Abstract
The maximum possible densities of random equal-sphere packing have been established. The maximum random packing densities Φn for spaces with dimensions n = 1–4 have been determined by numerical experiment based on the Monte Carlo simulation. If the established maximum possible density is exceeded, spatial correlations occur in the system. They are manifested as oscillations of the pair correlation function at small distances and as significantly greater viscosity of the sphere system. The application of the experimental results to polymer matrices reinforced with glass or basalt microspheres is under discussion. In particular, it has been reasonably assumed that compositions suitable for producing high-quality composites by die casting should not have packing density higher than Φ3 = 0.359 for a three-dimensional space.
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