Initial Conditions 1: Cold

I have finished some preliminary investigations into the sensitivity to the initial conditions. Below is a plot with 4 different runs of 1001, with different initial phase space configurations. The green and blue are simlar to runs you've seen before, the red has a more complicated velocity structure with an inflection point, and the yellow is still expanding rather than initially contracting. In all cases the initial positions are equally spaced out.



Here is the final configuration of these systems, after 4oo ATUs (arbitrary time units).


The final states look pretty similar, although the density profile is only sortof reflecting the r^-2 ness. The path these systems took to the final are quite different (although the phase space diagrams for all 4 are roughly the same at ~10 ATUs). Below are plots for 10, 20, and 40 ATUs:

10 ATU:

20 ATU:
40 ATU:

Also interesting are the specific energy distributions of the particles, and their evolution. Below I have histograms of the particle energies at times (0,10,20,40,400) ATUs:

0 ATU:


10 ATU:

20 ATUs:

40 ATUs:

and 400 ATUs:


There is probably some obvious explanation, but can either of you explain why the initial energy distributions are so identical, given the differences in the initial conditions??