Statistics Predict Random Circle Packing

The densest amorphous packing of rigid particles is known as random close packing (RCP). If you pack with a mixture of circle sizes, you can attain highly dense packing fractions. Mixtures of different sized circles are described by the probability distribution function (PDF) of circle radii. Previous results from our lab in 3D packing find the polydispersity and skewness of the underlying PDF determine the packing fractions of spheres. We find analogous results in 2D, that there is some function of polydispersity and skewness that determines the RCP packing fraction. In addition, 2D packings can spontaneously pack hexagonally, which requires introducing an additional PDF-dependent parameter to predict such non-random behavior. In this talk, we present the general formula for the density of random packed circles from their PDFs, and the theoretical underpinnings of the formula.