title: Interaction of two walkers: wave-mediated energy and force.
abstract: A bouncing droplet, self-propelled by its interaction with the waves it generates, forms a classical wave-particle association called a "walker." Previous works have demonstrated that the dynamics of a single walker is driven by its global surface wave field that retains information on its past trajectory. Here we investigate the energy stored in this wave field for two coupled walkers and how it conveys an interaction between them. For this purpose, we characterize experimentally the "promenade modes" where two walkers are bound and propagate together. Their possible binding distances take discrete values, and the velocity of the pair depends on their mutual binding. The mean parallel motion can be either rectilinear or oscillating. The experimental results are recovered analytically with a simple theoretical framework. A relation between the kinetic energy of the droplets and the total energy of the standing waves is established.
authors.affiliation: Laboratoire de Physique Théorique et Modélisation, Université de Cergy Pontoise, CNRS-UMR 8089, 2 avenue A. Chauvin, 95302 Cergy-Pontoise, France.
authors.forename: Christian
authors.initials: C
authors.lastname: Borghesi
authors.affiliation: Matière et Systèmes Complexes, Université Paris Diderot, CNRS-UMR 7057, 10 rue A. Domon et L. Duquet, 75013 Paris, France.
authors.forename: Julien
authors.initials: J
authors.lastname: Moukhtar
authors.affiliation: Institut Langevin, ESPCI ParisTech, CNRS-UMR 7587, 1 rue Jussieu, 75005 Paris Cedex 05, France.
authors.forename: Matthieu
authors.initials: M
authors.lastname: Labousse
authors.affiliation: Laboratoire de Physique et Mécanique des Milieux Hétérogènes, ESPCI ParisTech, CNRS-UMR 7636, 10 rue Vauquelin, 75005 Paris, France.
authors.forename: Antonin
authors.initials: A
authors.lastname: Eddi
authors.affiliation: Institut Langevin, ESPCI ParisTech, CNRS-UMR 7587, 1 rue Jussieu, 75005 Paris Cedex 05, France.
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Fort
authors.affiliation: Matière et Systèmes Complexes, Université Paris Diderot, CNRS-UMR 7057, 10 rue A. Domon et L. Duquet, 75013 Paris, France.
authors.forename: Yves
authors.initials: Y
authors.lastname: Couder