Hard-Spheres

Recently I found a beautiful, although unphysical behavior when I was implementing the dynamics of elastic billiard balls ( hard spheres in physics lingo). And the bug was not at all where I expected it to be. But since while debugging I did not find any resource helping me out with this, and I think there is a good general lesson to be learned, I thought I write it up. Pretty images Okay. Mindset we want to simulate balls flying around and bouncing off of things, with the total kinetic energy being conserved. There is nothing else acting on the balls. No gravity, no nada. ...

Prolog After I’ve recently been working on getting the dynamics simulation of hard spheres right, see my previous blog post, I was curious about color coding neighborhood symmetries. To see if my small simulations are already sufficient to see some sort of systematic change. Like can we see “melting” or “crystallization”? :-) Turns out yes, for a pretty animation see below. :-) You may think this is all settled and researchers have long moved on and everything is understood, spelled out in simple language, organized and filed away for easy grokking. But then you, as I was, would be mistaken. Study of hard spheres seems actually still a matter of ongoing research. There were even experiments done on the space shuttle in 2001, to study the transition between “liquid” and “solid” states (if you are interested in the general concept of “phases” and their transitions, I recommend this wiki page :-) ). And more definitive data on liquid-hexatic and hexatic-crystal transition was only collected in 2017. For what hexatic phases are see this wiki page. ...