Nils Berglund | Cherenkov radiation, with corrected refractive index @NilsBerglund | Uploaded May 2024 | Updated October 2024, 47 seconds ago.
Several recent videos on this channel, such as youtu.be/zCWwBysMM_w , showed Cherenkov radiation generated as a particle enters a medium in which the speed of light decreases below its own speed. These simulations showed a strange "singularity", where the shock wave emitted by the particle gets pinched to a single point. It turns out this singularity was due to a coding mistake, which set the refractive index to zero at that point, before it increased again linearly. This mistake has been corrected in the present simulation. I also found an error in the absorbing boundary conditions, which has also been corrected.
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, a particle moves at constant speed from left to right, emitting pulses at regular time intervals. The speed of light decreases linearly, from the left to the right boundary of the simulation rectangle, reaching 0 at the right border. When the speed of light in the medium becomes smaller than the speed of a particle, a shock wave appears, which is the origin of Cherenkov radiation.
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, slightly below the path of the particle.
Render time: 24 minutes 34 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: "Silver Lakes" by Wes Hutchinson
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
Several recent videos on this channel, such as youtu.be/zCWwBysMM_w , showed Cherenkov radiation generated as a particle enters a medium in which the speed of light decreases below its own speed. These simulations showed a strange "singularity", where the shock wave emitted by the particle gets pinched to a single point. It turns out this singularity was due to a coding mistake, which set the refractive index to zero at that point, before it increased again linearly. This mistake has been corrected in the present simulation. I also found an error in the absorbing boundary conditions, which has also been corrected.
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, a particle moves at constant speed from left to right, emitting pulses at regular time intervals. The speed of light decreases linearly, from the left to the right boundary of the simulation rectangle, reaching 0 at the right border. When the speed of light in the medium becomes smaller than the speed of a particle, a shock wave appears, which is the origin of Cherenkov radiation.
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, slightly below the path of the particle.
Render time: 24 minutes 34 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: "Silver Lakes" by Wes Hutchinson
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
