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Summary: Volume Fluctuations and Geometrical Constraints in Granular Packs
Tomaso Aste
Department of Applied Mathematics, RSPhysSE, The Australian National University, 0200 Australia
(Received 15 July 2005; revised manuscript received 3 October 2005; published 12 January 2006)
I study the structural organization and correlations in very large packings of equally sized spheres,
reconstructed in three dimensions with x-ray computed tomography. I show that the geometrical structure
can be conveniently studied as a packing of irregular tetrahedra with volume distribution that must decay
exponentially with parameters controlled by the conditions of mechanical stability, nonoverlapping, and
space filling. I argue that the system's structure can be described as constituted of two phases: (1) an
``unconstrained'' phase which freely shares the volume and (2) a ``constrained'' phase which assumes
configurations accordingly with the geometrical constraints. It results that the granular system exploits
heterogeneity maximizing freedom and entropy while constraining mechanical stability.
DOI: 10.1103/PhysRevLett.96.018002 PACS numbers: 45.70.ÿn
In this Letter I investigate how space is shared among
the particles in a granular pack and I discuss how the study
of such a space partition is essential for understanding both
the static properties of these structures and the dynamical
mechanisms which generate them. When equal spheres are
packed in a container they can arrange in a way to mini-
mize potential (gravitational) energy by maximizing the
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