density profile tests

I have done a few more tests on the initial density profiles.  This work is taxing and slow to proceed because the runs are often very slow, and many of them will not run at all, but when I start them it is hard to tell the one case from the other.  The following experiment had an initial density profile of $x^{-0.2}$ and 80k particles.  I used that many particles, so that the initial density profile would extend several orders of magnitude to the interior.  I did this to test the hypothesis that if the initial scaling is already in place, the system would not go to the $x^{-1/2}$ attractor.  However, the hypothesis was incorrect, as you can see in the plots below (initial and then final density profiles of the particles):

   Each of these took 4.5 days.  In fact I thought the runs had hung (but as an experiment, didn't kill it).  I found that 3 of them had been completed when I got back from the break (I think I will kill the other three, but I'll wait a day, because I am curious.  Run 4 seems to have permanently hung on the 0th step, which is the main failure mode, but this time I know how long I have to wait to find out if it is simply running very very slowly). 

   It's somewhat hard to be quantitative about this, but the final configuration looks to me to scale roughly like the initial scaling in the very interior, but roll to an $x^{-1/2}$ scaling over a few decades until the final rolloff.    This is qualitatively different from the cases with initial power law steeper than $x^{-1/2}$.  For example, before the break I was able to get $x^{-0.7}$ to run.  Here are the initial and final configurations:

I just wanted to make sure that what we had seen in the $x^{-0.8}$ scaling (from my last post) was not a fluke.   I have not successfully been able to get anything with initial slope steeper than $x^{-0.8}$ to run. 

My next steps, I think, will be to look at a warm run with initial scaling $x^{-0.8}$ and/or $x^{-0.5}$, and as a related question, find out what happens if I take one of the old cold runs and add a little velocity perturbation AFTER it has reached its final state.  Also, I have been trying to look at the analytic stuff Scott and Walter sent me, to see if I can see any qualitative difference between slopes steeper and shallower than $x^{-1/2}$. 


Comments anyone?