# Random distribution of spheres

1. Dec 17, 2012

### clamtrox

Hey guys, I need to fill up a box with uniformly distributed set of non-overlapping spheres. This is quite easy to do numerically. I was wondering what is expectation value for the asymptotic volume fraction of the spheres.

Suppose I have a big box with side L, and spheres with radius R<<L. I pick a random point x inside the box, and add it to my collection of spheres if |x-xn|>R for all spheres already in the collection. I can keep on doing this until there's no room in the box to add another sphere; suppose that leaves me with N spheres. What is $\frac{4\pi R^3}{3 L^3} E(N)$ ?

2. Dec 17, 2012