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

TL;DR

This study uses numerical simulations to explore how the top movement fluctuation relates to the surface state and avalanche dynamics in a sandpile, revealing power-law behavior and state-dependent exponents.

Contribution

It uncovers a new relation between top fluctuation power spectra and surface state characterized by avalanche time scales in sandpile formation.

Findings

Power spectrum of top movement follows a power law with an exponent depending on feeding interval and system size.

Surface state transitions from fluid-like to solid-like based on avalanche time scales.

Exponent of power spectrum correlates with the ratio of surface time scales.

Abstract

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^{\alpha}, and its exponent \alpha 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 \alpha is a function of T_{s}/T_{a}.