Sandpiles Subjected to Sinusoidal Drive

TL;DR

This study investigates how a sinusoidal external drive influences avalanche behavior in a sandpile model, revealing anisotropic avalanche elongation, a transition between regimes, and power-law spectral properties that depend on the drive period.

Contribution

The paper introduces a theoretical Green function model for driven sandpiles and uncovers a transition between anisotropic avalanche elongation regimes based on the drive period.

Findings

Avalanches become elongated in the oscillation direction at large periods.

A regime shift occurs where avalanches elongate perpendicular to oscillations.

Power spectra exhibit power-law behavior with exponents varying with the period T.

Abstract

This paper considers a sandpile model subjected to a sinusoidal external drive with the time period $T$. We develop a theoretical model for the Green function in a large $T$ limit, which predicts that the avalanches are anisotropic and elongated in the oscillation direction. We track the problem numerically and show that the system shows additionally a regime where the avalanches are elongated in the perpendicular direction with respect to the oscillations. We find a transition point between these two regimes. The power spectrum of avalanche size and the grains wasted from the parallel and perpendicular directions are studied. These functions show power-law behaviour in terms of the frequency with exponents, which run with $T$.