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

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)∼ f^α, 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, T_a, and the time required to cause an avalanche, T_s. The surface state is fluid-like when T_a∼ T_s, and it is solid-like when T_a≪ T_s. Our numerical results show that α is a function of T_s/T_a.