Nils Berglund | Fatty polymers and water, with and without soap @NilsBerglund | Uploaded June 2024 | Updated October 2024, 25 seconds ago.
This is an attempt at simulating the effect of soap, by comparing a simulation including only "fat" and water molecules with another one, in which part of the molecules have a polar end, modeling soap. It is a very simplified model of the real process, and I don't claim the result to be particularly convincing, though it seems the molecules mix slightly better in the presence of soap. Feel free to propose improvements if you are knowledgeable about how soap works.
Water and fat do not easily mix. This is related to the fact that water molecules are polar, while fats are not. Soap molecules consist of a hydrophobic and lipophilic "tail", that tends to mix with fat molecules, and a hydrophilic and lipophobic "head", that tends to mix with water molecules. This helps mixing fat and water, and therefore cleaning objects, and people from fatty dirt particles.
This simulation shows a simple model for soap molecules, interacting with water molecules. The soap molecules consist in a tail made of ten neutral atoms, and a head consisting of two atoms of opposite charge. The soap molecules tend to latch on the oxygen atoms in water molecules. There are periodic boundary conditions, and the temperature is controlled by a thermostat with slowly decreasing temperature.
This simulation has two parts, showing the evolution with and without "soap" molecules:
Without soap: 0:00
With soap: 1:43
The particles' color depends on their type. The background indicates the local charge density, slightly averaged over space and time. In the second part, the particles' color hue depends on their kinetic energy.
To save on computation time, particles are placed into a "hash grid", each cell of which contains between 3 and 10 particles. Then only the influence of other particles in the same or neighboring cells is taken into account for each particle.
The temperature is controlled by a thermostat, implemented here with the "Nosé-Hoover-Langevin" algorithm introduced by Ben Leimkuhler, Emad Noorizadeh and Florian Theil, see reference below. The idea of the algorithm is to couple the momenta of the system to a single random process, which fluctuates around a temperature-dependent mean value. Lower temperatures lead to lower mean values.
The Lennard-Jones potential is strongly repulsive at short distance, and mildly attracting at long distance. It is widely used as a simple yet realistic model for the motion of electrically neutral molecules. The force results from the repulsion between electrons due to Pauli's exclusion principle, while the attractive part is a more subtle effect appearing in a multipole expansion. For more details, see en.wikipedia.org/wiki/Lennard-Jones_potential
Render time: Part 1 - 15 minutes 54 seconds
Part 2 - 16 minutes 11 seconds
Compression: crf 23
Color scheme: Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Music: Finding the Balance by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. creativecommons.org/licenses/by/4.0
Source: incompetech.com/music/royalty-free/index.html?isrc=USUAN1100708
Artist: incompetech.com
Reference: Leimkuhler, B., Noorizadeh, E. & Theil, F. A Gentle Stochastic Thermostat for Molecular Dynamics. J Stat Phys 135, 261–277 (2009). doi.org/10.1007/s10955-009-9734-0
maths.warwick.ac.uk/~theil/HL12-3-2009.pdf
Current version of the C code used to make these animations:
github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Some outreach articles on mathematics:
https://images.math.cnrs.fr/_Berglund-Nils-1343_.html
(in French, some with a Spanish translation)
#molecular_dynamics #ions #soap
This is an attempt at simulating the effect of soap, by comparing a simulation including only "fat" and water molecules with another one, in which part of the molecules have a polar end, modeling soap. It is a very simplified model of the real process, and I don't claim the result to be particularly convincing, though it seems the molecules mix slightly better in the presence of soap. Feel free to propose improvements if you are knowledgeable about how soap works.
Water and fat do not easily mix. This is related to the fact that water molecules are polar, while fats are not. Soap molecules consist of a hydrophobic and lipophilic "tail", that tends to mix with fat molecules, and a hydrophilic and lipophobic "head", that tends to mix with water molecules. This helps mixing fat and water, and therefore cleaning objects, and people from fatty dirt particles.
This simulation shows a simple model for soap molecules, interacting with water molecules. The soap molecules consist in a tail made of ten neutral atoms, and a head consisting of two atoms of opposite charge. The soap molecules tend to latch on the oxygen atoms in water molecules. There are periodic boundary conditions, and the temperature is controlled by a thermostat with slowly decreasing temperature.
This simulation has two parts, showing the evolution with and without "soap" molecules:
Without soap: 0:00
With soap: 1:43
The particles' color depends on their type. The background indicates the local charge density, slightly averaged over space and time. In the second part, the particles' color hue depends on their kinetic energy.
To save on computation time, particles are placed into a "hash grid", each cell of which contains between 3 and 10 particles. Then only the influence of other particles in the same or neighboring cells is taken into account for each particle.
The temperature is controlled by a thermostat, implemented here with the "Nosé-Hoover-Langevin" algorithm introduced by Ben Leimkuhler, Emad Noorizadeh and Florian Theil, see reference below. The idea of the algorithm is to couple the momenta of the system to a single random process, which fluctuates around a temperature-dependent mean value. Lower temperatures lead to lower mean values.
The Lennard-Jones potential is strongly repulsive at short distance, and mildly attracting at long distance. It is widely used as a simple yet realistic model for the motion of electrically neutral molecules. The force results from the repulsion between electrons due to Pauli's exclusion principle, while the attractive part is a more subtle effect appearing in a multipole expansion. For more details, see en.wikipedia.org/wiki/Lennard-Jones_potential
Render time: Part 1 - 15 minutes 54 seconds
Part 2 - 16 minutes 11 seconds
Compression: crf 23
Color scheme: Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Music: Finding the Balance by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. creativecommons.org/licenses/by/4.0
Source: incompetech.com/music/royalty-free/index.html?isrc=USUAN1100708
Artist: incompetech.com
Reference: Leimkuhler, B., Noorizadeh, E. & Theil, F. A Gentle Stochastic Thermostat for Molecular Dynamics. J Stat Phys 135, 261–277 (2009). doi.org/10.1007/s10955-009-9734-0
maths.warwick.ac.uk/~theil/HL12-3-2009.pdf
Current version of the C code used to make these animations:
github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Some outreach articles on mathematics:
https://images.math.cnrs.fr/_Berglund-Nils-1343_.html
(in French, some with a Spanish translation)
#molecular_dynamics #ions #soap
![[Flash warning] A planar wave crossing a gradient index lens at an angle](https://i.ytimg.com/vi/vZ_pKzjFXvo/hqdefault.jpg "[Flash warning] A planar wave crossing a gradient index lens at an angle
The first part of this video shows some flashing due to the formation of standing waves.
This is a variant of the simulation https://youtu.be/CdpTq3dSrXA , in which the incoming planar wave makes a small angle with the axis of symmetry of the lens. 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 planar wave being focused at a point in the 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: 1:03
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 periodic boundary conditions between the top and bottom boundaries, absorbing boundary conditions on the right boundary, and a time-periodic signal is imposed on the left boundary. The display at the right shows the signal along the focal plane, which is indicated by a vertical line.
Render time: 30 minutes 1 second
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
https://github.com/bastibe/twilight
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
https://github.com/BIDS/colormap
Music: Chicago by Joe Bagale
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")
