Video

Thanks. "Percolation-style" is not an official name. I called the arrangement of obstacles that because it is obtained by randomly deleting points from a regular square lattice. This is similar to what is done when studying percolation, see czcams.com/play/PLAZp3rbgWLo2fNvxVGgpeR2F9K6D660fc.html

thank you!

There will soon be some simulations where the polygons stick together.

Good idea, perhaps I will try that later on.

I suspect this to be mostly numerical. When I started developing the code for this, I got much worse instabilities, that I was able to mostly suppress by designing more carefully the behavior at the corners. See czcams.com/video/bNCZtAnlVfc/video.html for similar effects. One possible explanation for the remaining instabilities is that I still have missed something about the corners. But it can also be a time step issue, or an effect of the thermostat.

@@NilsBerglund ty

The interaction seemed quite natural to me, because it is a slightly smoothed version of what one would do for the real dynamics of rigid solids. But contact forces are notoriously hard to compute, so I replaced them by one-sided harmonic forces.

If you prefer, an alternate title would be "Effect of a uniform gravitational field on rigid three-sided regular polygonal solids interacting via a one-sided repulsive harmonic potential", or something in that vein.

Thanks - it should work now.

Wie hier in etwa? czcams.com/video/BJuz4rE36xc/video.html

Good idea. Here is an earlier example of such a simulation: czcams.com/users/shortsOBGIriSydI8

@@NilsBerglund Thanks .,yes like this . For my idea Instead of already dropping , they flow into it like water in a sink.

You think so? To me, it looks like the phase velocity is indeed larger than the wave velocity, which is also consistent with the fact that the wavelength is increased. But of course the group velocity remains the same.

I checked frame by frame. So it is not reflexions because it appears before any reflexions on the sides. It looks more like a dispersion which would explained the result. I don't know if it's correlated but, to me, it seems to be caused by scattering which would explain the vertical spreading. Each wave front bounces and is divided into smaller wavelets that then reconbines with others wavelets to create the low frequency wave.

The size of the discs, or perhaps rather of the space between them, seems to have something to do with it. The phenomenon appeared when I increased the radius of the disc, keeping the distance between their centers constant.

The sticks do rotate. But I put a high friction on rotation, so there is almost no inertia. The next simulation in this series will improve on that.

You make a very good point

I used a high rotational friction, which essentially kills inertia. This is the "tweaking parameters" I allude to in the description: one could use a lower friction by increasing the moment of inertia of the sticks. Forthcoming simulations will involve polygons with 3 sides or more, for which the parameter choices have been improved.

also it seems the sticks can overlap on occasion

@JosuaKrause: Indeed. This is because the spring constant in the harmonic interaction is large but finite. I managed to improve that for polygons with three or more sides, as a forthcoming video will show.

Here I added gravity mainly to help the molecules coagulate. Think of a centrifuge, if you like.

It's quite impressive, isn't it? I made another video having a closer look at that effect.

Thanks. Here is a tutorial: czcams.com/video/z9xSq73a0n4/video.html

@@NilsBerglund thank you 🙏

Thanks, the link should work now. Finite differences seemed the easiest way to implement the simulation, and I have not tried other algorithms. How fast it runs will mainly depend on whether the code is compiled or not, and on the hardware you run it on. And also on how efficient the code is, of course, here I have benefited from advice to make the original code much faster.

The frequency is too low here to get an audible sound. One would need to speed it up and have a much longer sample to be able to hear something. But there are some samples for a different situation here: www.idpoisson.fr/berglund/isospectral.html

I don't use any of these. I develop my own C code, which is run directly on my laptop. The code uses some OpenGL libraries, but apart from that is is essentially made from scratch. The video description contains a link to a GitHub page with the code.

@@NilsBerglund Thank you very much for your quick response. Unfortunately, I am not a programmer and I am forced to search "ready-to-use" solutions for wave simulations.

The temperature is relatively stable. It starts about 1k and goes to 8k. Over the range of the temperature this is a small percentage. It likely would not produce a different effect. E.g., one could also ask about starting off with a much higher temperature to see the effect. Both can be done and there will be differences but the basic difference will essentially be to change the average size of the "holes". Higher temp would produce smaller holes while lower temps would produces larger holes, on average. Likely some middle temp actually would have a maximum hole size. E.g., maybe something better would be to calculate the average hole size(basically a density calculation) and plot that as the temperature changes. The temperature would have to get hot enough to break a lot of "bonds" to see a more gaseous phase. Plotting the density would show the effect of temperature on the substances. (with a very high temp one would get a lower density)

@@MDNQ-ud1ty I see... about the "holes". wov, I would expect reverse, warmer, bigger. but I get the idea. warmer, means weaker bonds, hence, easier to break the structure arround big holes... Thank you for your comprehensive answer.

@@emrahyalcin Well, if the temperature is high enough it might be bigger in some sense unless the volume is fixed. Think of ice melting. It has holes in it when solid(air pockets) and when it melts all those pockets will be released. As the atoms move around faster and faster they will have more of a chance to move into a free space(a hole) which would reduce the size(the size is technically hard or impossible to define). But think of all the atom all stacked up in a corner then there would be one large hole vs if they were uniformly spread out which there would be a slot of "small holes"(there would be no holes because the atoms wouldn't be connected but the sort of "average density" would be very different).

Numerical algorithms such as temperature cycling and simulated annealing use this idea to try and find, at least approximately, the minimum of a complicated energy landscape. If you freeze a system too quickly (this is called quenching), it will typically end up in a state with a lot of holes. Move the temperature up and down with decreasing step size, and the system will be able to find a denser state. The idea apparently goes back to metallurgic processes centuries ago.

See also here: czcams.com/video/DbikgFefxEs/video.html