Nils Berglund | Waves of two different frequencies crossing a Poisson disc lattice @NilsBerglund | Uploaded June 2024 | Updated October 2024, 5 minutes ago.
Some recent simulations on this channel, such as youtu.be/Y9Zn8T8dYgg , showed waves of two different frequencies, produced by two different sources, crossing a regular lattice of scatterers. Here the regular lattice has been replaced by a random Poisson disc process (also known as blue noise process). Several previous simulations on this channel have shown that such a distribution of points is more effective as a barrier against waves than regular distributions, an effect related to Anderson localization. This is also the case here, and the energy color scale has been adapted to make the waves crossing the obstacles more visible.
The frequency of the lower source is three times the frequency of the upper one. The resulting wavelengths are such that the open intervals in the grating are between both wavelengths. As a result, waves of the lower source pass the grating more easily, as can be best seen on the energy plot.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:19
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, averaged over a sliding time window. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy).
Render time: 35 minutes 28 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Not Impossible" by The 126ers@hutchinw
See also https://images.math.cnrs.fr/Des-ondes-dans-mon-billard-partie-I.html for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #diffraction #grating
Some recent simulations on this channel, such as youtu.be/Y9Zn8T8dYgg , showed waves of two different frequencies, produced by two different sources, crossing a regular lattice of scatterers. Here the regular lattice has been replaced by a random Poisson disc process (also known as blue noise process). Several previous simulations on this channel have shown that such a distribution of points is more effective as a barrier against waves than regular distributions, an effect related to Anderson localization. This is also the case here, and the energy color scale has been adapted to make the waves crossing the obstacles more visible.
The frequency of the lower source is three times the frequency of the upper one. The resulting wavelengths are such that the open intervals in the grating are between both wavelengths. As a result, waves of the lower source pass the grating more easily, as can be best seen on the energy plot.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:19
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, averaged over a sliding time window. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy).
Render time: 35 minutes 28 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Not Impossible" by The 126ers@hutchinw
See also https://images.math.cnrs.fr/Des-ondes-dans-mon-billard-partie-I.html for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #diffraction #grating
