Longer version of continuous Rayleigh-Taylor instability on the sphere скачать в хорошем качестве

Longer version of continuous Rayleigh-Taylor instability on the sphere

This variant of the simulation    • A continuous analogue of the Rayleigh-Tayl...   uses a longer time step, and a hash grid with more cells, in order to decrease the computation time. This can be done if the speed of the particles is not too large. A Rayleigh-Taylor instability occurs when there are two layers of fluid, subject to gravity, and the upper layer has a larger density than the lower one. Here the effect is reproduced with particles interacting via a Lennard-Jones potential. The initial state is a random arrangement, with the lightest, red particles near the south pole, and the heaviest, dark blue particles near the north pole. The dark blue particles are 50 times heavier. The particles are coupled to a thermostat, keeping the temperature fixed, and subject to gravity directed towards the south pole of the sphere. Note that the light red particles start "boiling" when they approach the surface. This is analogous to decompression sickness, also known as "the bends", which affect divers that ascend too quickly, causing nitrogen in their body to become gaseous. 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). The color of the particles depends on their mass, which is a function of their initial latitude. 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: 1 hours 56 minutes 2D part: 1 hour 26 minutes Color scheme: Turbo, by Anton Mikhailov https://gist.github.com/mikhailov-wor... Music: "That Slapper" by Otis McDonald‪@OtisMacMusic‬ 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)