Spatio-Temporal Dynamics in a Ring of Coupled Pendula: Analogy with Bubbles

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.