Unbalanced Gas Dynamics

In this two dimensional animation I model the time change of spatial and energy distribution of atoms of a gas that is initially unbalanced. The simulation gives a choice of having the right hand side of the container either composed of gas discs with no energy or of a vacuum. The purpose is to see how the gas density and energy distribution becomes uniform along the horizontal direction. The discs interact via a Lennard Jones force the potential of which has the form
V(r)=4*epsilon*((sigma/r)^12-(sigma/r)^6)
where r is the separation between disc centers, sigma has units of length, and epsilon is the depth of the potential well. The borders of the container also have an exponential potential to keep the discs from escaping. As can be seen, the discs' energy centroid and density centroid vary sinusoidally with time and this period is roughly related to the average initial x velocity of the discs and the length of the container, L, as period=L/. The energy and density centroid motion actually correspond to a damped acoustic wave. The energy of the individual disc is color coded and the code can be read from color bar at the left. The simulation takes several minutes to finish while storing about 4 GB of image video. I have therefore provided a movie so that the animation can be run more rapidly. I also show that the energy distribution for the discs follows a simple exponential as expected by Maxwell for a 2D gas.