More particles under increasing gravity on the sphere скачать в хорошем качестве

More particles under increasing gravity on the sphere

This is a variant of the simulation    • Particles under increasing gravity on the ...   with more particles. Both are spherical versions of simulations such as    • Lennard-Jones particles in increasing grav...   , showing interacting particles under increasing gravity. Gravity is directed here from the North pole to the South pole of the sphere - nothing to do with gravity on a planet, think rather of particles confined to the surface of a sphere inside a rocket accelerating at an increasing rate. As gravity is increased, the particles settle in an approximation of a hexagonal close packing configuration, which however has defects due to the spherical geometry. After a while, gravity is reset to its initial value, allowing the particles to disperse. This simulation has two parts, showing the same evolution with two different visualizations: 3D view: 0:00 2D view: 1:39 In the 3D part, the observer moves around the sphere in an orbit at constant latitude, located below the equator. The 2D part shows an equirectangular projection (the x- and y-coordinates are proportional to longitude and latitude). Unlike in previous simulations, the particles are represented by ellipses, instead of circles, to reflect the distortion of the projection near the poles. The particles' color represents their kinetic energy. 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. 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 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 https://en.wikipedia.org/wiki/Lennard... Render time: 3D part: 59 minutes 2D part: 33 minutes 22 seconds Color scheme: Turbo, by Anton Mikhailov https://gist.github.com/mikhailov-wor... Music: "Bullish" by Density & Time‪@TheGreyRoom‬ Reference: Leimkuhler, B., Noorizadeh, E. & Theil, F. A Gentle Stochastic Thermostat for Molecular Dynamics. J Stat Phys 135, 261–277 (2009). https://doi.org/10.1007/s10955-009-97... http://www.maths.warwick.ac.uk/~theil... Current version of the C code used to make these animations: https://github.com/nilsberglund-orlea... https://www.idpoisson.fr/berglund/sof... Some outreach articles on mathematics: https://images.math.cnrs.fr/_Berglund... (in French, some with a Spanish translation)