Centre de Mathématiques et de Leurs Applications

Orateur :  Marco Mancini, CMLA

Titre : Déformations cycliques d'un amas désordonné de bulles 2d: cycles périodiques et réversibilité des transformations topologiques.

 Résumé :
Two-dimensional clusters of mono-sized bubbles are submitted to a cyclic and quasi-static deformation by varying the area of a central bubble.
We present the numerical results obtained by Surface Evolver simulations and some preliminary experimental results.

Two regimes are observed.

The transient regime, during some cycles, characterized by T1 (topological changes) events anywhere in the cluster; and the periodic regime where the structure of the cluster after any cycle is unchanged and the most of the T1 are localized near the deforming bubble.

The first law of thermodynamics is demonstrated for this system. At any step, the variation of the cluster energy is given by the work applied to the system to vary the deforming bubble area; plus the energy dissipated (by heat) by T1. For a cycle in the periodic regime, the energy variation vanishes and the energy given to the cluster by work is completely dissipated by T1.

During the deflation, the shape of the bubbles is more oblong and the energy dissipated by T1s is smaller with respect to the inflation. We explain this asymmetry by a simple model.

Avalanches of topological events are observed for both transient and periodic regimes. The number of T1, as a function of the deforming area, is well fitted by a line. The entropy and the second moment of the number of edges distribution are also observed.