Colored Sandpile

TL;DR

This paper introduces a colored sandpile model where particles of different colors move along specific axes and interact through toppling, resulting in unique steady states and avalanche distributions, expanding understanding of non-abelian sandpile universality classes.

Contribution

The study presents a novel colored sandpile model with directed particle motion and non-abelian interactions, revealing new steady states and avalanche behaviors.

Findings

Different steady states compared to traditional models

Distinct avalanche size distributions observed

Non-trivial spatial structures identified

Abstract

After the introduction of sandpile model a number of different variants have been studied. In most of these models sand particles are indistinguishable. Here we have painted the sand particles using a few distinct colors, and restrict them to move in linear trajectories only along their assigned lattice axes, one axis reserved for one color. Different colored particles interact among themselves through the toppling of unstable sand columns. Consequently, the avalanches or in general the self-organization processes in the sandpile has no overall preferred direction, though the individual particles execute directed motion. For such non-abelian colored sandpiles the steady states are found to be different and also the avalanche size distributions. This sandpile so defined has a non-trivial spatial structure and belongs to a different universality class of sandpile models. Dynamics of a granular heap with grains of different colors and properties may be described using this sandpile.