Force correlations and arches formation in granular assemblies

Abstract

In the context of a simple microscopic schematic scalar model we study the effects of spatial correlations in force transmission in granular assemblies. We show that the parameters of the normalized weights distribution function, $P(v)\sim v^{\alpha }\exp (-v/\varphi )$, strongly depend on the spatial extensions, ${\xi }_V$, of such correlations. We show, then, the connections between measurable macroscopic quantities and microscopic mechanisms enhancing correlations. In particular we evaluate how the exponential cut-off, $\varphi ({\xi }_V)$, and the small forces power law exponent, $\alpha ({\xi }_V)$, depend on the correlation length, ${\xi }_V$. If correlations go to infinity, weights are power law distributed.

6 pages

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