Hydrodynamic behaviour of an Abelian Sandpile Model with Laplacian rules

TL;DR

This paper introduces a modified Abelian Sandpile Model incorporating Laplacian rules, which maintains mathematical properties while exhibiting more realistic hydrodynamic behavior.

Contribution

The paper presents a new sandpile model with Laplacian rules that preserves abelianity and demonstrates enhanced hydrodynamic features compared to traditional models.

Findings

Model preserves abelian property

Displays realistic hydrodynamic behavior

Shares mathematical properties with original model

Abstract

We present a sandpile model, in which the instability of a site is determined also by the variables in a neighbourhood. This is a modification of the Abelian Sandpile Model, in which abelianity is preserved: it shares several mathematical properties of the original abelian model, while producing a more realistic dynamics. We show how our model presents interesting hydrodynamic features.