Random packing of elliptical disks

The dense packing of hard objects is a recurrent paradigm in physics, for example in early models of crystallinity, and also in theories of granular materials which are under active debate today [1, 2]. Generally speaking the objects are taken to be spheres, leading to the formulation of the Kepler Problem (what is their closest packing?) and the investigations begun by Bernal on disordered packings (what is the nature of their random packing?). Even for spheres the subject is surprisingly rich in interesting questions, some answered, some remaining open, and some difficult even to define [3]. There is no precise definition of ‘‘densest random packing’’ of spheres; nevertheless it is a concept to which we have become accustomed and one that is supported by the approximate reproducibility of the density found in a variety of experimental and computational procedures. It may be estimated as F1⁄4 0.64 0.02, where the stated uncertainty reflects a small variation in dense packings prepared by one procedure to another. While significant, this variation is small in relation to the difference between random and ordered packing, which has F 1⁄4 =ð3 ffiffiffi