ABSTRACT : “When a droplet is placed onto a vertically vibrated bath, it can bouncewithout coalescing. Upon an increase of the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well-defined speed.We investigate the confinement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that one-dimensional confinement is optimal for narrow channels of width of D  1.5λF . Thereby, the walker follows a quasilinear path.We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels.”

Filoux, B., Hubert, M., Schlagheck, P., & Vandewalle, N. (2017). Walking droplets in linear channels. Physical Review Fluids, 2(1), 013601.

https://www.researchgate.net/publication/312353846_Walking_droplets_in_linear_channels

ABSTRACT : “We investigate the crossing of an energy barrier by a self-propelled particle described by a Rayleigh friction term. We show that a sharp transition between low and large amplitude of the external force field occurs. It corresponds to a saddle point transition in the velocity flow phase space, and would therefore occur for any type of force field. We use this approach to describe the results obtained by Eddi et al. [Phys. Rev. Lett. 102, 240401 (2009)] in 2009 who studied the interaction between a drop propelled by its own generated wave field and a submarine obstacle. It has been shown that this wave particle entity can overcome barrier of potential, suggesting the existence of a ”macroscopic tunnel effect”. We show that the effect of self-propulsion is sufficiently enough to generate crossing of high energy barrier. By assuming a random distribution of initial angles, we define a probability to cross the barrier of potential that matches with the data obtained by Eddi et al.. This probability appears similar to the one encountered in statistical physics for Hamiltonian systems i.e. a Boltzmann exponential law.”

Hubert, M., Labousse, M., & Perrard, S. (2017). Self-propulsion with random initial conditions: how to cross an energy barrier?. arXiv preprint arXiv:1701.01937.

Click to access 1701.01937.pdf

https://www.researchgate.nethttps://www.researchgate.net/profile/Matthieu_Labousse/publication/317945959_Self-propulsion_and_crossing_statistics_under_random_initial_conditions/links/59632e4f458515a3575449d5/Self-propulsion-and-crossing-statistics-under-random-initial-conditions.pdf

Dubertrand, R., Hubert, M., Schlagheck, P., Vandewalle, N., Bastin, T., & Martin, J. (2016). Scattering theory of walking droplets in the presence of obstacles. arXiv preprint arXiv:1605.02370.

We aim to describe a droplet bouncing on a vibrating bath. Due to Faraday instability a surface wave is created at each bounce and serves as a pilot wave of the droplet. This leads to so called walking droplets or walkers. Since the seminal experiment by Couder et al [Phys. Rev. Lett. 97, 154101 (2006)] there have been many attempts to accurately reproduce the experimental results. Here we present a simple and highly versatile model inspired from quantum mechanics. We propose to describe the trajectories of a walker using a Green function approach. The Green function is related to Helmholtz equation with Neumann boundary conditions on the
obstacle(s) and outgoing conditions at infinity. For a single slit geometry our model is exactly solvable and reproduces some general features observed experimentally. It
stands for a promising.

http://arxiv.org/pdf/1605.02370.pdf

Filoux, B., Hubert, M., Schlagheck, P., & Vandewalle, N. (2015). Waveguides for walking droplets. arXiv preprint arXiv:1507.08228.

When gently placing a droplet onto a vertically vibrated bath, a drop can bounce permanently. Upon increasing the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well dened speed. We investigate the connement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that 1d connement is optimal for narrow channels. We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels.

http://arxiv.org/pdf/1507.08228.pdf

Filoux, B., Hubert, M., & Vandewalle, N. (2015). Strings of droplets propelled by coherent waves. arXiv preprint arXiv:1504.00484.

Bouncing walking droplets possess fascinating properties due to their peculiar wave/particle interaction. In order to study such walkers in a 1d system, we considered the case of a few droplets in an annular cavity. We show that, in this geometry, they spontaneously form a string of synchronized bouncing droplets that share a common coherent wave propelling the group at a speed faster
than single walkers. The formation of this coherent wave and the collective droplet behaviors are captured by a model, which sheds a new light on droplet/wave interactions.

http://arxiv.org/pdf/1504.00484.pdf