Nils Berglund | Waves of two different frequencies crossing a larger regular square lattice @NilsBerglund | Uploaded June 2024 | Updated October 2024, 2 minutes ago.
This is a variant of the video youtu.be/pObtx2xmZDA , showing waves from sources with two different frequencies, crossing a regular square lattice of scatterers. The lattice is here broader than in the previous simulation, and the obstacles have a larger radius, in order to provide a better separation between wavelengths. One feature I found quite striking is that waves from the top source seem to accelerate when they reach the lattice. The speed of waves being fixed by the simulation, this has to be a situation where the phase velocity exceeds the group velocity.
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 roughly between both wavelengths. As a result, waves of the lower source pass the grating a bit 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: 1:20
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: 37 minutes 23 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
github.com/BIDS/colormap
Music: "Alone" by Emmit Fenn@emmitfenn
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 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
This is a variant of the video youtu.be/pObtx2xmZDA , showing waves from sources with two different frequencies, crossing a regular square lattice of scatterers. The lattice is here broader than in the previous simulation, and the obstacles have a larger radius, in order to provide a better separation between wavelengths. One feature I found quite striking is that waves from the top source seem to accelerate when they reach the lattice. The speed of waves being fixed by the simulation, this has to be a situation where the phase velocity exceeds the group velocity.
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 roughly between both wavelengths. As a result, waves of the lower source pass the grating a bit 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: 1:20
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: 37 minutes 23 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
github.com/BIDS/colormap
Music: "Alone" by Emmit Fenn@emmitfenn
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 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
