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

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

2003-05-26

arxiv.org/abs/cond-mat/0305592v1

Physics

Condensed Matter

Soft Condensed Matter

7 pages, 8 figures, accepted for publication in PRE

Scientific paper

10.1103/PhysRevE.67.051306

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 $\tau$ = 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 $\alpha = D - d_B$ = 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.

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