Cherenkov radiation of two particles moving in opposite directions @NilsBerglund

Nils Berglund | Cherenkov radiation of two particles moving in opposite directions @NilsBerglund | Uploaded June 2024 | Updated October 2024, 2 hours ago.
This video was suggested in comments to a previous video on Cherenkov radiation. It features two particles moving in opposite directions in a medium with varying refractive index.
Cherenkov radiation is produced when a fast moving particle enters a medium in which the speed of light is smaller than the speed of the particle. This does not contradict special relativity, because only the speed of light in a vacuum cannot be reached by a massive particle, while the speed of light in a medium is in general smaller than in a vacuum.
In this simulation, two particles move at constant speed, one from left to right and the other one from right to left, emitting pulses at regular time intervals. The lower particle emits waves of smaller amplitude, to avoid that its radiation completely masks the radiation of the upper particle. The speed of light decreases linearly, dropping to 0 at the right boundary. When the speed of light in the medium is smaller than the speed of the particle, a shock waves appears, which is the origin of Cherenkov radiation. No shock wave is produced when the particle moves in a region where the speed of light is larger than its own speed.
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.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the bottom shows the signal along a horizontal line, located halfway between the paths of the two particles.

Render time: 28 minutes 59 seconds
Compression: crf 20
Color scheme: Part 1 - Twilight by Bastian Bechtold
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap

Music: "The Coldest Shoulder" by The 126ers@hutchinw

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 #Cherenkov #shock_wave

$Cherenkov radiation of two particles moving in opposite directions This video was suggested in comments to a previous video on Cherenkov radiation. It features two particles moving in opposite directions in a medium with varying refractive index. Cherenkov radiation is produced when a fast moving particle enters a medium in which the speed of light is smaller than the speed of the particle. This does not contradict special relativity, because only the speed of light in a vacuum cannot be reached by a massive particle, while the speed of light in a medium is in general smaller than in a vacuum. In this simulation, two particles move at constant speed, one from left to right and the other one from right to left, emitting pulses at regular time intervals. The lower particle emits waves of smaller amplitude, to avoid that its radiation completely masks the radiation of the upper particle. The speed of light decreases linearly, dropping to 0 at the right boundary. When the speed of light in the medium is smaller than the speed of the particle, a shock waves appears, which is the origin of Cherenkov radiation. No shock wave is produced when the particle moves in a region where the speed of light is larger than its own speed. 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. There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the bottom shows the signal along a horizontal line, located halfway between the paths of the two particles. Render time: 28 minutes 59 seconds Compression: crf 20 Color scheme: Part 1 - Twilight by Bastian Bechtold Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Music: The Coldest Shoulder by The 126ers@hutchinw 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 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 #Cherenkov #shock_wave$

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