Effect of boundaries on the force distributions in granular media

The effect of boundaries on the force distributions in granular media is illustrated by simulations of 2D packings of frictionless, Hertzian spheres. To elucidate discrepancies between experimental observations and theoretical predictions, we distinguish between the weight distribution {\cal P} (w) measured in experiments and analyzed in the q-model, and the distribution of interparticle forces P(f). The latter one is robust, while {\cal P}(w) can be obtained once the local packing geometry and P(f) are known. By manipulating the (boundary) geometry, we show that {\cal P}(w) can be varied drastically.Comment: 4 pages, 4 figure

Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, $\phi_c$, at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of $\phi_c$ values becomes narrower as the system size increases, so that essentially all configurations jam at the same $\phi$ in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure