Nils Berglund | Foam bath: Coagulating pentagonal molecules @NilsBerglund | Uploaded June 2024 | Updated October 2024, 6 minutes ago.
The molecules in this simulation have a pentagonal symmetry, except that the symmetry is broken by the charge they are carrying. Some molecules have 3 positively and 2 negatively charged atoms, while for other molecules, the charge distribution is the other way round. When molecules come close enough, they can merge, gradually forming larger clusters.
I once again had in mind the formation of some kind of quasicrystal, but the molecules appear not to be rigid enough for that. The resulting effect looks more like a foam bath. One can observe one cluster expelling atoms near the end of the simulation: This is due to a safety mechanism, that dissociates molecules when they start vibrating too much.
The particles in this simulation interact via a Coulomb potential when they belong to different molecules, and a harmonic potential within the same molecule. The Coulomb potential is complemented by a Lennard-Jones interaction between particles of opposite charge, to avoid their collapse on a single point.
There are periodic boundary conditions, and the temperature is controlled by a thermostat with increasing temperature.
This simulation has two parts, showing the evolution with two different color gradients:
Charge: 0:00
Clusters: 1:39
In the first part, the particles' color depends on their charge, while the background indicates the local charge density, slightly averaged over space and time. In the second part, the particles' color is constant in each cluster.
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
I will be traveling for a few days, and may not be able to reply to comments before I return.
Render time: 20 minutes 13 seconds
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - HSL/Jet
Music: Kool Kats 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=USUAN1100601Artist: 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 #foam
The molecules in this simulation have a pentagonal symmetry, except that the symmetry is broken by the charge they are carrying. Some molecules have 3 positively and 2 negatively charged atoms, while for other molecules, the charge distribution is the other way round. When molecules come close enough, they can merge, gradually forming larger clusters.
I once again had in mind the formation of some kind of quasicrystal, but the molecules appear not to be rigid enough for that. The resulting effect looks more like a foam bath. One can observe one cluster expelling atoms near the end of the simulation: This is due to a safety mechanism, that dissociates molecules when they start vibrating too much.
The particles in this simulation interact via a Coulomb potential when they belong to different molecules, and a harmonic potential within the same molecule. The Coulomb potential is complemented by a Lennard-Jones interaction between particles of opposite charge, to avoid their collapse on a single point.
There are periodic boundary conditions, and the temperature is controlled by a thermostat with increasing temperature.
This simulation has two parts, showing the evolution with two different color gradients:
Charge: 0:00
Clusters: 1:39
In the first part, the particles' color depends on their charge, while the background indicates the local charge density, slightly averaged over space and time. In the second part, the particles' color is constant in each cluster.
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
I will be traveling for a few days, and may not be able to reply to comments before I return.
Render time: 20 minutes 13 seconds
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - HSL/Jet
Music: Kool Kats 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=USUAN1100601Artist: 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 #foam
