We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly nonaffine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number.

Shear induced alignment of elongated particles is studied experimentally and numerically. We show that shear alignment of ensembles of macroscopic particles is comparable even on a quantitative level to simple molecular systems, despite the completely different types of particle interactions. We demonstrate that for dry elongated grains the preferred orientation forms a small angle with the streamlines, independent of shear rate across three decades. For a given particle shape, this angle decreases with increasing aspect ratio of the particles. The shear-induced alignment results in a considerable reduction of the effective friction of the granular material.

We probe the nature of the jamming transition of frictional granular media by studying their vibrational properties as a function of the applied pressure $p$ and friction coefficient $\mu$. The density of vibrational states exhibits a crossover from a plateau at frequencies $\omega \gtrsim {\omega }^{*}(p,\mu )$ to a linear growth for $\omega \lesssim {\omega }^{*}(p,\mu )$. We show that ${\omega }^{*}$ is proportional to $\mathrm{\Delta }z$, the excess number of contacts per grain relative to the minimally allowed, isostatic value. For zero and infinitely large friction, typical packings at the jamming threshold have $\mathrm{\Delta }z\to 0$, and then exhibit critical scaling. We study the nature of the soft modes in these two limits, and find that the ratio of elastic moduli is governed by the distance from isostaticity.

We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of the system is found to be a propagating coherent wave front followed by random oscillations made of multiply scattered waves. We find that the coherent wave front is insensitive to details of the packing: force chains do not play an important role in determining this wave front. The coherent wave propagates linearly in time, and its amplitude and width depend as a power law on distance, while its velocity is roughly compatible with the predictions of macroscopic elasticity. As there is at present no theory for the broadening and decay of the coherent wave, we numerically and analytically study pulse propagation in a one-dimensional chain of identical elastic balls. The results for the broadening and decay exponents of this system differ significantly from those of the random packings. In all our simulations, the speed of the coherent wave front scales with pressure as $p^{1∕6}$; we compare this result with experimental data on various granular systems where deviations from the $p^{1∕6}$ behavior are seen. We briefly discuss the eigenmodes of the system and effects of damping are investigated as well.

We report scanning tunneling microscopy observations, which imply that all atoms in a Cu(001) surface move frequently, even at room temperature. Using a low density of embedded indium “tracer” atoms, we visualize the diffusive motion of surface atoms. Surprisingly, the indium atoms seem to make concerted, long jumps. Responsible for this motion is an ultralow density of surface vacancies, diffusing rapidly within the surface. This interpretation is supported by a detailed analysis of the displacement distribution of the indium atoms, which reveals a shape characteristic for the vacancy mediated diffusion mechanism that we propose.