Universality of slip avalanches in flowing granular matter.

The search for scale-bridging relations in the deformation of amorphous materials presents a current challenge with tremendous applications in material science, engineering and geology. While generic features in the flow and microscopic dynamics support the idea of a universal scaling theory of deformation, direct microscopic evidence remains poor. Here, we provide the first measurement of internal scaling relations in the deformation of granular matter. By combining macroscopic force fluctuation measurements with internal strain imaging, we demonstrate the existence of robust scaling relations from particle-scale to macroscopic flow. We identify consistent power-law relations truncated by systematic pressure-dependent cutoff, in agreement with recent mean-field theory of slip avalanches in elasto-plastic materials, revealing the existence of a mechanical critical point. These results experimentally establish scale-bridging relations in the flow of matter, paving the way to a new universal theory of deformation.

Relation between self-organized criticality and grain aspect ratio in granular piles.

We investigate experimentally whether self-organized criticality (SOC) occurs in granular piles composed of different grains, namely, rice, lentils, quinoa, and mung beans. These four grains were selected to have different aspect ratios, from oblong to oblate. As a function of aspect ratio, we determined the growth (ß) and roughness (α) exponents, the avalanche fractal dimension (D), the avalanche size distribution exponent (τ), the critical angle (γ), and its fluctuation. At superficial inspection, three types of grains seem to have power-law-distributed avalanches with a well-defined τ. However, only rice is truly SOC if we take three criteria into account: a power-law-shaped avalanche size distribution, finite size scaling, and a universal scaling relation relating characteristic exponents. We study SOC as a spatiotemporal fractal; in particular, we study the spatial structure of criticality from local observation of the slope angle. From the fluctuation of the slope angle we conclude that greater fluctuation (and thus bigger avalanches) happen in piles consisting of grains with larger aspect ratio.

Extremal dynamics and the approach to the critical state: experiments on a three dimensional pile of rice.

The evolution of the growth of a ricepile is studied in three dimensions. With time, the pile approaches a critical state with a certain slope. Assuming extremal dynamics in the evolution of the pile, the way the critical state is approached is dictated by the scaling properties of the critical state itself. Experimentally, we determine the envelope of the maximal slope, which is a measure for the distance from the critical state, as well as the growth of the average avalanche size with time. These quantities obey power-law scaling, where the experimental exponents are in good agreement with those obtained from an earlier determination of the critical state properties and extremal dynamics. Furthermore, we discuss the influence of the transient state on the avalanche size distribution, which may have applications in the prevention of large avalanches in natural systems.