Avalanche dynamics, surface roughening, and self-organized criticality: Experiments on a three-dimensional pile of rice.

We present a two-dimensional system that exhibits features of self-organized criticality. The avalanches that occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical exponents are tau=1.21(2) for the avalanche size distribution and D=1.99(2) for the cutoff size. Furthermore, the geometry of the avalanches is studied, leading to a fractal dimension of the active sites of d(B)=1.58(2). Using a set of scaling relations, we can calculate the roughness exponent alpha=D-d(B)=0.41(3) and the dynamic exponent z=D(2-tau)=1.56(8). This result is compared with that obtained from a power-spectrum analysis of the surface roughness, which yields alpha=0.42(3) and z=1.5(1) in excellent agreement with those obtained from the scaling relations.