@NilsBerglund

@NilsBerglund

Nils Berglund | Classics revisited: The dark side of the pool @NilsBerglund | Uploaded August 2024 | Updated October 2024, 2 hours ago.
This is a remake of the video youtu.be/kPwNzWu_gqs of waves generated on the boundary of an ellipse, in much higher resolution. In the limit of geometric optics, that is, for negligible wave length, the wave front develops an infinite number of singularities due to reflections, as illustrated by the video youtu.be/0arOgc5iVIs . This property is partly conserved by the wave equation, though interference and diffraction mask the smallest details of the effect.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:55
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.
The wave source is located at the right apex of the ellipse, and emits pulses at regular time intervals.

Render time: 35 minutes 9 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Magma by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap

Music: Drifting 2 by Audionautix is licensed under a Creative Commons Attribution 4.0 licence. creativecommons.org/licenses/by/4.0
Artist: audionautix.com

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 #ellipse

$Classics revisited: The dark side of the pool This is a remake of the video https://youtu.be/kPwNzWu_gqs of waves generated on the boundary of an ellipse, in much higher resolution. In the limit of geometric optics, that is, for negligible wave length, the wave front develops an infinite number of singularities due to reflections, as illustrated by the video https://youtu.be/0arOgc5iVIs . This property is partly conserved by the wave equation, though interference and diffraction mask the smallest details of the effect. This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:55 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. The wave source is located at the right apex of the ellipse, and emits pulses at regular time intervals. Render time: 35 minutes 9 seconds Compression: crf 23 Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing Part 2 - Magma by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Music: Drifting 2 by Audionautix is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/by/4.0/ Artist: http://audionautix.com/ 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 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 #resonator #ellipse$

More stable weather with 16 pressure systems - vorticity and wind direction

A mass spectrometer

Welcome to Gattaca: This starts looking more like DNA

Adding tracers in 3D to vortex simulations on a rotating sphere

How tides could look if the Moon were much closer to Earth

$Waves crossing a less dense percolation-style arrangement of obstacles 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 https://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 https://github.com/bastibe/twilight Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt https://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 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 #diffraction #phase_velocity$

Numerical aperture of a lens in a wall (re-upload)

Weather on the Earth, with 17 pressure systems

Enhance 34 to 46: DNA replication (short version)

$Waves of two different frequencies crossing a biconvex lens Someone asked about the effect of the lights frequency on the working of a lens. The theory of geometrical optics, or ray optics, considers an idealized situation in which the wavelength is negligibly small, and much of basic optics relies on this approximation. Increasing the wavelength results in effects such as diffraction, which may degrade the quality of the lens. In this simulation, two sources at different frequencies emit light crossing a biconvex lens. The frequency of the lower source is three times the frequency of the upper one. While the difference of frequencies has an effect on the waves interference, the energy profile in the focal plane does not show any important difference. This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:15 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 right shows the square of the signal along the focal plane, averaged over a time window. The focal plane and the plane containing the sources are roughly symmetrical with respect to the vertical symmetry axis of the lens. Render time: 34 minutes 41 seconds Compression: crf 23 Color scheme: Part 1 - Twilight by Bastian Bechtold https://github.com/bastibe/twilight Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Music: Bright Idea by Geographer@geographermusic 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 #lens #focus$ $3D representation of a gradient index lens This is a 3D representation of the simulation https://youtu.be/KB_Roqs38F8 showing the light of two point sources crossing a gradient index lens. The simulation is still two-dimensional, but the z-coordinate is used to represent a combination of the wave height or energy, and of the refractive index. Several recent videos on this channel, such as https://youtu.be/CdpTq3dSrXA and https://youtu.be/aYvsBgyJgIE , showed planar waves crossing a gradient index lens. In this video, we look instead at two light sources that are located quite close to the lens. The lens is indeed able to focus the light on two spots located in the focal plane. In practice, one seldom has light sources located so close to the lens (except perhaps in macro photography), but this set-up was better suited to the simulation method used here. To be able to get such a small focal length, the refractive index has been chosen rather large in the center of the lens, with a value of 1.82. The videos are inspired by Huygens Optics recent short https://youtube.com/shorts/VGd3Ajnp6e0 showing the principle of a gradient index lens. Lenses focus incoming rays of light by delaying them more near the center of the lens than at its periphery. This is often done with a material of constant index of refraction, by making the lens thicker near the center, as shown for instance in the simulation https://youtu.be/rrJJBh9ubUE . However, one can also build lenses of constant thickness, by making the index of refraction of their material depend on the location in the lens. In this simulation, the index decreases like sqrt(n0² - a*r²), where r is the distance to the axis of symmetry. This results in the incoming waves being focused at two points in the (estimated) focal plane, marked by a vertical line. The plot to the right shows a time-averaged value of the field along that plane. This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:23 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 from the beginning of the simulation. The z-coordinate shows the sum of the wave height or energy and of the local refractive index. There are absorbing boundary conditions on the exterior borders of the simulation. Render time: 1 hour 35 minutes Compression: crf 23 Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Music: Cloud Patterns by Silent Partner 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 #lens #gradient_index$

Classics revisited: The dark side of the pool @NilsBerglund