[26 - non-locality ] So , the trajectory of a walker does not only depend on its position and speed at a given time, but it also depends on its history. That is what we have called path memory.

This is a kind of temporal non locality : we need to consider the whole past trajectory if we want to calculate the future trajectory of the walker.

It can be shown that this is equivalent to a spatial non locality : without knowledge of the past trajectory of the walker, we can still calculate its future trajectory  

We need to know its position and speed of course, but also, on top of that, we need to have an exact and full knowledge of the full wave field at  a given time t.

This is a spatial non-locality.

2 days ago

[26 - non-locality ] So , the trajectory of a walker does not only depend on its position and speed at a given time, but it also depends on its history. That is what we have called path memory.

This is a kind of temporal non locality : we need to consider the whole past trajectory if we want to calculate the future trajectory of the walker.

It can be shown that this is equivalent to a spatial non locality : without knowledge of the past trajectory of the walker, we can still calculate its future trajectory

We need to know its position and speed of course, but also, on top of that, we need to have an exact and full knowledge of the full wave field at a given time t.

This is a spatial non-locality.
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[25 - Wave Equation ] : The wave equation describes how the wave fields evolves through time.

The wave field is the sum of the fields created at all previous bounces of the dot.

Each of these is a circular standing wave (Mathematician model this as a Bessel Function J0 ) that is slowly damped.

The damping parameter is the memory of the system : the less damping, the more memory.

From this, we can see that the evolution of the wave field depends on the whole history of the trajectory of the walker.

3 days ago

[25 - Wave Equation ] : The wave equation describes how the wave fields evolves through time.

The wave field is the sum of the fields created at all previous bounces of the dot.

Each of these is a circular standing wave (Mathematician model this as a Bessel Function J0 ) that is slowly damped.

The damping parameter is the memory of the system : the less damping, the more memory.

From this, we can see that the evolution of the wave field depends on the whole history of the trajectory of the walker.
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[24 - dot Equation ]And now for some mathemagics !

The equation of motion of a walker is split in two part : one for the dot and one for the wave.

The dot follows a classical Newtonian equation mass times acceleration equals the sum of force applied to the dot.

Among those forces, there is what we call a Wave force : the force applied by the wave to the droplet at the bounce. That force is proportional to the slope of the wave (What mathematicians call the gradient) , and thus, it depends on the local shape of the wave field at the position of the dot.

3 days ago

[24 - dot Equation ]And now for some mathemagics !

The equation of motion of a walker is split in two part : one for the dot and one for the wave.

The dot follows a classical Newtonian equation mass times acceleration equals the sum of force applied to the dot.

Among those forces, there is what we call a Wave force : the force applied by the wave to the droplet at the bounce. That force is proportional to the slope of the wave (What mathematicians call the gradient) , and thus, it depends on the local shape of the wave field at the position of the dot.
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[23 - Path Memory ]

6 days ago

[23 - Path Memory ] Add a droplet on top of this bath with memory, and you will get : path memory.

Each time the droplet touches the bath, it creates a circular standing wave that will continue to oscillate a certain time.

This will repeat 30 times per second, so that the field created by the droplet all over the bath is the superposition of the fields created at each bounce.

In the wake of its path, the walker creates a trail, made of a string of localized circular standing waves, that continue to oscillate as long as the memory of the bath allows (See 22 - bath memory)

All these waves interfere and that interference pattern can be observed in the wake of the walker.
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[22 - Bath Memory]

7 days ago

[22 - Bath Memory]

In 2011, 6 years after the initial Discovery, a new important step was made in the study of walkers. The Paris Team showed that the bath on which the droplet were moving had a memory.

Oh a strange kind of memory : a Wave memory !

Look at the surface of the bath, when it is vibrated below the instability threshold : its surface is still. Lets make a small perturbation with a tooth pick : this perturbation will create a local circular standing wave, that will take a certain time to dissipate.

That time is the amount of Memory of the system : the bath memory.

We can tune it by adjusting the vibration amplitude closer and closer to the instability threshold without exceeding it.
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1 week ago

[21 - Bound state ] Here we can see two different views of the same phenomenon : the bound state of two Walkers, through a wave mediated interaction.
- With a visible vertical dynamics : "boucing walkers"
- With a filtered vertical dynamics : "levitating walkers"
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1 week ago

[20 - Stroboscopic Effect] But the vertical dynamic of the droplet, or the study of its different ways of bouncing, is not the main interest of Walkers.
The main interest is : the association of the dot and the wave.

Lets look at this very same video [19], but we keep only frames corresponding to the times where droplets are on the top of their trajectory. Doing so, we can erase the vertical dynamic through stroboscopic effect, as with any periodic motion.

The dot vibrates vertically 30 times per second. If we take a movie at 30 images per second, we will get the impression the dot is not moving vertically : it will float .

And its associated local Faraday wave field will follow. But we will not see it vibrate.

In all videos that will come up next, we will now mostly use this stroboscopic effect.
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2 weeks ago

[19] The dot creates the wave. The wave guides the dot

Let's see very concretely how a walker is made : all you need is ...a tooth pick 😄

Dip it in the vibrating bath and remove it quickly : a droplet will form and the magic will begin.

The Wave-Particle duality of this phenomenon appears :
- Without the dot, there is no wave. The dot is creating the wave.
- Without the wave, there is no motion. The wave is guiding the dot. It is the local slop of the wave at the point of contact that is guiding the dot.

That is why walkers are called a realization of a pilot wave system.

What you can also notice here is the bounce of the droplet : it is not a single drop as you may think at first: the droplet touches the bath twice quicky, and that can only be seen with a fast camera. This one of different kind of bouciong for droplets....
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[18] The walking droplet behaviour occurs only for certain combination of the forcing (or driving) acceleration and of the droplet size

Now,  take a look a these two phase diagrams. One is from 2006 and the other from 2013 : we can see how science has made progress in between those two dates ! 
- On the horizontal axis, we have the acceleration of the vibrating bath : the forcing, or driving, acceleration.
- On the vertical y axis, the size of the droplet (Or the vibration number, which is a more elaborate adimensionnal number containing information about the droplet geometry and physical characteristics)

There is only a small portion of this parameter space which allows for the formation of a walking droplet.

2 weeks ago

[18] The walking droplet behaviour occurs only for certain combination of the forcing (or driving) acceleration and of the droplet size

Now, take a look a these two phase diagrams. One is from 2006 and the other from 2013 : we can see how science has made progress in between those two dates !
- On the horizontal axis, we have the acceleration of the vibrating bath : the forcing, or driving, acceleration.
- On the vertical y axis, the size of the droplet (Or the vibration number, which is a more elaborate adimensionnal number containing information about the droplet geometry and physical characteristics)

There is only a small portion of this parameter space which allows for the formation of a walking droplet.
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2 weeks ago

[17] The interesting part now !

Under certain conditions, the bouncing droplet will land on top of a wave created a previous impact.

Because it cannot always land exactly on top of the central peak, it will at some time land a little bit on the side.

And on the side, there is a slope.The droplet is then bouncing on this slope. That is what gives it momentum to move forward.
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Here we take closer look at the transition from bouncing to walking.

At first the droplet is bouncing at the same period as the bath. The more we shake the bath, the more high the droplet is bouncing and at some point the period of the droplet is doubling. The bath moves twice as the droplet goes one bouncing cycle.

So the drop frequency and the Faraday Wave Frequency become the same (Remember Faraday wave frequency is also the double of the forcing frequency)  : that is why the drop and the bath now can interact in a propulsive way....

2 weeks ago

Here we take closer look at the transition from bouncing to walking.

At first the droplet is bouncing at the same period as the bath. The more we shake the bath, the more high the droplet is bouncing and at some point the period of the droplet is doubling. The bath moves twice as the droplet goes one bouncing cycle.

So the drop frequency and the Faraday Wave Frequency become the same (Remember Faraday wave frequency is also the double of the forcing frequency) : that is why the drop and the bath now can interact in a propulsive way....
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2 weeks ago

Now, let’s get back to our droplet : we shake the oil bath, but just a little bit. That is, below the instability threshold. The free surface of the bath is still.

Then we make a droplet of oil, and we deposit it on the surface of the bath. It will not coalesce. It will not mix with the oil bath below.

That is because there is a thin film of air between the oil bath and the droplet, which acts like a trampoline on which the droplet bounces. That layer of air reconstitutes itself between each rebound, and prevents contact between the oil bath and the droplet.

Please notice that, while the drop is bouncing, it creates a local Faraday Wave Pattern around the point of impact, which has a circular shape.
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2 weeks ago

In that case, the free surface does not present any structure any more, as can be seen here. It's just like if the crystal structure seen previously starts melting

And, you might ask, what happens if you shake even more….well… you’ve got oil all over your face 😉

NEXT, we'll start the real droplet magick 🤹
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If you shake with more force, the structure of the Faraday waves starts « melting » and the well ordered structure disappears.

3 weeks ago

If you shake with more force, the structure of the Faraday waves starts « melting » and the well ordered structure disappears. ... See MoreSee Less

The structure can take different forms, for example hexagonal, like here at the bottom left.

Please notice that the Faraday Wave are oscillating in time twice more slowly than the vibrating plate. This means that the frequency of the Faraday Wave is half the forcing frequency.

I usually vibrate the plate at a forcing frequency of 60 Hz. So the Faraday Wave has a frequency of 30 Hz.

3 weeks ago

The structure can take different forms, for example hexagonal, like here at the bottom left.

Please notice that the Faraday Wave are oscillating in time twice more slowly than the vibrating plate. This means that the frequency of the Faraday Wave is half the forcing frequency.

I usually vibrate the plate at a forcing frequency of 60 Hz. So the Faraday Wave has a frequency of 30 Hz.
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3 weeks ago

That means : if the acceleration of the oil bath is superior to 5g, the free surface is not still anymore. A pattern appears, which can have different shapes, depending on the shape of the container itself and on the vibrating amplitude.

The Faraday Waves have a Wavelength of approximately 5 mm

If you shake just a little bit above the threshold, the Faraday Wave presents a crystal like structure well ordered.

This is an example of what happens far from the boundary of the container : the faraday wave pattern has a square crystal-like structure.
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Now, what happens when you vibrate the plate supporting the oil.

Nothing happens if you vibrates slowly : the free surface of the liquid stands still.

If you add some amplitude, at a certain point, an instability of the free surface appears : it is called the Faraday Instability. With the oil I have been using, the threshold at which this instability appears is approximately at an acceleration rate of  5g,

3 weeks ago

Now, what happens when you vibrate the plate supporting the oil.

Nothing happens if you vibrates slowly : the free surface of the liquid stands still.

If you add some amplitude, at a certain point, an instability of the free surface appears : it is called the Faraday Instability. With the oil I have been using, the threshold at which this instability appears is approximately at an acceleration rate of 5g,
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So I built my own setup  in a true DIY Fashion,  without any professional vibrating pots, semi-reflective mirrors, or high speed cameras : A tripod vibrating device made up from three loud speakers.I have called this device a Cymatron, from the greek word κῦμα Cyma meaning Wave ;) 

There is a removable transparent plate on top, on which the container for oil is placed.
Through transparency, the experimental cell can be shot either from top, or down, thanks to a mirror placed at 45 degrees below the apparatus.
 I have used a cheap and simple modified Go pro camera capable of shooting at 240 frames per second. This is just  enough for analyzing the vertical dynamics of the droplets.

3 weeks ago

So I built my own setup in a true DIY Fashion, without any professional vibrating pots, semi-reflective mirrors, or high speed cameras : A tripod vibrating device made up from three loud speakers.I have called this device a Cymatron, from the greek word κῦμα Cyma meaning Wave 😉

There is a removable transparent plate on top, on which the container for oil is placed.
Through transparency, the experimental cell can be shot either from top, or down, thanks to a mirror placed at 45 degrees below the apparatus.
I have used a cheap and simple modified Go pro camera capable of shooting at 240 frames per second. This is just enough for analyzing the vertical dynamics of the droplets.
... See MoreSee Less

 

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Well, tristan gilet published recently a paper on multifrequency excitation. About the tripod, it better be equilibrated or it would probably break....

So you have three speakers that produce the vibrations. I assume they are connected to the same source of the electro-acoustic wave therefore they are in-sync. I wonder what would happen if you set different frequencies, or same frequency with phase shift on either speaker (and how would that influence the droplet behavior).

Here you can see a basic DIY setup for creating a bouncing, or dancing, or walking droplet, which I brought as a demo for a conference I gave 2015

There is a loud Speaker filled with oil, a light system, and a camera. That is enough to produce a simple and nice image !

The limitation of this setup is that you cannot easily view vertically from top : you have to shoot from the side.

Also, you cannot easily place and control obstacles in the domain where droplets are walking, and yet this can be very interesting for further investigations...

3 weeks ago

Here you can see a basic DIY setup for creating a bouncing, or dancing, or walking droplet, which I brought as a demo for a conference I gave 2015

There is a loud Speaker filled with oil, a light system, and a camera. That is enough to produce a simple and nice image !

The limitation of this setup is that you cannot easily view vertically from top : you have to shoot from the side.

Also, you cannot easily place and control obstacles in the domain where droplets are walking, and yet this can be very interesting for further investigations...
... See MoreSee Less

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3 weeks ago

[Audio On] The droplet will start bouncing on top of the bath, at the very same frequency as the speaker. And it will not coalesce with the bath. It will not mix.
Here, for fun, I have sent a mix of frequency to the speaker : the bouncing droplet then becomes a dancing droplet 😉

It can be seen clearly that the droplet creates a local circular standing wave, around its point of impact.
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How does it work ?

Take a container. Place it on a vibrating device, like a vibrating pot or more easily use a loud speaker. Fill the container with oil. Even though several oils can work, the one which is usually used is silicon oil of viscosity 50 Centistokes (Cst)

The speaker is set to vibrate at frequency between 40 and 80 vibrations per seconds.

I usually work at 60 Hertz 

You have to make the speaker vibrate, but not too much, so that the free surface of the liquid stays still despite vibrations

Then, put a small droplet of that very same oil on top of the bath.

3 weeks ago

How does it work ?

Take a container. Place it on a vibrating device, like a vibrating pot or more easily use a loud speaker. Fill the container with oil. Even though several oils can work, the one which is usually used is silicon oil of viscosity 50 Centistokes (Cst)

The speaker is set to vibrate at frequency between 40 and 80 vibrations per seconds.

I usually work at 60 Hertz

You have to make the speaker vibrate, but not too much, so that the free surface of the liquid stays still despite vibrations

Then, put a small droplet of that very same oil on top of the bath.
... See MoreSee Less

 

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With different liquid I guess it could work, but when the droplet would eventually coalesce, and with the repetition of experiments, the bath would become "corrupted" ...

What if you use different liquids for bath and for droplet?

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4 weeks ago

For me, it all started in 2011, after I read a feature article in the French version of Scientific American at the local library.

I was amazed at what was described : Wave-Particle duality at human scale. So, it might be possible to do « quantum physics » at my workshop ?

I immediately decided to try and reproduce the experiment, and after some weeks, I found the genuine oil, put it in a loud speaker, and I was lucky enough to obtain this video.

Many interesting features can be seen :
-The association of waves with a moving particle
- Elastic collisions
- Rotation of two walkers around each others

So I decided I wanted to know more and since then, I have not stopped playing with WALKERS..a kind of unsual sunday hobby 😉
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will you tell me how you made this system?

Since then, several teams joined the research, among which : 
-The fluid dynamics laboratory of Professor John BUSH at MIT, which is a leader in the field now with the Paris Team,
-The Quandrops team in Belgium at Liège University.

Several PhD thesis have been written, and approximately a hundred authors are working on the subject.

I must also cite here Dr. Dan Harris, formerly from the MIT Team, who is now at Brown University, and who has produced many stunning photos and videos which got quite a big coverage in  Nature Magazine for example, but also on social medias.

4 weeks ago

Since then, several teams joined the research, among which :
-The fluid dynamics laboratory of Professor John BUSH at MIT, which is a leader in the field now with the Paris Team,
-The Quandrops team in Belgium at Liège University.

Several PhD thesis have been written, and approximately a hundred authors are working on the subject.

I must also cite here Dr. Dan Harris, formerly from the MIT Team, who is now at Brown University, and who has produced many stunning photos and videos which got quite a big coverage in Nature Magazine for example, but also on social medias.
... See MoreSee Less

So…when did it all start ? The first publication describing this new physical object called a walking droplet dates back September 2005, when a duo of French researchers published in Nature :
- Yves Couder : a senior and well known soft-physics researcher at École Normale Supérieure de Paris. 
- His accomplice Emmanuel Fort  : from Ecole Supérieure de Physique et Chimie Industrielle de Paris.

The story of this discovery is one of serendipity, as often. An undergraduate was studying the bouncing of liquid droplets on a vibrating bath, when he observed by chance that, under certain conditions, the droplet would become self propelled and set itself in motion.

The attention of researchers was immediately drawn to this strange phenomenon associating wave, particle and motion, and a first experiment proposing a link between walker and the quantum physics was produced, which got a certain impact :  the realization, at a macroscopic scale, of a single particle slit diffraction experiment.

4 weeks ago

So…when did it all start ? The first publication describing this new physical object called a walking droplet dates back September 2005, when a duo of French researchers published in Nature :
- Yves Couder : a senior and well known soft-physics researcher at École Normale Supérieure de Paris.
- His accomplice Emmanuel Fort : from Ecole Supérieure de Physique et Chimie Industrielle de Paris.

The story of this discovery is one of serendipity, as often. An undergraduate was studying the bouncing of liquid droplets on a vibrating bath, when he observed by chance that, under certain conditions, the droplet would become self propelled and set itself in motion.

The attention of researchers was immediately drawn to this strange phenomenon associating wave, particle and motion, and a first experiment proposing a link between walker and the quantum physics was produced, which got a certain impact : the realization, at a macroscopic scale, of a single particle slit diffraction experiment.
... See MoreSee Less

Here is the plan, 80-or-so more slides should follow

4 weeks ago

Here is the plan, 80-or-so more slides should follow ... See MoreSee Less

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4 weeks ago

"Wave particle Duality at human scale : a DIY Exploration" ... See MoreSee Less

#moogfest

5 months ago

#moogfest ... See MoreSee Less

5 months ago

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#QUANTUM_WALKERS

5 months ago

#QUANTUM_WALKERSThe Church of Space
@ PSI theater / Moogfest 2017
w/ Marc Fleury / Monsieur Fleury / Uli Sigg / Christof Veillon / Sheba Love / Bj Campbell / Liquid sky berlin and many many more
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6 months ago

Am I Wrong ? ... See MoreSee Less

 

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