Warm Initial Conditions I: density plots.

I have started studying the effects of adding small random deviations to the positions and/or velocities of the particles in the 1D collapse study. What I am finding is that the $r^{-1/2}$ scaling behavior is lost if the particles have some randomness in their initial conditions. The plots look fairly similar to one another, but for completeness, I will show all three.

1) In this simulation, I have perturbed the positions of the particles by 5% of the inter-particle spacing. The perturbations are drawn from a normal distribution. The final density profile at 700 ATUs looks like this:

2) In this simulation I have left the positions evenly spaced, but have perturbed the velocities by 5% of the amplitude of the velocities (supplied by the user to the code). The density profile after 700 ATUs looks like:


3) And finally, applying both perturbations at the same time:


The most obvious thing about these (other than the departure from $r^{-1/2}$) are the density spikes that happen in the exterior. I am not sure what kind of structure this is due to, but since these curves are averages of the 6 runs, I will have to look into whether they are appearing in all six in the same location, or whether the behavior is being dominated by a single individual run. Later on I will also post movies, and the distributions of the particle energies... It might also be interesting to check if these get closer to the scaling in the cold runs if I put (e.g.) 1000 times smaller perturbations into the initial conditions.

I have a separate line of investigation that I will tell you about soon, where I have perturbed the masses of the particles, but not the initial conditions of either the positions or velocities. I wanted to see if either the number density or the mass density would scale as $r^{-1/2}$ (initial plots suggest the number density does not), and also wanted to see if the mass distribution of particles in each bin remains roughly constant. I thought of compensating the velocities to offset the mass perturbations (to keep the kinetic energy of the perturbed particle the same) but the potential energies are still perturbed, so I didn't know quite what I would learn from that, and didn't attempt it.