| Summary: | <p>We prepare static granular beds under gravity in different stationary states by tapping the system with pulsed excitations of controlled amplitude and duration. The macroscopic state---defined by the ensemble of static configurations explored by the system tap after tap---for a given tap intensity and duration is studied in terms of volume, $V$, and force moment tensor, $Sigma$. In a previous paper [Pugnaloni et al., Phys. Rev. E 82, 050301(R) (2010)], we reported evidence supporting that such macroscopic states cannot be fully described by using only $V$ or $Sigma$, apart from the number of particles $N$. In this work, we present an analysis of the fluctuations of these variables that indicates that $V$ and $Sigma$ may be sufficient to define the macroscopic states. Moreover, we show that only one of the invariants of $Sigma$ is necessary, since each component of $Sigma$ falls onto a master curve when plotted as a function of $m{Tr}(Sigma)$. This implies that these granular assemblies have a common shape for the stress tensor, even though it does not correspond to the hydrostatic type. Although most results are obtained by molecular dynamics simulations, we present supporting experimental results.</p><p><strong>Received:</strong> 11 May 2011, <strong>Accepted:</strong> 15 July 2011; <strong>Edited by:</strong> J-C. Géminard; <strong>Reviewed by:</strong> B. Tighe, Instituut-Lorentz, Universiteit Leiden, Netherlands; <strong>DOI:</strong>http://dx.doi.org/10.4279/PIP.030004</p><p><strong>Cite as:</strong> L. A. Pugnaloni, J. Damas, I. Zuriguel, D. Maza, Papers in Physics 3, 030004 (2011)</p>
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