This paper describes two algorithms for the generation of random packings of spheres with arbitrary diameter distribution. The first algorithm is the force‐biased algorithm of Mościński and Bargieł. It produces isotropic packings of very high density. The second algorithm is the Jodrey‐Tory sedimentation algorithm, which simulates successive packing of a container with spheres following gravitation. It yields packings of a lower density and of weak anisotropy. The results obtained with these algorithms for the cases of log‐normal and two‐point sphere diameter distributions are analysed statistically, i. e. standard characteristics of spatial statistics such as porosity (or volume fraction), pair correlation function of the system of sphere centres and spherical contact distribution function of the set‐theoretical union of all spheres are determined. Furthermore, the mean coordination numbers are analysed. These results are compared for both algorithms and with data from the literature based on other numerical simulations or from experiments with real spheres.

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The paper describes an algorithm for the generation of random packings of ellipsoids of revolution, which is a natural generalization of an older algorithm for the case of spherical particles and belongs to the class of collective rearrangement algorithms. It yields packings with a broad spectrum of densities and geometrical properties, aspect ratio which depend on and the various para-meters controlling the motions of ellipsoids during the simulation. The ellipsoid systems obtained are characterized by second-order characteristics, namely pair correlation and orientation correlation functions. Furthermore, the constructed packings are described in a phase diagram taken from statistical physics.

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This paper reports on spatial-statistical analyses for simulated random packings of spheres with random diameters. The simulation methods are the force-biased algorithm and the Jodrey-Tory sedimentation algorithm. The sphere diameters are taken as constant or following a bimodal or lognormal distribution. Standard characteristics of spatial statistics are used to describe these packings statistically, namely volume fraction, pair correlation function of the system of sphere centres and spherical contact distribution function of the set-theoretic union of all spheres. Furthermore, the coordination numbers are analysed.