Animation of 2D Velocity and Energy Distributions Using Hard Sphere Collisions

Introduction

            In this animation I have chosen to show how both the standard 2D energy and velocity probability distributions evolve from fairly arbitrary initial energy distributions. 

Figures:

Figure 1: Initial Energy and velocity distributions.

 

As is seen in Figure 1, in (V_x,V_y) space, the positions of the initial velocities for a mono-energetic initial energy distribution make up a circle centered around (V_x,V_y)=(0,0). 

 

Figure 2: Energy and velocity distributions after evolving toward their expected functional forms.

 

As is seen in Figure 2, in (V_x,V_y) space the positions of the initial velocity make up a cloud centered around (V_x,V_y)=(0,0).  The V_x distribution is a gaussian that is plotted (green) along the x axis, while the V_y distribution is a gaussian (blue) that is plotted along the y axis.  The energy forms an exponential that is also plotted along the x axis.