On this video you will see how a walking droplet in a small 1D cavity moves “randomly” if the memory of the system is high enough (ie if the forcing is strong enough, but still below the Faraday Thresold)

A walking droplet is placed in a square box, at the onset of Faraday thresold.

The trajectory of the droplet is mapped.
In the long time limit, does a self-interference pattern appear ? what’s its shape ? How does it relate to the square cavity surface wave eigen-modes ?

In short, we try to reproduce the experiment of Bush et al, but in a square box.

First result :

A walking droplet in a square cavity shows random motion, but with time, its trajectory is building a statistic reminiscent of the resonant mode of the cavity.

This can be seen by the naked eye in this movie excerpt :

This is then confirmed with optical tracking measurment of the trajectory :

Trajectory of the walking droplet

The position distribution (~probability density) is then computed :

This is how precise my temporal resolution can be with my modified goPro and (at last) a good lens : 240 fps ( @848×480 )

Forcing freq is 60 Hz, so Faraday Freq is 30Hz, so for the usual walking mode we have 8 frame during the period of the vertical dynamic. Hence we can observe the dynamic without any strobe effect.

Question: What is the (m, n) mode of the first droplet shown in the movie ?

On this purely deterministic superfluid simulation of a dotwave in a harmonic potential ( dot attached to a spring, no viscous dissipation, D=0), the dot has successive clockwise and anti-clockwise circle-like motions, separated by intermittences with null mean angular momentum

Surfer attached to a spring moving with no viscosity

Integration of motion equation is done continuously via matlab DELAY DIFERENTIAL EQUATION (ddesd) solver

Hence, the dot “reads” continuously the value of the field

In the mean time, the dot “writes” to the field evry T_F (that is a “bounce”) : at each bounce, a local wave field represented by a Bessel JO function is created, which is then slowly damped (That is the memory Me parameter)

Interferences between the waves created by the last previous 300 bounces (THAT IS THE CUTOFF parameter) are computed at each integration step to obtain the shape of the wave and the motion of the dot.

On this purely deterministic superfluid simulation of a dotwave in a harmonic potential ( dot attached to a spring, no viscous dissipation, D=0), the dot has successive clockwise and anti-clockwise circle-like motions, separated by intermittences with null mean angular momentum

On this video, the walking droplet is confined in a small cavity (Approx. 6 to 8 times the faraday wavelength)

We observe the emergence of several normal modes of vibration of a walking droplet in a circular corral.

At first, the movement seems “random”, then, the whole wave-particle system synchronizes, and starts turning alltogether.

Differrent modes are possible, with different radius for the droplet trajectory : on this video we see a mode with the droplet on a large radius trajectory, and also a mode where the droplet is on a short radius trajectory

Its seems that thoses radius coincide with with the knots ofs thefaraday standing waves of the cavity, hence we have a quantization of the radius of the different trajectories.