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

TL;DR

This study investigates avalanche behavior and surface roughening in a 3D rice pile, demonstrating self-organized criticality with specific scaling exponents and fractal dimensions, validated through experiments and power spectrum analysis.

Contribution

It provides experimental evidence of self-organized criticality in a 3D rice pile and determines key scaling exponents and fractal dimensions through surface and avalanche analysis.

Findings

Avalanche size distribution follows finite size scaling with exponent τ=1.21.

Fractal dimension of active sites is approximately 1.58.

Surface roughness exponents are around 0.41-0.42, consistent across methods.

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 $\tau$ = 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.