Particles on a cube скачать в хорошем качестве

Particles on a cube

This simulation is not to be taken too seriously. Since some of my recent simulations of particles on a sphere used a potential, acting in some sense as a deformation of the sphere, it occurred to me that the potential can be chosen according to the distance of the faces of a cube to its center. The force constant has been chosen by trial and error in such a way that the particles seem to move on straight lines between collisions. There is no friction acting on the particles, and also no thermostat. The motion of the particles is governed solely by a Lennard-Jones interaction between them and the force deriving from the potential. The video has two parts, showing the same simulation with two different representations: 3D view: 0:00 2D view: 1:18 In both parts, the color of the particles depends on their kinetic energy. In part 2, the background color depends of the value of the potential, potential wells or dimples appear in darker blue. The 2D part shows an equirectangular projection, meaning that the x- and y-coordinates are proportional to the longitude and latitude of the particles. Particles move in apparently curved lines due to the projection - you see similar paths for spacecraft and satellites orbiting the Earth. Particles should actually have elongated elliptical shapes when approaching the poles, but we chose not to do this here. This is also why atoms of the same molecule can appear to be far from each other near the poles. In the 3D parts, the observer moves around the sphere in a plane containing the center of the sphere. The number of particles that have fallen into pockets over time is shown at the top right. 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. Render time: 3D part: 17 minutes 50 seconds 2D part: 4 minutes 38 seconds Compression: crf 28 ffmpeg added noise option: -vf noise=alls=10:allf=t+u Color scheme: Turbo, by Anton Mikhailov https://gist.github.com/mikhailov-wor... Music: "No Combat" by Telecasted@/UCssF9ySY_aHU9NZtNhDClwg 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/auteurs/n... (in French, some with a Spanish translation) #particles #sphere #LennardJones