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Local origins of volume fraction fluctuations in dense granular materials

Fluctuations of the local volume fraction within granular materials have previously been observed to decrease as the system approaches jamming. We experimentally examine the role of boundary conditions and inter-particle friction $μ$ on this relationship for a dense granular material of bidisperse particles driven under either constant volume or constant pressure. Using a radical Voronoï tessellation, we find the variance of the local volume fraction $ϕ$ monotonically decreases as the system becomes more dense, independent of boundary condition and $μ$. We examine the universality and origins of this trend using experiments and the recent granocentric model \cite{Clusel-2009-GMR,Corwin-2010-MRP}, modified to draw particle locations from an arbitrary distribution ${\cal P}(s)$ of neighbor distances $s$. The mean and variance of the observed ${\cal P}(s)$ are described by a single length scale controlled by $\bar ϕ$. Through the granocentric model, we observe that diverse functional forms of ${\cal P}(s)$ all produce the trend of decreasing fluctuations, but only the experimentally-observed ${\cal P}(s)$ provides quantitative agreement with the measured $ϕ$ fluctuations. Thus, we find that both ${\cal P}(s)$ and ${\cal P}(ϕ)$ encode similar information about the ensemble of observed packings, and are connected to each other by the local granocentric model.