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2D Maxwell–Boltzmann distribution

Simulation of 2000 soft sphere particles in a circular boundary accompanied with probability distribution graphs. The probability distribution graph curve f(v) is the theoretical 2D Maxwell-Boltzmann distribution calculated from the root mean square velocity of the particles. The colors of the particles match the velocities and corresponding histogram bars in all but the first video segment. The unconventional soft sphere potential used in this model is a compactly supported bump function potential which has smooth derivatives of all orders. This allows for O(n*log(n)) collision detection and application of symplectic integrators respectively. This system was treated as a Hamiltonian system and was simulated and rendered in real time with application of low order symplectic integrators yielding high robustness and long-term energy-conservation. 0:00 rectangular initial positions (3D intro) 0:45 rectangular initial positions with right momentum 1:19 spiral initial positions with inward momentum 1:32 random initial positions with inward momentum