Random packing of hyperspheres and Marsaglia's parking lot test

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 te...

Parking lot test: fact or fiction!

From Parking Lot to Paradise.

Packing hyperspheres in high-dimensional Euclidean spaces.

We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions d=4, 5, and 6 to be phi(MRJ) approximately 0.46, 0.31, and 0.20, respectively. To a good approximation, t...

Reversible polydisperse parking lot model.

We use an improved reversible parking lot model to study the compaction of vibrated polydisperse media. The particle sizes are distributed according to a truncated power law. We introduce a self-consistent desorption mechanism with a hierarchical initialization of the system. In this way, we approach densities close to unity. The final density depends on the polydispersity of the system as well...