[ 72 - Cavities eigenstates ]
The final strech of this presentation now : a pot-pourri, ie a mix of pictures and videos showing several interesting effect, starting with these pictures of stationnary waves inside cavities : so called eigenstates :)

16 hours ago

[ 72 - Cavities "eigenstates" ]
The final strech of this presentation now : a "pot-pourri", ie a mix of pictures and videos showing several interesting effect, starting with these pictures of stationnary waves inside cavities : so called "eigenstates" 🙂
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2 days ago

[ 68-71 Bibliorgasmy (2/2) ]
- Instantaneous time mirrors
- self-organization into quantized eigenstates
- "superposition" and tunable Multi-stability
- parameters analogy
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1 week ago

[ 64-67 Bibliorgasmy (1/2) ]
- Experimental Auto-orbits
- Do-it-Not-Yourself : the MIT Apparatus
- Full Hydrodynamical Model : Navier-Stokes inside
- Lattices of bouncing droplets
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[ 63 - Memory induced calligraphy ]

2 weeks ago

[ 63 - Memory induced calligraphy ] Because these trajectories are pretty, aren't they ? <3 🙂
A dotwave walker is simulated with a very simple discrete code (no fancy integration scheme)
The bouncing in a square box is computed with a simple specular reflection.
It is like a pool table seen from atop. But the surface of the table has a wavelike memory, so that the walker is interacting with its own past and self interfering.
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So Great that You've been able to Achieve that "with a very simple discret code (no fancy integration scheme)". It means for us that You are Closer to find an Universal Code, Algorithm, To Generate Everything by "AB INITIO" programing, very as I have advised You on a previous comment, if I remember well 🙂 If so, if You Achieve that, it could mean that You got in the same time, the "INITIO PRINCIPLES OF THE PHYSICAL FUNDAMENTAL SUBSTRATE" (how ever we call it: "Dirac's Sea", "Quantum Foam" or "Aether" 😉 ). Very Well Done for this MOST Interesting Progress in your Researches 🙂 👍👍👍👍

[ 61 - Collision - Attraction - Bound state]

2 weeks ago

[ 61 - Collision - Attraction - Bound state] Here we visualize only the dots. They are trapped on a pool table...well..a pool table with memory ... 😉
And as usual, they interact at a distance through their associated wave field.
This brings up a stable 2-bodies attractor.
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[ 60 - a simple discrete model]

2 weeks ago

[ 60 - a simple discrete model] The walker simulation can also be written in a more simple fashion, without fancy integration scheme. Some of the main features of walkers are reproduced :
- Memory of the wave field leading to self-interference
- Shape of the wave field associated with a walker
- Wave mediated interactions between two walkers

Unlike the previous "surfing droplet" simulation, this simple time-step Euler integration scheme is not suitable for simulating motion in a potential (e.g. harmonic) because it might diverge. Also, the speed of the walker is not constant.

But it can be used in free motion, or in a box where the boundaries are materialized by a simple specular reflection.

And the code runs much faster 😉
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Can you link the momentum and angular momentum exchange to the Moire patterns visible at the moment of interaction?

[  59 - Intermittences ]

3 weeks ago

[ 59 - Intermittences ] In this simulation, the walker is placed in a harmonic potential, ie linked to the center via a spring, and has an initial velocity tangential to a circle.

The memory-induced self interference creates random inversion of its spin.
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[ 58 - Qubit Hunting ]

3 weeks ago

[ 58 - Qubit Hunting ] In this simulation, the dotwave is trapped in a harmonic potential, in a 1D Channel.

We want to see if the wave field oscillates between several well defined pattern that occur one after the other.

"Superposition as a succession of metastable attractors" ?
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[57 - 2 dotwaves in a box ]

3 weeks ago

[57 - 2 dotwaves in a box ]
The simulation can be extended and accommodate 2 walkers.
Each walker interacts with its own past AND with the other walker's trajectory and past.
Here, 2 walkers are placed in a square potential well with a repulsive force at the boundary (no wave reflections)
Only the wave field is represented. Still, it is easy to imagine where the dots are located.
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[56 -  Sonification of wave field ]

3 weeks ago

[56 - Sonification of wave field ]
SOUND ON for this video where you will hear the "quantum drum" ( Clown Inside )

The dot is moving in a harmonic potential (tied to a spring located at the center of the image)

The field is spatially sampled and its variations are summed at a certain location above the 2D surface, simulating the postion of a microphone above the vibrating plate.

The sound is generated from its derivative, since the ear is sensitive to the derivative of the pressure field.
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[55 - Harmonic potential ] Another qualitative comparison between experimental and numerical

3 weeks ago

[55 - Harmonic potential ] Another qualitative comparison between experimental and numerical ... See MoreSee Less

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1 month ago

[ 54 - Harmonic Potential ] Here, we can compare qualitatively the experimental result and the simulation of a walking droplet in a harmonic potential, that is : "attached to a spring which is tied to the center of the apparatus" (a central attractive force)

The experimental trajectories were recorded by the Paris Team with a ferromagnetic droplet in a magnetic field (See slide [39] )
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[ 53 free motion ]

1 month ago

[ 53 free motion ] To qualify this model, let's compare : the wake and the "wings" look quite alike .... ... See MoreSee Less

[ 52 - Numericall ] Lets now continue with some numerical models based on the so called strobocopic approximation :  in this model, the dynamical vertical of the droplet is not taken care of.

The dot is surfing on the wave and periodically emits in its wake a circular wave that decays slowly (the speed of decay depends on the memory of the bath)

Please note : this model is non local (hence non physical ?) since the circular wave that is emitted periodically by the dot  propagates instantly in the whole space.

1 month ago

[ 52 - Numericall ] Let's now continue with some numerical models based on the so called strobocopic approximation : in this model, the dynamical vertical of the droplet is not taken care of.

The dot is surfing on the wave and periodically emits in its wake a circular wave that decays slowly (the speed of decay depends on the memory of the bath)

Please note : this model is non local (hence non physical ?) since the circular wave that is emitted periodically by the dot "propagates" instantly in the whole space.
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2 months ago

[51 - "entanglement" ] The idea is the following :
- 2 resonant cavities each containing a dot as in [49]
- Cavities can communicate trough waves but the dot cannot go through
- In each cavity, the dot would follow a "random" trajectory with a ststistical build-up like in [49]

Then, how would the two "random-but-with-a-wavelike-statistics" trajectories correlate ???
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So Great that You are Progressing So Much in your simulations and experiments 🙂 Just would like to remember You that in the Bell experiment, the pair of particles are in OPPOSITE PHASES due of one been the ANTIPARTICLE of the other. So I guess that MORE YOU WILL GO TOWARDS THIS CONFIGURATION, MORE THE PROBABLE TRUE PHENOMENON SHOULD BECOME OBVIOUS. Also, the experiment is about the SEPARATION of the pair from a centre, which implies a SYNCHRONISATION OF PHASES (even if in opposition) which TRIGGERED THE READING at the sensors in both extremities 😉 Hoping it can Help ^_^ Regards.

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2 months ago

[50 - "Entanglement" ] I pursued the kind of effects shown beautifully in the previous MIT Video : Wave mediated interaction of dotWaves trapped in separate cavities.

My approach was to use two Quasi-1D resonant cavities linked by a channel. Through the channel, only the wave can pass, but not the dot.

Please note: resonant cavities means here : the level of liquid is below the boundaries. (Unlike "Spin lattice of walking droplet")
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Video image

2 months ago

Meanwhile, let's take a break and admire this beautifull work from the MIT Magic droplet team

www.youtube.com/watch?v=-2yYgfaU6IkSpin lattices of walking droplets Pedro Saenz, MIT Pucci Giuseppe , MIT Alexis Goujon, MIT Tudor Cristea-Platon, MIT Jörn Dunkel, MIT John Bush, MIT DOI: htt...
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Louis de Broglie was right!!!

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3 months ago

[ 49 - Self-interference in 1D box ... again ]

Random Motion but wavelike statistics --> 3 peaks

(With wave reflections at the boundaries)
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Now that's great! Does the pattern depend on the box length?

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3 months ago

[ 48 - Memory-induced Self Interference ]

Here we see the influence of memory on self-interference in a quasi-1D cavity.

The stronger we vibrate of the bath (While staying below the Faraday Instability Thresold)
-->The closer we are to the Faraday Thresold
-->The higher the self-interference effect
--> The more noticeable will be the statistical pattern on the position of the dot

NB : please notice the shape of the standing wave that is created from sec 20 and onwards
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3 months ago

[47 - Quasi 1D - particle Tracking ]

Another manifestation of self-interference in a confined geometry with wave reflections at the boundaries.

The cavity is a channel in which the dot can only move along a straight line (With a little transverse motion, hence the "quasi" prefix)

The motion of the dot seems random, but when you look at it statistically, you get a position distribution with peaks.
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Are these peaks reproducible? The strange thing is that the pattern is asymmetric.

[ 46 - Quasi-1D DIY Setup ]

We can do the same kind of experiment in a mono-dimensional channel.

Please notice the high-level sophistication of the experimental setup 😂🤣😅

3 months ago

[ 46 - Quasi-1D DIY Setup ]

We can do the same kind of experiment in a mono-dimensional channel.

Please notice the high-level sophistication of the experimental setup 😂🤣😅
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[ 45 - square cavity with wave reflections ]

3 months ago

[ 45 - square cavity with wave reflections ]

In this case, the walls around the square cavity emerge above the oil level. So, Waves are reflected by the boundary.

The motion of the dot seems random but it likes to dwell in some preferential places. This can be seen by the naked eye on the video, and this can be measured with particle tracking : the droplet trajectory and its position statistics show that a statistical pattern emerges from the random motion.

We can compare this behaviour with the previous slide [44] : there, without wave reflections at the boundary, no statistical pattern emerges.

So we may think that the statistical pattern build up is driven by the reflections of the waves at the cavity boundaries.
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3 months ago

[ 44 - Square cavity without reflections ]

One image is worth a thousand words, they say ...
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[ 43 - particle tracking ]

3 months ago

[ 43 - particle tracking ] The goal of the experiment is to track the dot's motion while it is trapped in the square cavity, so as to be able to compute statistics on its position and velocity .... ... See MoreSee Less

[42 - Self-interference - Memory induced chaos ]

3 months ago

[42 - Self-interference - Memory induced chaos ]

So a walker can walk on its own footsteps and thus interfere with its own past. I like to call this phenomenon self interference.

We have seen this in a confined geometry like a circular corral. I reproduced this in a square corral.

Please note that in this video the waves do not reflect on the border of the square cavity : there is a "beach" on each side, with a shallow depth of oil, on top of which the waves are vanishing.
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[ 40-41 Quantization In a Harmonic potential ] The central force is attracting the walker towards the center. So, if the walker has an initial velocity, it will reach a circular orbit, which radius depends on the initial velocity.

But if the memory of the bath is high enough, it will have a significant influence because the walker will walk on its own footsteps while going round the circle trajectory. And it will reach a place where the waves created a few time ago are still present. 

These waves, maintained from the past thanks to the memory of the bath, will interact with the position of the walker. 

The resultant memory-induced effect is that only certain radius can be observed if the memory of the bath is sufficient.

That is what can be seen on chart [40] : 
- On the X axis is the memory the bath
- On the Y axis, the radius of trajectory observed

--> When memory is increased, only certain radius can be observed.

But we can go further : by varying the stiffness of the spring, we can create different kind of trajectories for the walker : circular but also lemniscate (trefoil-like) ...

If the Memory of the system is high enough, only certain trajectory are allowed : radius and angular momentum (that is the speed at which the walker is going round) are both quantified. [42]

--> Double quantization in a central harmonic potentialImage attachment

3 months ago

[ 40-41 Quantization In a Harmonic potential ] The central force is attracting the walker towards the center. So, if the walker has an initial velocity, it will reach a circular orbit, which radius depends on the initial velocity.

But if the memory of the bath is high enough, it will have a significant influence because the walker will walk on its own footsteps while going round the circle trajectory. And it will reach a place where the waves created a few time ago are still present.

These waves, maintained from the past thanks to the memory of the bath, will interact with the position of the walker.

The resultant memory-induced effect is that only certain radius can be observed if the memory of the bath is sufficient.

That is what can be seen on chart [40] :
- On the X axis is the memory the bath
- On the Y axis, the radius of trajectory observed

--> When memory is increased, only certain radius can be observed.

But we can go further : by varying the stiffness of the spring, we can create different kind of trajectories for the walker : circular but also lemniscate ("trefoil-like") ...

If the Memory of the system is high enough, only certain trajectory are allowed : radius and angular momentum (that is the speed at which the walker is going round) are both quantified. [42]

--> Double quantization in a central harmonic potential
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[39 - the ferrofluid experiment ]
And this is another very extraordinary version of the walker experiment. I was luck enough to go in Paris and visit Yves Couder’s lab. He was with his PhD student Stéphane PERRARD, who was finishing his PhD by that time.

I call tis experiment a “Tour de force” because they manage to attach a spring to the walker.

Of course, not a real spring : they have used a ferrofluid and a magnetic field to place the walker in a harmonic potential : at any moment, the walker is attracted towards the center of the apparatus with a force proportional to the distance to the center.

You can see the apparatus with two big coils and a small moving magnet for tuning the strength of the magnetic field.

That is, the stiffness of the virtual spring attached to the walker can even be tuned.

3 months ago

[39 - the ferrofluid experiment ]
And this is another very extraordinary version of the walker experiment. I was luck enough to go in Paris and visit Yves Couder’s lab. He was with his PhD student Stéphane PERRARD, who was finishing his PhD by that time.

I call tis experiment a “Tour de force” because they manage to attach a spring to the walker.

Of course, not a real spring : they have used a ferrofluid and a magnetic field to place the walker in a harmonic potential : at any moment, the walker is attracted towards the center of the apparatus with a force proportional to the distance to the center.

You can see the apparatus with two big coils and a small moving magnet for tuning the strength of the magnetic field.

That is, the stiffness of the virtual spring attached to the walker can even be tuned.
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[38 - Circular corral DIY ]

3 months ago

[38 - Circular corral DIY ] I have reproduced this experiment with a circular cavity : but in my case, the boundaries of the circular cavity were exceeding the level of oil in the corral.

The difference in the boundary conditions have great importance because the waves do not behave the same. In a case they reflect at the boundary, on the other case they are simply vanishing on the region with shallow depth.

Nevertheless, I found a similar result with circular – like region where the walker was more likely to be found.

( Slides 42-45 will show a DIY reproduction of this experiment in a square cavity, showing the influence of boundary conditions )
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[37 - Circular corral ] Now :  one of the most intriguing and well know experiment, which was built together by the French and American team at Paris and MIT.

Put a walker in a circular cavity : it will follow a random trajectory inside the circular corral. But if you follow it long enough, you will notice that the walker is most likely to be found in specific region of the circular corral. This is what is depicted in the right picture : a statistical patterns builds up even though the droplet motion seems to be random

By the words of Professor Bush himself : “The observed statistical behavior is thus roughly analogous to that reported in the quantum corral experiments (Crommie et al. 1993) in which the density of electrons trapped on a copper substrate was found to have a wavelike pattern with the de Broglie wavelength,, and a form prescribed by the corral shape “

3 months ago

[37 - Circular corral ] Now : one of the most intriguing and well know experiment, which was built together by the French and American team at Paris and MIT.

Put a walker in a circular cavity : it will follow a random trajectory inside the circular corral. But if you follow it long enough, you will notice that the walker is most likely to be found in specific region of the circular corral. This is what is depicted in the right picture : a statistical patterns builds up even though the droplet motion seems to be random

By the words of Professor Bush himself : “The observed statistical behavior is thus roughly analogous to that reported in the quantum corral experiments (Crommie et al. 1993) in which the density of electrons trapped on a copper substrate was found to have a wavelike pattern with the de Broglie wavelength,, and a form prescribed by the corral shape “
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[36 - Orbital Quantization induced by path memory]

If a walker is submitted to Coriolis Forces, by rotating the vibrating bath, its trajectory is circular. 

But if the memory of the bath is strong enough, only certain radii are allowed.

This is a memory-induced quantization of trajectories

3 months ago

[36 - Orbital Quantization induced by path memory]

If a walker is submitted to Coriolis Forces, by rotating the vibrating bath, its trajectory is circular.

But if the memory of the bath is strong enough, only certain radii are allowed.

This is a memory-induced quantization of trajectories
... See MoreSee Less

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