Figure 1

The geometric construction around grain $g$. The vectors ${\overrightarrow{r}}_{lg}$ connect contact points clockwise around each grain $g$ and give rise to anticlockwise loops $l$ around each void. The vectors ${\overrightarrow{R}}_{lg}$ connect from grain centers to loop centers. A one-grain geometric tensor is defined as ${\widehat{C}}_g=\sum _l{\overrightarrow{R}}_{lg}{\overrightarrow{r}}_{lg}$.Reuse & Permissions

Figure 2

The volume (left axis) and density (right axis) of a trivalent granular assembly of monodisperse circular grains. The moduli of the intragranular vectors connecting the contact points are taken to be correlated in the calculation. The PDFs of $\gamma$ and $R$ are, respectively, Gaussian and a $\delta$ function at the periodic lattice value $R_0=2D/\sqrt{3}$. Two density plots are presented: one assuming independent $r$ variables (squares) and the other taking the intragranular correlations into account (+). For $X>X_0=0.265$, the correlations compactify the system while below this value they lead to an opposite effect for the reason discussed in the text. A significant feature is that the difference between the two plots is quite small. The densities of the two calculations differ only by 0.009 ($\approx 2\%$) at $\lambda X=5$ and by 0.021 at $\lambda X=0.04$ ($\approx 4\%$).Reuse & Permissions