Sandpile Dynamics

 

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The Rice Pile Project

The rice pile project was initiated at the Departement of Physics at the University of Oslo in 1992. The project is an attempt to test the experimental basis for self-organized criticality in piles of grains.

Self-organized criticality was originally coined by Bak and coworkers in 1987 as an explanation for how many slowly driven dissipative systems evolve into a critical state with no intrinsic length or time scale. The generic example is a naive, theoretical sand pile model. As grains of sand are added to a pile, the pile builds up, increasing the local slopes within the pile. If a local slopes exceeds a threshold value that depends on the maximum shear force a grain can sustain before sliding, the grain slides down to a neighboring position. The slope at that position may also exceed the critical value, and the avalanche continues until no more grains are moved. The distribution of energy dissipation events in this simple model is power-law distributed for a two-dimensional model. Similar models have been applied to explain the occurence of power-law event sizes in systems as diverse as earthquakes, front depinning and biological evolution.

The original rice pile experiment measured the internal energy dissipation in a pile of rice confined between two glass plates. The energy of the pile was found by taking pictures of the pile from the side and calculating the potential energy from the distribution of mass in the pile. The experiment showed that for elongated grains of rice, the distribution of avalanche sizes were described by a power-law. However, for rounder grains the distribution was best described as a stretched exponential distribution with a characteristic size. It was speculated that the difference was due to differences in inertial effects in the two systems. However, the main conclusion was the self-organized criticality can be relevant to the description of granular systems, but it is not a universal behavior.

The experiment was performed in several stages. During the first experimental period, pictures of the pile were taken with a video camera. However, it turned out that the spatial resolution and the stability of the video signal was not good enough to produce a reasonable scaling range for the measured energy. A second series of experiments were therefore performed with a $100.000 CCD camera with a striking 2000x2000 spatial resolution with 12 bits of grayscale resolution was used. However, even with this camera, the system size was limited. In order to ascertain that very large piles did not behave significantly different, as have been claimed by several researchers, an experiment was performed on a 2.5m times 3m pile. The pile did not behave significantly different than the 80cm wide pile tested previously.

The experimental crew consisted of:
Vidar Frette
Kim Christensen
Anders Malthe-Sorenssen

This site gives some references on self-organized criticality and the rice pile experiment and particular. You'll also find pictures of both experiment and experimenters.