title: Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits.
abstract: We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet's horizontal motion is described by an integro-differential trajectory equation, which is found to admit steady orbital solutions. Predictions for the dependence of the orbital radius and frequency on the strength of the radial harmonic force field agree favorably with experimental data. The orbital quantization is rationalized through an analysis of the orbital solutions. The predicted dependence of the orbital stability on system parameters is compared with experimental data and the limitations of the model are discussed.
authors.affiliation: Institut Langevin, ESPCI Paristech, CNRS, UMR No. 7587, PSL Research University, Université Pierre and Marie Curie, 1 Rue Jussieu, 75005 Paris, France, EU.|Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, Sorbonne Paris Cité, CNRS, UMR No. 7057, 10 Rue A. Domon and L. Duquet, 75013 Paris, France, EU.
authors.forename: M
authors.initials: M
authors.lastname: Labousse
authors.affiliation: Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
authors.forename: A U
authors.initials: AU
authors.lastname: Oza
authors.affiliation: Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, Sorbonne Paris Cité, CNRS, UMR No. 7057, 10 Rue A. Domon and L. Duquet, 75013 Paris, France, EU.
authors.forename: S
authors.initials: S
authors.lastname: Perrard
authors.affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
authors.forename: J W M
authors.initials: JW
authors.lastname: Bush