Nils Berglund | More rigid falling pentagons @NilsBerglund | Uploaded June 2024 | Updated October 2024, 5 seconds ago.
This simulation is similar to the one shown in the video youtu.be/wtFSczmOxkE of pentagonal molecules in a gravitational field. The difference is that the pentagons have been made more rigid. Each molecule is composed of 11 atoms, all interacting with a stiff harmonic potential, making them hard to deform.
The molecules in the 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.
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.
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
Orientation: 1:04
In the first part, the particles' color depends on their kinetic charge, while the background indicates the local charge density, slightly averaged over space and time. In the second part, the molecules' color depends on the orientation modulo 72 degrees, because of the five-fold symmetry.
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: 1 hour 5 minutes
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - HSL/Jet
Music: "Memory Card Full" by Birocratic@UCrEAQx48oTZy7f9ZWsDawK
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
This simulation is similar to the one shown in the video youtu.be/wtFSczmOxkE of pentagonal molecules in a gravitational field. The difference is that the pentagons have been made more rigid. Each molecule is composed of 11 atoms, all interacting with a stiff harmonic potential, making them hard to deform.
The molecules in the 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.
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.
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
Orientation: 1:04
In the first part, the particles' color depends on their kinetic charge, while the background indicates the local charge density, slightly averaged over space and time. In the second part, the molecules' color depends on the orientation modulo 72 degrees, because of the five-fold symmetry.
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: 1 hour 5 minutes
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - HSL/Jet
Music: "Memory Card Full" by Birocratic@UCrEAQx48oTZy7f9ZWsDawK
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