Random Packing of Particles: Simulation With a One Dimensional Parking Model

Abstract

The linear space filling or “parking” problem is extended to allow sequential parking of cars of random length along a curb and to invoke parking rules that utilize a termination probability for rejecting curb spaces shorter than some cars. The latter innovation permits interpretation of termination as being analogous to blocking of interstices in the multi-dimensional particle packing problem. Parking densities are determined by numerical solution of integral equations as functions of the parameters of the car length distribution function. Some verification of a conjecture made by Lewis and Goldman, that the density of packed particulate materials is an increasing function of coefficient of variation, is provided in the one dimensional case for specified families of three

KEY WORDS:

• Random Packing
• Space Filling
• Particle Size Distributions
• Packing Density