Boundary-induced anisotropy of the avalanches in the sandpile automaton

TL;DR

This study numerically investigates how boundary effects influence avalanche anisotropy in a 2D sandpile model, revealing size-dependent boundary influence without lattice-induced anisotropy up to size 1001.

Contribution

It demonstrates the boundary-induced anisotropy in avalanches and shows that larger avalanches are affected by system boundaries, with no lattice anisotropy observed up to size 1001.

Findings

Smaller avalanches are isotropic near the center.

Larger avalanches are increasingly affected by the boundary.

No lattice-induced anisotropy observed up to size 1001.

Abstract

We study numerically the avalanches in a two--dimensional critical height sandpile model with sand grains added at the center of the system. Smaller avalanches near the center of the system are isotropic. Larger avalanches are, however, affected by the boundary of the system, to a degree that increases with the avalanche size. Up to linear system size $L=1001$, we did not find an obvious indication for lattice--induced anisotropy.