Waves of two different frequencies crossing a diffraction grating @NilsBerglund

Nils Berglund | Waves of two different frequencies crossing a diffraction grating @NilsBerglund | Uploaded May 2024 | Updated October 2024, 55 seconds ago.
In this simulation, waves emitted at two different frequencies encounter a diffraction grating, made of regularly spaced circular reflectors. 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: 1:04
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.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the bottom shows the signal along the horizontal symmetry axis of the simulated rectangular area.

Render time: 33 minutes 33 seconds
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap

Music: "Ready-Set-Go!" by Magic In The Other@MagicInTheOther

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

$Waves of two different frequencies crossing a diffraction grating$

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$Almost a branched flow: Waves crossing a finer percolation-style arrangement Like the video https://youtu.be/QhRmQ_ZX31Y , this one shows waves originating from a point interacting with obstacles obtained by randomly deleting circles from a regular square lattice. 15% of the points of the regular lattice have been kept. The arrangement is more random than a square lattice, but not as random as a Poisson disc process. The lattice is finer as in the previous simulation, as it contains four times as many points. I also chose different color gradients. In particular the energy part shows a filamentation of the energy distribution not unlike that of a branched flow, illustrated for instance in the video https://youtu.be/kOR6OiRlL8Y This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:27 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: 36 minutes 12 seconds Compression: crf 23 Color scheme: Part 1 - Cividis by Jamie R. Nuñez, Christopher R. Anderton, Ryan S. Renslow https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0199239 Part 2 - Turbo, by Anton Mikhailov https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a Music: Magical Gravity by Asher Fulero@AsherFulero See also https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ 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 https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf C code: https://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$

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$When waves crossing a square lattice have a larger phase than group velocity The simulation https://youtu.be/15fpsopRyn8 , that showed waves from two different sources having different frequencies cross a regular square grid of obstacles, revealed another interesting feature: After a while, the waves from the source with a lower frequency seemed to propagate through the lattice at a larger speed than the wave speed. This has to be an instance of the situation where the phase velocity (measuring how fast wave fronts move) is larger than the group velocity (measuring the speed of energy transfer). This video focuses on this phenomenon, by using only one source, having the lower frequency, and an additional plot of the signal in the x-direction. This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:16 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 displays at the right and bottom show 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: 30 minutes 28 seconds Compression: crf 23 Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Music: Future Girl by RKVC@rkvc See also https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ 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 https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf C code: https://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 #phase_velocity$

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