Spatio-Temporal Dynamics in a Ring of Coupled Pendula: Analogy with Bubbles
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 ge
- PDF / 447,155 Bytes
- 12 Pages / 439.36 x 666.15 pts Page_size
- 101 Downloads / 165 Views
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.
V.J. Sánchez-Morcillo () N. Jiménez Instituto de Investigación para la Gestión, Integrada de las Zonas Costeras, Universitat Politécnica de Valencia, c/ Paranimf no. 1, 46730 Grao de Gandia, Spain e-mail: [email protected] J. Chaline A. Bouakaz Unité Mixte de Recherche Inserm U930 “Imagerie et Cerveau, Université François-Rabelais PRES Centre Val de Loire Université, 10 boulevard Tonnellé, 37032 Tours Cedex, France S. Dos Santos ENI Val de Loire, 3 Rue de la Chocolaterie BP 3410, F-41034 Blois cedex, France Unité Mixte de Recherche Inserm U930 “Imagerie et Cerveau, Université François-Rabelais PRES Centre Val de Loire Université, 10 boulevard Tonnellé, 37032 Tours Cedex, France R. Carretero-González et al. (eds.), Localized Excitations in Nonlinear Complex Systems, Nonlinear Systems and Complexity 7, DOI 10.1007/978-3-319-02057-0__13, © Springer International Publishing Switzerland 2014
251
252
V.J. Sánchez-Morcillo et al.
1 Introduction The spatio-temporal dynamics of a gas bubble in a fluid under the action of an external oscillating pressure field has been the subject of intense investigations during the last decades [1]. An acoustically forced bubble experiences different instabilities as the driving parameters (mainly the amplitude and the frequency of the external field) are changed. One of such instabilities leads to the formation of surface patterns, similar to the Faraday patterns observed in the free surface of vertically vibrated fluids, by means of parametric excitation of subharmonic modes [2,3]. Nonlinear patterns on the bubble surface have been however much less explored. Only recently, the existence of localized soliton-type surface waves has been theoretically considered [11]; their existence has been evidenced by different experimental observations. An interesting extension is the bubble with an artificial coating, so called ultrasound contrast agent (UCA), with cu
Data Loading...
