A geometric probabilistic approach to random packing of hard disks in a plane

In this paper, the random packing fraction of hard disks in a plane is analyzed, following a geometric probabilistic approach. First, the random close packing (RCP) of equally sized disks is modelled. Subsequently, following the same methodology, a simple, statistical geometric model is proposed for the random loose packing (RLP) of monodisperse disks. This very basic derivation of RLP leads to a packing value (approximate to 0.66) that is in very good agreement with values that have been obtained previously for 2D disk packings. The present geometrical model also enables a closed-form expression for the contact (coordination) number as a function of the packing density at different states of compaction. These predictions are thoroughly compared with empirical and simulation results, among others the Renyi parking model, yielding good agreement. In this paper, the random packing fraction of hard disks in a plane is analyzed, following a geometric probabilistic approach.

Automated summary

This paper analyzes the random packing fraction of hard disks in a plane using a geometric probabilistic approach. A simple, statistical geometric model for the random loose packing of monodisperse disks is proposed. The model provides a close approximation to the packing value and enables the calculation of the contact number at different states of compaction.