Dynamics of Eulerian walkers

TL;DR

This paper studies the behavior of Eulerian walkers as a model of self-organized criticality, analyzing avalanche structures, critical exponents, and diffusion properties during evolution from randomness to criticality.

Contribution

It provides a detailed description of avalanche structures, determines the critical exponent, and characterizes the diffusion law in the critical state of Eulerian walkers.

Findings

Avalanche distribution follows a power law with exponent τ=2.

Eulerian walkers exhibit simple diffusion in the critical state.

System evolves from a random to a critical state with identifiable dynamics.

Abstract

We investigate the dynamics of Eulerian walkers as a model of self-organized criticality. The evolution of the system is subdivided into characteristic periods which can be seen as avalanches. The structure of avalanches is described and the critical exponent in the distribution of first avalanches $\tau=2$ is determined. We also study a mean square displacement of Eulerian walkers and obtain a simple diffusion law in the critical state. The evolution of underlying medium from a random state to the critical one is also described.