Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Random distribution of spheres

  1. Dec 17, 2012 #1
    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 [itex] \frac{4\pi R^3}{3 L^3} E(N) [/itex] ?
  2. jcsd
  3. Dec 17, 2012 #2
    This problem is called the "parking lot test" for random numbers. I am sure you will find the answer by googeling for it.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook