$1\mathrm{/}{f}^{\alpha }$ fluctuations in a ricepile model

The temporal fluctuation of the average slope of a ricepile model is investigated. It is found that the power spectrum $S(f)$ scales as $1\mathrm{/}{f}^{\alpha }$ with $\alpha \approx 1.3$ when grains of rice are added only to one end of the pile. If grains are randomly added to the pile, the power spectrum exhibits $1\mathrm{/}{f}^2$ behaviour. The profile fluctuations of the pile under different driving mechanisms are also discussed.