A new kind of simulation using Smoothed particle hydrodynamics by Diego Molteni, Università degli studi di Palermo, Dipartimento di Fisica e Chimic

Carmigniani, R., Lapointe, S., Symon, S., & McKeon, B. J. (2013). Influence of a local change of depth on the behavior of bouncing oil drops. arXiv preprint arXiv:1310.2662.

http://arxiv.org/pdf/1310.2662.pdf

Full (Subscription required) : http://www.sciencedirect.com/science/article/pii/S0894177713003038

From caltech Mc Keon Research Group : http://www.mckeon.caltech.edu/publications/journal.html

Abstract :

The work of Couder et al [1] (see also Bush et al [3, 4]) inspired consideration of the impact of a submerged obstacle, providing a local change of depth, on the behavior of oil drops in the bouncing regime. In the linked videos, we recreate some of their results for a drop bouncing on a uniform depth bath of the same liquid undergoing vertical oscillations just below the conditions for Faraday instability, and show a range of new behaviors associated with change of depth.

This article accompanies a uid dynamics video entered into the Gallery of Fluid Motion of the 66th Annual Meeting of the APS Division of Fluid Dynamics.

And a very interesting video showing the influence of depth on the trajectory :

Source : http://arxiv.org/src/1310.2662v1/anc/V102356_InfluenceLocalChangeDepth_BouncingDrop.mp4

Chu, H. Y., & Fei, H. T. (2014). Vortex-mediated bouncing drops on an oscillating liquid. Physical Review E, 89(6), 063011

 http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.063011 (Subsrciption required)

Stunning Vizualisization of undersurface flows

Abstract :

We have investigated the behavior of bouncing drops on a liquid surface by using particle image velocimetry analysis. A drop on an oscillating liquid surface is observed to not coalesce with the liquid and to travel along the surface if the oscillation is strong enough. A streaming vortex pair, induced by the alternatively distorted liquid surface, shows up below a bouncing drop. The time-averaged flow fields of the vortices are measured. In our quasi-one-dimensional setup, there are three stable distances for the drops, which can be characterized by the Faraday wavelength. The interactions of the vortex-mediated bouncing drops are deduced from the streamlines in the liquid bulk. We further show that a three-dimensional vortex ring is induced by a bouncing drop in a square cell.

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 ?

Faraday instability in a a square container not very well tuned : it has 4 quadrants :
– upper left : a crystal-like pattern
– upper right and lower left : linear pattern
– lower left : below faraday thresold (with a droplet)

Andersen, A., Madsen, J., Reichelt, C., Ahl, S. R., Lautrup, B., Ellegaard, C., … & Bohr, T. (2014). Comment on Y. Couder and E. Fort:” Single-Particle Diffraction and Interference at a Macroscopic Scale”, Phys. Rev. Lett.(2006).arXiv preprint arXiv:1405.0466.

Where a danish team argue that Couder’sDouble Slit Experiment reported in  Single-Particle Diffraction and Interference at a Macroscopic Scale   is not convincing.

They tried to replicate the experiment but they did not manage.

Plus : a quick report of a numerical experimentation of Schrödinger equation with a “”walker-like”  source term

Abstract :

In a paper from 2006, Couder and Fort [1] describe a version of the famous double slit experiment performed with drops bouncing on a vibrated fluid surface, where interference in the particle statistics is found even though it is possible to determine unambiguously which slit the “walking” drop passes. It is one of the first papers in an impressive series, showing that such walking drops closely resemble de Broglie waves and can reproduce typical quantum phenomena like tunneling and quantized states [2–13]. The double slit experiment is, however, a more stringent test of quantum mechanics, because it relies upon superposition and phase coherence. In the present comment we first point out that the experimental data presented in [1] are not convincing, and secondly we argue that it is not possible in general to capture quantum mechanical results in a system, where the trajectory of the particle is well-defined.

http://arxiv.org/pdf/1405.0466.pdf

Keywords : Madelung-Bohm equation

Oza, A. U., Harris, D. M., Rosales, R. R., & Bush, J. W. (2014). Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization. Journal of Fluid Mechanics, 744, 404-429.

We present the results of a theoretical investigation of droplets walking on a
rotating vibrating fluid bath. The droplet’s trajectory is described in terms of an
integro-differential equation that incorporates the influence of its propulsive wave
force. Predictions for the dependence of the orbital radius on the bath’s rotation
rate compare favourably with experimental data and capture the progression from
continuous to quantized orbits as the vibrational acceleration is increased. The orbital
quantization is rationalized by assessing the stability of the orbital solutions, and may
be understood as resulting directly from the dynamic constraint imposed on the drop
by its monochromatic guiding wave. The stability analysis also predicts the existence
of wobbling orbital states reported in recent experiments, and the absence of stable
orbits in the limit of large vibrational forcing

http://math.mit.edu/~auoza/JFM_2.pdf

Perrard, S., Labousse, M., Miskin, M., Fort, E., & Couder, Y. (2014). Self-organization into quantized eigenstates of a classical wave-driven particle.Nature communications, 5.

A growing number of dynamical situations involve the coupling of particles or singularities with physical waves. In principle these situations are very far from the wave particle duality at quantum scale where the wave is probabilistic by nature. Yet some dual characteristics were observed in a system where a macroscopic droplet is guided by a pilot wave it generates. Here we investigate the behaviour of these entities when confined in a two-dimensional harmonic potential well. A discrete set of stable orbits is observed, in the shape of successive generalized Cassinian-like curves (circles, ovals, lemniscates, trefoils and so on). Along these specific trajectories, the droplet motion is characterized by a double quantization of the orbit spatial extent and of the angular momentum. We show that these trajectories are intertwined with the dynamical build-up of central wave-field modes. These dual self-organized modes form a basis of eigenstates on which more complex motions are naturally decomposed.

http://www.nature.com/ncomms/2014/140130/ncomms4219/full/ncomms4219.html

http://arxiv.org/ftp/arxiv/papers/1402/1402.1423.pdf

Quantization of trajectories of a dotwave in a harmonic potential

Even if the ear cannot detect any transition on this one, it might give somebody … ideas ?

( Sound is the derivative of the sum of all field values at the center )

Because we like it 🙂

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

Grössing, G., Fussy, S., Pascasio, J. M., & Schwabl, H. (2014, April). Relational causality and classical probability: Grounding quantum phenomenology in a superclassical theory. In Journal of Physics: Conference Series (Vol. 504, No. 1, p. 012006). IOP Publishing.

Abstract. : By introducing the concepts of \superclassicality” and \relational causality”, it is shown here that the velocity eld emerging from an n-slit system can be calculated as an
average classical velocity eld with suitable weightings per channel. No deviation from classical probability theory is necessary in order to arrive at the resulting probability distributions.
In addition, we can directly show that when translating the thus obtained expression for said velocity eld into a more familiar quantum language, one immediately derives the basic
postulate of the de Broglie-Bohm theory, i.e. the guidance equation, and, as a corollary, the exact expression for the quantum mechanical probability density current. Some other direct
consequences of this result will be discussed, such as an explanation of Born’s rule and Sorkin’s first and higher order sum rules, respectively.

http://iopscience.iop.org/1742-6596/504/1/012006/pdf/1742-6596_504_1_012006.pdf

classical probability theory

n-slit system

guidance equation

Analysis of currrent state of the art modelling

Reflexions in a 1D Cavity

Computer simulations

(proceedings of RIO 2014  workshop)

http://www.personal.psu.edu/alm24/IMPA/talks/IMPANachbin.pdf

An interesting (almost) state of the art review with historical perspectives and some  (negative) nobel prizes insights.

http://www.simonsfoundation.org/quanta/20140624-fluid-tests-hint-at-concrete-quantum-reality/

Shirokoff, D. (2013). Bouncing droplets on a billiard table. Chaos: An Interdisciplinary Journal of Nonlinear Science, 23(1), 013115.

http://arxiv.org/pdf/1203.2204.pdf

Discrete numerical simulation

Attractor ets

In this PDF, you will find the equation of motion used in the numerical simulation, based on the work of BUSH et al. from the MIT team.

DotWaveSimulation

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

Wave particle in a 1-D box, tracking and statistics