Spatiotemporal Intermittency on the Growing Surface of Coupled Sandpiles

The surface of conservative coupled sandpiles in the self-organized cooperative critical state is found to exhibit intermittency in both time and space. The spatiotemporal intermittent structure is also found to be a multifractal. The probability density of sand grain heights on the surface is an asymptotic power law but with an exponential cut-off. The power spectra of the time series of sand grain heights show a diversity of low-frequency components over different sites on the surface and also over different ensemble samples. This means that the long-term prediction according to the nearby observations and the history experiences is very difficult in the world of coupled sandpiles. Unlike the low-frequency spectra, the high-frequency spectra seem to obey a universal $f^{-2}$ law.