Pushing farther in

In response to Scott's inquiry:

For x=0.001 x_max (about the inner edge of your plots) and N=10^4 there should still be 300 particles or so. So why can't you carry the plots to smaller distances?

Indeed, you'll see that the number of particles/bin that I selected (in the titles of the plots) were 100, 200, 300. No reason why you could not push this to smaller numbers, although the error bars get big. Here are some examples (with error bars):



So, the power law behavior goes in for at least another decade or more it seems like. This comparison also shows that I DO have an issue with the normalization. I was being clever using the "normed=True" option in making the histogram, because the particles all have mass 1/N, but I think in the case of uneven binning it is doing something unexpected. I can fix this, just wanted to confirm that I did in fact have a problem.

Incidentally, these error bars come from six separate runs, with the same initial conditions (in principle, tho I mucked it up, see below) except they differ by a couple of particles in the total number. I did this because the sim is deterministic. I wasn't sure if the numerical noise would duplicate itself or cause there to be some variation in the long term, but changing the number of particles by 3 (out of 10k) seemed to be a reasonable way to do an "independant" run of the same initial conditions.

Sadly, I got too ambitious, and I ran the warm and the cold initial conditions at the same time. It should have worked, because the scripts were out of phase, and it seemed like the liklihood that they would BOTH try and copy the mkinit file over and compile the code at the same time was extremely small. But I goofed something up because the runs seem to have gotten all mixed up with one another. So these error bars are probably overestimated because they come from computing the variance among 6 runs, some of which started cold and some warm. I am re-running in a less "clever" more straightforward way now. On the bright side, I can (preliminarily) confirm that the warm initial conditions do not seem to yield this r^-0.5 behavior.

Scott's next questions:

It looks like all of your runs show x^{-1/2} behavior except r4. Any idea what's different about this one?

It started out expanding, rather than collapsing. My best guess is that it's just not finished yet. I am running it for a LONGER time to confirm this hypothesis. If not, then we have an interesting issue, because it's NOT due to the merger, the red run has a merger too.

How long do these take and how much further could you push N?

This one I am plotting took around 67 minutes. Walter says the code scales (if I recall correctly) pretty close to N log N. But it's not so easy to answer your question since the more particles there are, the longer it takes to be done virializing. But if we wanted to run one for like a week, then the answer is: quite a lot more.