Wind-Willassen, Ø., Moláček, J., Harris, D. M., & Bush, J. W. (2013). Exotic states of bouncing and walking droplets. Physics of Fluids, 25, 082002.

http://windw.dk/2013Bouncing.pdf

Phase diagram refinement : the different styles of bouncing

Moláček, J., & Bush, J. W. (2013). Drops walking on a vibrating bath: towards a hydrodynamic pilot-wave theory. Journal of Fluid Mechanics, 727, 582-617.

http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/07/MB2-2013.pdf

The most advanced theoretical model

Harris, D. M., Moukhtar, J., Fort, E., Couder, Y., & Bush, J. W. (2013). Wavelike statistics from pilot-wave dynamics in a circular corral. Physical Review E, 88(1), 011001.

Abstract : Bouncing droplets can self-propel laterally along the surface of a vibrated fluid bath by virtue of a resonant interaction with their own wave field. The resulting walking droplets exhibit features reminiscent of microscopic quantum particles. Here we present the results of an experimental investigation of droplets walking in a circular corral. We demonstrate that a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral. The statistical behavior of the walking droplets is demonstrated to be analogous to that of electrons in quantum corrals.

http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/07/Harris-Corrals-2013.pdf

Statistical behavior of a walking droplet in a confined geometry

When  two walking droplets start turning around each other, the distance between them is n times the  wavelength (with n an integer) plus a constant.

Oriols, X., & Mompart, J. (2012). Overview of Bohmian Mechanics. arXiv preprint arXiv:1206.1084.

http://arxiv.org/pdf/1206.1084.pdf

Overview of the guiding wave quantum physics theory, known as “Bohmian mechanics”

Eddi, A., Decelle, A., Fort, E., & Couder, Y. (2009). Archimedean lattices in the bound states of wave interacting particles. EPL (Europhysics Letters), 87(5), 56002.

http://stilton.tnw.utwente.nl/people/eddi/Papers/epl_Cristaux.pdf

Cristal lattices of bouncing droplets

Fort, E., Eddi, A., Boudaoud, A., Moukhtar, J., & Couder, Y. (2010). Path-memory induced quantization of classical orbits. Proceedings of the National Academy of Sciences, 107(41), 17515-17520.

http://stilton.tnw.utwente.nl/people/eddi/Papers/PNAS_2010.pdf

Rotating bath

Quantization of trajectories

“L’organisation du manuscrit est la suivante : dans le premier chapitre, nous rappelons les premieres experiences realisees avec les gouttes rebondissantes, en particulier les regimes ou elles sont statiques. Nous presentons egalement l’instabilite de Faraday qui permet d’expliquer le couplage entre goutte et ondes a l’origine des marcheurs. Leurs proprietes sont discutees, en particulier dans le cas des experiences de diraction. Dans un second chapitre, nous presentons le montage experimental ainsi que l’ensemble des techniques de mesure utilisees. Le troisieme chapitre est dedie a l’etude d’un analogue de l’eet tunnel pour les marcheurs. Le quatrieme est consacre a l’etude des ondes de surface generees par un marcheur, en particulier le lien avec l’instabilite de Faraday a l’origine de la memoire de chemin. Enfin, dans le chapitre cinq, nous analysons la nature des trajectoires circulaires d’un marcheur soumis a une force orthogonale au mouvement. L’in uence de la memoire de chemin sur la quantication des rayons est presentee en detail, pour comprendre comment cet analogue macroscopique des niveaux de Landau se met en place avec des marcheurs.”

Eddi, A. (2011). Marcheurs, Dualité onde-particule et Mémoire de chemin (Doctoral dissertation, Université Paris-Diderot-Paris VII).

http://tel.archives-ouvertes.fr/docs/00/57/56/26/PDF/these_A_Eddi.pdf

Bouncing and walking droplet

Image from D. Terwagne, see : http://walkingdroplet.com/the-role-of-deformations-in-the-bouncing-droplet-dynamics/

Frame of IBM latest atomic movie

Terwagne, D., Ludewig, F., Vandewalle, N., & Dorbolo, S. (2013). The role of the droplet deformations in the bouncing droplet dynamics. Physics of Fluids (1994-present), 25(12), 122101.

http://www.grasp.ulg.ac.be/article/2013_terwagne_POF.pdf

ArXiv Preprint  :

Terwagne, D., Ludewig, F., Vandewalle, N., & Dorbolo, S. (2013). The role of deformations in the bouncing droplet dynamics. arXiv preprint arXiv:1301.7463.

http://arxiv.org/pdf/1301.7463v1.pdf

Editor Postprint :

http://orbi.ulg.ac.be/handle/2268/159838

Automatic droplet generator

Period doubling transition of bouncing droplet, bifurcation diagram

Simulation with mass-spring system

Terwagne, D. (2011). Bouncing droplets, the role of deformations.

http://bictel.ulg.ac.be/ETD-db/collection/available/ULgetd-09262011-010800/unrestricted/2011_Terwagne_these.pdf

APENDIX C describes a automatic droplet generator

Brady, R. (2013). The irrotational motion of a compressible inviscid fluid. arXiv preprint arXiv:1301.7540.

http://arxiv.org/pdf/1301.7540v1.pdf

A new quasi-particled called Sonon, which, it seems, can be related to walking droplets.

Walking droplet trapped in a square box escapes after many rebounds.

( Watch a “tunnel effect” at 2’30)

Rajchenbach, J., Clamond, D., Leroux, A., & Dieudonné, Z. J. A. (2013). Observation of star-shaped surface gravity waves. Physical Review Letters,110(9), 094502.

http://www.unice.fr/rajchenbach/star-wave.pdf

Related to the walking droplet experiment beacause the authors vibrate silicon oil.

Bouncing, colliding, mixing, dancing, floating droplets

Trapped in a circular box, shot at 1000 frames per second .

One of my first videos, and the most successfull on Youtube

Juffmann, T., Milic, A., Müllneritsch, M., Asenbaum, P., Tsukernik, A., Tüxen, J., … & Arndt, M. (2012). Real-time single-molecule imaging of quantum interference. Nature nanotechnology, 7(5), 297-300

http://www.physics.kku.ac.th/forum/sites/default/files/Real-time%20single-molecule%20imaging%20of%20quantum%20interference.pdf

This experiment  isn’t about droplet, but it shows full 2-dimensionnal build-up of quantum interference pattern in real time for Phtalocyanine molecules.

A single particle creates waves that interfere after passing through two slits.