title: Interaction, coalescence, and collapse of localized patterns in a quasi-one-dimensional system of interacting particles.
abstract: We study the path toward equilibrium of pairs of solitary wave envelopes (bubbles) that modulate a regular zigzag pattern in an annular channel. We evidence that bubble pairs are metastable states, which spontaneously evolve toward a stable single bubble. We exhibit the concept of topological frustration of a bubble pair. A configuration is frustrated when the particles between the two bubbles are not organized in a modulated staggered row. For a nonfrustrated (NF) bubble pair configuration, the bubbles interaction is attractive, whereas it is repulsive for a frustrated (F) configuration. We describe a model of interacting solitary wave that provides all qualitative characteristics of the interaction force: It is attractive for NF systems and repulsive for F systems and decreases exponentially with the bubbles distance. Moreover, for NF systems, the bubbles come closer and eventually merge as a single bubble, in a coalescence process. We also evidence a collapse process, in which one bubble shrinks in favor of the other one, overcoming an energetic barrier in phase space. This process is relevant for both NF systems and F systems. In NF systems, the coalescence prevails at low temperature, whereas thermally activated jumps make the collapse prevail at high temperature. In F systems, the path toward equilibrium involves a collapse process regardless of the temperature.
authors.affiliation: Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France.
authors.forename: Tommy
authors.initials: T
authors.lastname: Dessup
authors.affiliation: Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France.
authors.forename: Christophe
authors.initials: C
authors.lastname: Coste
authors.affiliation: Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France.
authors.forename: Michel
authors.initials: M
authors.lastname: Saint Jean