Re: Packing different sized spheres

Ian Wanless wrote:
> 
> A colleague in our chemistry department asked me for assistance in working
> out how some particles are arranging themselves. Basically it is a packing
> problem with spheres with diameters ranging from, say, 1 to 20 microns.
> 
 
> Is it possible to achieve a density arbitrarily close to 1 by using
> spheres of arbitrary sizes?  

Yes. Take a sphere packing and add smaller spheres in the holes, 
and repeat this...

It is unlikely that there is significant literature on this since once you allow
several sizes, the problem gets messy from a mathematical point of view, and
only numerical solutions are 
of interest. Thus it reduces to a global optimization problem.
Hard, but probably approximately tractable by stochastic methods.


Arnold Neumaier