Abstract
Many systems in nature, like drops, bubbles or some macromolecules present circular or spherical symmetry. Under the influence of some external force, such objects often develop surface patterns whose properties are greatly influenced by the underlying geometry. However, differently from the planar case, patterns in curved geometries have been much less explored. Despite the complexity of the particular physical problems, the basic dynamical features are often captured by simple models of coupled oscillators. Here we present a theoretical and experimental study of the spatial instabilities of circular ring of coupled pendula parametrically driven by a vertical harmonic force. Normal oscillation modes (breathing, dipole, quadrupole) and localized patterns of different types (breathers and kinks) are predicted and observed. The analogy between the considered discrete mechanical system and a gas bubble cavitating under the action of an acoustic field is established. On the basis of this analogy, the oscillation patterns and localized modes observed experimentally in acoustically driven bubbles are interpreted and discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
T. Leighton, The Acoustic Bubble (Academic, London, 1997)
A.I. Eller, L.A. Crum, Instability of the motion of a pulsating bubble in a sound field. J. Acoust. Soc. Am. 47, 762 (1970)
A. Prosperetti, Viscous effects on perturbed spherical flows. Appl. Math. 84, 339 (1977)
A.O. Maksimov, T. Leighton, Pattern formation on the surface of a bubble driven by an acoustic field. Proc. R. Soc. A 468, 57 (2011)
B. Denardo, B. Galvin, A. Greenfield, A. Larraza, S. Putterman, W. Wright, Observations of localized structures in nonlinear lattices: domain walls and kinks. Phys. Rev. Lett. 68, 1730 (1992)
W.-Z. Chen, Experimental observation of solitons in a 1D nonlinear lattice. Phys. Rev. B. 49, 15063 (1994)
M. Versluis, D.E. Goertz, P. Palanchon, I.L. Heitman, S.M. van der Meer, B. Dollet, N. de Jong, D. Lohse, Microbubble shape oscillations excited through ultrasonic parametric driving. Phys. Rev. E 82 (2010)
O.M. Braun, Y.S. Kivshar, The Frenkel-Kontorova model: Concepts, Methods and Applications (Springer, Berlin/New York, 2004)
J. Cuevas, L.Q. English, P.G. Kevrekidis, M. Anderson, Discrete breathers in a forced-damped array of coupled pendula: modeling, computation, and experiment. Phys. Rev. Lett. 102, 224101 (2009)
N.V. Alexeeva, I.V. Barashenkov, G.P. Tsironis, Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators. Phys. Rev. Lett. 84, 3053 (2000)
A.O. Maksimov, T.G. Leighton, P.R. Birkin, Self focusing of acoustically excited Faraday ripples on a bubble wall. Phys. Lett. A 372, 3210 (2008)
Acknowledgements
The work was supported by Spanish Ministry of Science and Innovation and European Union FEDER through project FIS2011-29731-C02-02.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Sánchez-Morcillo, V.J., Jiménez, N., Chaline, J., Bouakaz, A., Santos, S.D. (2014). Spatio-Temporal Dynamics in a Ring of Coupled Pendula: Analogy with Bubbles. In: Carretero-González, R., Cuevas-Maraver, J., Frantzeskakis, D., Karachalios, N., Kevrekidis, P., Palmero-Acebedo, F. (eds) Localized Excitations in Nonlinear Complex Systems. Nonlinear Systems and Complexity, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-02057-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-02057-0_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02056-3
Online ISBN: 978-3-319-02057-0
eBook Packages: EngineeringEngineering (R0)