SMALLEY1 has recently proposed the problem of determining the density of O-spheres distributed randomly on a line and has given some Monte Carlo estimates. In this communication I largely solve this problem, so far as the expectation of the density is concerned.

By iterative methods of solving difference equations (or by a Monte Carlo method), statistical parameters are calculated for a number of models concerned with linear lattices. These contain sites… Expand

As a result of making a theoretical study of travel distances in towns, Fairthorne (1964) was led to consider the distribution of the distance between two points P and Q, where P is uniformly… Expand

Abstract Particle packings are relevant to many aspects of the Earth sciences, and there is a long history of the study of packings from an Earth science viewpoint. Packings have also been studied in… Expand

Abstract One-dimensional 'parking' simulations are used to lay a foundation for analysis of packing problems encountered in particulate materials processing. Parking simulations involve a random… Expand

Some structural properties of packed bed systems on both the local and overall scales which are available in the literature and of interest in chemical engineering applications are discussed. Regular… Expand

A SPHERE can be defined as the locus of a point at a constant distance from a fixed point. A sphere in n dimensions is bounded by an (n−1) dimensional envelope. This value (n−1) can be used to define… Expand