Moláček, J., & Bush, J. W. (2013). Drops bouncing on a vibrating bath. Journal of Fluid Mechanics, 727, 582-611.
http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/07/MB1-2013.pdf
Linear and logarithmic spring model of a boucing droplet
Exotic states of bouncing and walking droplets
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
Drops walking on a vibrating bath : towards a hydrodynamic wave theory
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
Wavelike statistics from pilot-wave dynamics in a circular corral
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
Overview of Bohmian Mechanics
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”
Archimedean lattices in the bound states of wave interacting particles
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
Path-memory induced quantization of classical orbits
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
Marcheurs, Dualité onde-particule et Mémoire de chemin
“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 di raction. 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’e et 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
The role of the droplet deformations in the bouncing droplet dynamics
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
Bouncing droplets, the role of deformations (Thèse)
Terwagne, D. (2011). Bouncing droplets, the role of deformations.
APENDIX C describes a automatic droplet generator
The irrotational motion of a compressible inviscid fluid
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.
Observation of star-shaped surface gravity waves
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.
Real-time single-molecule imaging of quantum interference
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
This experiment isn’t about droplet, but it shows full 2-dimensionnal build-up of quantum interference pattern in real time for Phtalocyanine molecules.
[VIDEO] The pilot-wave dynamics of walking droplets
A GREAT video by John BUSH and his team at MIT
[VIDEO] Dynamical phenomena: Walking and orbiting droplets
From Couder’s Lab
Self-organization of bouncing oil drops: Two-dimensional lattices and spinning clusters
Lieber, S. I., Hendershott, M. C., Pattanaporkratana, A., & Maclennan, J. E. (2007). Self-organization of bouncing oil drops: Two-dimensional lattices and spinning clusters. Physical Review E, 75(5), 056308.
http://www.physics.emory.edu/~weeks/lab/papers/lieber-pre07-drop.pdf
Level Splitting at Macroscopic Scale
Eddi, A., Moukhtar, J., Perrard, S., Fort, E., & Couder, Y. (2012). Level Splitting at Macroscopic Scale. Physical Review Letters, 108(26), 264503.
http://stilton.tnw.utwente.nl/people/eddi/Papers/PhysRevLett_Zeeman.pdf
A synthetic Schlieren method for the measurement of the topography of a liquid interface
Moisy, F., Rabaud, M., & Salsac, K. (2009). A synthetic Schlieren method for the measurement of the topography of a liquid interface. Experiments in fluids,46(6), 1021-1036.
Particle–wave association on a fluid interface
Protière, S., Boudaoud, A., & Couder, Y. (2006). Particle-wave association on a fluid interface. Journal of Fluid Mechanics, 554(10), 85-108.
From Bouncing to Floating: Noncoalescence of Drops on a Fluid Bath
Couder, Y., Fort, E., Gautier, C. H., & Boudaoud, A. (2005). From bouncing to floating: Noncoalescence of drops on a fluid bath. Physical review letters,94(17), 177801.
http://www.lps.ens.fr/~boudaoud/Publis/Couder05Bounc.pdf