & Fleury, M. (2019). State space geometry of the chaotic pilot-wave hydrodynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(1), 013122. https://doi.org/10.1063/1.5058279
Budanur, Nazmi B, and Marc Fleury. “State Space Geometry of the Chaotic Pilot-Wave Hydrodynamics.” Chaos: An Interdisciplinary Journal of Nonlinear Science 29, no. 1 (2019): 013122. https://doi.org/10.1063/1.5058279.
N. B. Budanur and M. Fleury, “State space geometry of the chaotic pilot-wave hydrodynamics,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 29, no. 1, p. 013122, 2019.
Budanur NB, Fleury M. 2019. State space geometry of the chaotic pilot-wave hydrodynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science. 29(1), 013122.
Budanur, Nazmi B., and Marc Fleury. “State Space Geometry of the Chaotic Pilot-Wave Hydrodynamics.” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 29, no. 1, AIP Publishing, 2019, p. 013122, doi:10.1063/1.5058279.

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