Nils Berglund | Waves escaping a ring of obstacles: Logarithmic spirals @NilsBerglund | Uploaded July 2024 | Updated October 2024, 4 minutes ago.
This is a simulation of waves originating from a point source crossing a set of circular obstacles placed on 60 logarithmic spirals, having 25 discs each. On each logarithmic spiral, the radial coordinate grows linearly, while the angular coordinate is an affine function of the logarithm of the radius. One particularity of this design is that the energy appears to leave the ring on straight lines that are not radial, but tangent to the spirals at their endpoints.
This video has two parts, showing the same evolution with two different color gradients:
Averaged wave energy: 0:00
Wave height: 1:14
In the first part, the color hue depends on the energy of the wave, averaged over a sliding time window. In the second part, it depends on the height of the wave. 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.
The color in the central region has been brightened to white, because the waves tend to make large-amplitude oscillations there, which would not be very pleasant to watch.
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: 26 minutes 6 seconds
Compression: crf 23
Color scheme: Part 1 - Inferno by Nathaniel J. Smith and Stefan van der Walt
Part 2 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firinggithub.com/BIDS/colormap
Music: "Plaidness" by Francis Preve@francispreve
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
This is a simulation of waves originating from a point source crossing a set of circular obstacles placed on 60 logarithmic spirals, having 25 discs each. On each logarithmic spiral, the radial coordinate grows linearly, while the angular coordinate is an affine function of the logarithm of the radius. One particularity of this design is that the energy appears to leave the ring on straight lines that are not radial, but tangent to the spirals at their endpoints.
This video has two parts, showing the same evolution with two different color gradients:
Averaged wave energy: 0:00
Wave height: 1:14
In the first part, the color hue depends on the energy of the wave, averaged over a sliding time window. In the second part, it depends on the height of the wave. 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.
The color in the central region has been brightened to white, because the waves tend to make large-amplitude oscillations there, which would not be very pleasant to watch.
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: 26 minutes 6 seconds
Compression: crf 23
Color scheme: Part 1 - Inferno by Nathaniel J. Smith and Stefan van der Walt
Part 2 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firinggithub.com/BIDS/colormap
Music: "Plaidness" by Francis Preve@francispreve
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
