Nils Berglund | A wave source on the boundary of a parabolic resonator @NilsBerglund | Uploaded August 2024 | Updated October 2024, 16 seconds ago.
This video follows a question asked in a comment to the video youtu.be/NzFFJpI0BfI showing a wave source emitting pulses from the boundary of an ellipse. In that case, the wave fronts make a large number of reflections on the boundary (theoretically an infinite number), and the question was what happens when the ellipse is replaced by a set of confocal parabolas.
This video shows that in that case, the infinite number of reflections does not occur, which has to do with how the curvature of the boundary changes. It looks like the waves are almost focused back to the source after hitting the opposite parabola, but this is not exactly the case. If the source were placed on the common focal point, the wave fronts would switch between arcs of circles and lines, as shown in the video youtu.be/jRhrbb9Hhq0 in the approximation of geometrical optics, and in the video youtu.be/AUPhTGrukHY for waves.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 2:12
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.
Render time: 29 minutes 51 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: "Don't Fret" by Quincas Moreira@QuincasMoreira
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 #resonator
This video follows a question asked in a comment to the video youtu.be/NzFFJpI0BfI showing a wave source emitting pulses from the boundary of an ellipse. In that case, the wave fronts make a large number of reflections on the boundary (theoretically an infinite number), and the question was what happens when the ellipse is replaced by a set of confocal parabolas.
This video shows that in that case, the infinite number of reflections does not occur, which has to do with how the curvature of the boundary changes. It looks like the waves are almost focused back to the source after hitting the opposite parabola, but this is not exactly the case. If the source were placed on the common focal point, the wave fronts would switch between arcs of circles and lines, as shown in the video youtu.be/jRhrbb9Hhq0 in the approximation of geometrical optics, and in the video youtu.be/AUPhTGrukHY for waves.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 2:12
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.
Render time: 29 minutes 51 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: "Don't Fret" by Quincas Moreira@QuincasMoreira
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 #resonator
