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Perfect packings of spheres and bearings

By: Reza M. Baram
From: CFTC
At: Complexo Interdisciplinar, Anfiteatro
[2009-04-29] 12:00

The search for the perfect packing has a long history and although much is known about monodisperse or bidisperse systems, the real challenge lies in polydispersity. Materials of very high resistance made of an originally granular mixture as it is the case for high performance concrete (HPC) and for hard ceramics are manufactured by trying to reach the highest possible densities. From the fracture mechanics point of view, higher densities imply less and smaller microcracks and therefore higher resistance and reliability. This goal can be reached as shown clearly for the case of HPC by mixing grains of very different sizes (gravel, sand, ordinary cement, limestone filler, silica fume), where the size distribution of the mixture follows as closely as possible a powerlaw distribution. In fact it is known that configurations of density one are obtained for spherical particles in so-called Apollonian packings (albeit not yet physically realisable) and constitute the idealized final goal of a completely space filling packing having absolutely no defects. In the first part of my talk, I will introduce algorithms for constructing perfect, both regular and irregular, packings of spherical shaped particles in two and three dimensions including packings with the important property of having only two classes of spheres such that no spheres from the same class touch each other. We refer to this packing as the bichromatic packing. The second part of my talk will be devoted to applications of bichromatic packings in modeling techtonic plates and transport of heavy particles by turbulent flows.