Longitudinally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces

The reason for this animation is that a previous hard sphere animation was shown not able to carry an acoustic wave. My gas physics menu item demonstrates agreement of hard sphere gas physics with almost all other aspects of gas physics but acoustic waves do not seem to be demonstrable with hard spheres. Any wave that is started decays away in just a few mean free paths. I thought that this decay could be caused by their lack of connectivity between particles. An inter-particle potential might provide that connectivity so that is what is being done here. An acoustic wave is a wave where the pressure and density variations are periodic and move at a speed of approximately c=sqrt(B/rho) where B is the bulk modulus and rho is the density. For this animation I have modulated at radian frequency omega the horizontal position of the containing potential sinusoidally in such a way as keep the gas volume constant and therefore to not compress the gas. The enclosure has "soft" repelling potentials (see color bar for scale). The soft potentials rise as exponentials so that there are no harsh collisions with the boundaries. Also the particles are kept apart by soft repelling Lennard-Jones potentials. Since the wave vector k= omega/c we expect to see spatial wavelengths equal to lambda=2*pi/k=2*pi*c/omega. Both the particle density and the particle pressure are expected have these spatial wavelengths. Of course, since the particle motion is random, we cannot expect to easily see the spatial variations. For that reason, the density and pressure Vs x are separated into bins and to these a Fast Fourier Fransform (FFT) is applied to find the frequency content. The FFTs show "some" agreement with the expected wavelengths but I'd have to say that this is far from conclusive. Perhaps it will be necessary to complete the Lennard Jones force by adding its attractive force. That would be like saying that the gas has to have some properties of a liquid in order to carry an acoustic wave and would be a major departure from the way we think of gases. In addition to exploring the acoustic wave aspects of this animation, I am showing at left how the energy distribution behaves as the disc energy increases due to the motion of the enclosure. That is the Accumulated N(E) plot at the left. For a 2D group of particles we expect the N(E) to be a simple Boltzmann exponential N(E)=N0*exp(-E/) where is the average kinetic energy. Since changes as time goes on, I chose to sum the energy number bins for just 200 frames and plot the distribution as these 200 frames accumulate and then dump the previous bins. The agreement with the Boltzmannn distribution is very good even under these dynamic conditions.