Fluctuation of the Top Location and Avalanches in the Formation Process of a Sandpile

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We investigate the formation processes of a sandpile using numerical simulation. We find a new relation between the fluctuation of the motion of the top and the surface state of a sandpile. The top moves frequently as particles are fed one by one every time interval T. The time series of the top location has the power spectrum which obeys a power law, S(f)∼fα, and its exponent α depends on T and the system size w. The surface state is characterized by two time scales; the lifetime of an avalanche, Ta, and the time required to cause an avalanche, Ts. The surface state is fluid-like when Ta∼Ts, and it is solid-like when Ta<<Ts. Our numerical results show that α is a function of Ts⁄Ta.

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