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Avalanche dynamics, surface roughening and self-organized criticality - experiments on a 3 dimensional pile of rice

C. M. Aegerter·R. Günther·R. J. Wijngaarden
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Abstract

We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical exponents are $τ$ = 1.21(2) for the avalanche size distribution and $D$ = 1.99(2) for the cut-off 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 $α= D - d_B$ = 0.41(3) and the dynamic exponent $z = D(2 - τ)$ = 1.56(8). This result is compared with that obtained from a power spectrum analysis of the surface roughness, which yields $α$ = 0.42(3) and $z$ = 1.5(1) in excellent agreement with those obtained from the scaling relations.

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C. M. Aegerter, R. Günther, R. J. Wijngaarden. 2003-05-26. Avalanche dynamics, surface roughening and self-organized criticality - experiments on a 3 dimensional pile of rice. https://doi.org/10.1103/physreve.67.051306

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