Nils Berglund | Waves crossing a less dense percolation-style arrangement of obstacles @NilsBerglund | Uploaded July 2024 | Updated October 2024, 1 minute ago.
The arrangement of obstacles in this video is obtained by randomly deleting circles from a regular square lattice. The points are less dense in the video youtu.be/alN6VPaUmx8 , in which 25% of the points were kept, while here only 15% of points are kept. The arrangement is more random than a square lattice, but not as random as a Poisson disc process. A point source emits waves at constant frequency, and the video shows how the waves interact with the obstacles.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:24
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 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Smile Quiet Looking Up" by Puddle Of Infinity
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 #phase_velocity
The arrangement of obstacles in this video is obtained by randomly deleting circles from a regular square lattice. The points are less dense in the video youtu.be/alN6VPaUmx8 , in which 25% of the points were kept, while here only 15% of points are kept. The arrangement is more random than a square lattice, but not as random as a Poisson disc process. A point source emits waves at constant frequency, and the video shows how the waves interact with the obstacles.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:24
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 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Smile Quiet Looking Up" by Puddle Of Infinity
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 #phase_velocity
