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SpongeBob's N-body problem finally reaches viral equilibrium

SpongeBob's N-body problem finally reaches viral equilibrium


by Antonio Perez

The more celestial bodies there are, the more difficult it is to analyze the orbits and movements of stars.N body problem''Simulation, animation''SpongeBobPeter Rosselló, an astrophysics student at the University of La Laguna, has released an animation of the famous SpongeBob character.

SpongeBob's Gravity Collapse

You can see how viral equilibrium is eventually reached pic.twitter.com/Sm9p8cB3os

-PeRossello (@PeRossello)

The “Universal Law of Gravitation”, which states that all objects have a gravitational force that attracts them to each other, is a law of physics discovered by British scientist Isaac Newton in the 17th century. By applying this law of universal gravitation, we can calculate the forces acting between celestial bodies, and calculate their movements and paths.

But when the number of celestial bodies increases to three or more, this calculation becomes very difficult. This problem is called the “N-body problem” in the world of astrophysics because it becomes impossible to solve the equation of motion of N particles with gravity analytically.

Mr. Rosselló released an animation simulating the movement of 100,000 particles in 5 hours and 2,000 steps. The initial position of the object particle N is SpongeBob-shaped.

If you simulate motion assuming that all particles have gravity, the particles will move so that they are concentrated at one point,Gravity collapseI will show you. What is shown on the right is a diagram showing the equilibrium state of kinetic energy (Kinect energy) and gravitational potential energy (potential energy), where gravitational potential energy is converted into kinetic energy.

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After that, the particles disperse and move as if they were focused on two points. When we look at the state of energy balance, the kinetic energy is now converted into gravitational potential energy.

In the end, the 100,000 particles that were SpongeBob were once again concentrated into a single point, finally settling into a galaxy-like shape. The graph showing the energy balance bounces up and down, but the movement suddenly stops, indicating a state of equilibrium. “N particlesビリアル, balanceIt was reported that it had been “reached”.

Rosselló said the simulation was coded in Python.anestheticIn parallel with,matplotlibIt is said to be withdrawn.The code isMr. Rosselló's GitHub repositoryIt is said to be hosted on .

N-body simulation made with Python, parallelized with numba, and animated with matplotlib.

N=100,000. The calculation time is about 5 hours for 2,000 steps. About 1 second of computing time per step. Collisions are treated with softening length.

The code will be up on my github, eventually pic.twitter.com/aIMJhr9yqi

-PeRossello (@PeRossello)

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