Archimedean lattices in the bound states of wave interacting particles

¹  Matières et Systèmes Complexes, Université Paris 7 Denis Diderot, CNRS, UMR 7057, Bâtiment Condorcet 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France, EU
²  Laboratoire de Physique Théorique et Modèles Statistiques Université Paris-Sud, CNRS, UMR 8626, Bâtiment 100 15 rue Georges Clémenceau, 91405 Orsay Cedex, France, EU
³  Institut Langevin, ESPCI ParisTech and Université Paris Diderot, CNRS, UMR 7587 - 10 rue Vauquelin, 75231 Paris Cedex 05, France, EU

Corresponding author: antonin.eddi@univ-paris-diderot.fr

Received: 12 June 2009
Accepted: 20 August 2009

Abstract

The possible periodic arrangements of droplets bouncing on the surface of a vibrated liquid are investigated. Because of the nature of the interaction through waves, the possible distance of binding of nearest neighbors is multi-valued. For large amplitude of the forcing, the bouncing becomes sub-harmonic and the droplets can have two different phases. This effect increases the possible distances of binding and the formation of various polygonal clusters is observed. From these elements it is possible to assemble crystalline structures related to the Archimedean tilings of the plane, the periodic tesselations which tile uniformly the 2D plane with convex polygons. Eight of the eleven possible configurations are observed. They are stabilized by the coupling of two sub-lattices of droplets of different phase, both contributing to sustain a common wave field.