Random packing of hyperspheres and Marsaglia's parking lot test

Many studies of randomly packed hyperspheres in multiple dimensions have been performed using Monte Carlo or Molecular Dynamics simulations to probe the behaviour of the systems. The calculations are usually initiated by randomly placing the hyperspheres in some D dimensional box until some randomly loosely packed density is achieved. Then either a compression algorithm or a particle scaling technique is used to reach higher packing fractions. The interesting aspect in the initial random placing of the hyperspheres is that it is closely related to a test of random number generators that was proposed by Marsaglia, the ”Parking Lot” test. It is this relationship that is investigated in this paper. [email protected]