Nils Berglund | Looking for quasicrystals: Interacting kites-and-darts-type molecules @NilsBerglund | Uploaded June 2024 | Updated October 2024, 2 minutes ago.
This is a first attempt of producing something like a quasicrystal, using molecules with "kite" and "dart" shapes. The kites are quadrilaterals with angles 144° and three times 72°, while the darts have two angles of 36°, one angle of 72° and one angle of 216°. These are modeled by using four charges atoms on the vertices of the quadrilateral, and two additional neutral atoms on the symmetry axis for kites, and on the long sides for darts.
I'm not quite satisfied with this first try, because the single atoms still stand out too much. I may be able to improve things by modeling the molecules as collections of segments instead of point particles.
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. There is a constant gravitational force directed downward.
This simulation has two parts, showing the evolution with two different color gradients:
Type: 0:00
Orientation: 1:08
In the first part, the particles' color depends on their type (kites or darts), 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.
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: 17 minutes 10 seconds
Compression: crf 23
Color scheme: Part 1 - Particle: Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Background: Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - HSL/Jet
Music: "So Sweet" by Lish Grooves@LishGrooves
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 #quasicrystal
This is a first attempt of producing something like a quasicrystal, using molecules with "kite" and "dart" shapes. The kites are quadrilaterals with angles 144° and three times 72°, while the darts have two angles of 36°, one angle of 72° and one angle of 216°. These are modeled by using four charges atoms on the vertices of the quadrilateral, and two additional neutral atoms on the symmetry axis for kites, and on the long sides for darts.
I'm not quite satisfied with this first try, because the single atoms still stand out too much. I may be able to improve things by modeling the molecules as collections of segments instead of point particles.
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. There is a constant gravitational force directed downward.
This simulation has two parts, showing the evolution with two different color gradients:
Type: 0:00
Orientation: 1:08
In the first part, the particles' color depends on their type (kites or darts), 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.
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: 17 minutes 10 seconds
Compression: crf 23
Color scheme: Part 1 - Particle: Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Background: Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - HSL/Jet
Music: "So Sweet" by Lish Grooves@LishGrooves
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 #quasicrystal
