Sandpile Model for Relaxation in Complex Systems

TL;DR

This paper introduces a sandpile model to simulate relaxation phenomena in complex systems, capturing features like long tails, aging, and fractal time distributions through simple simulations.

Contribution

It presents a novel sandpile-based model incorporating avalanches and feedback to replicate complex relaxation behaviors.

Findings

Reproduces long tail relaxation dynamics.

Demonstrates aging effects in the model.

Shows fractal distribution of characteristic times.

Abstract

The relaxation in complex systems is in general nonexponential. After an initial rapid decay the system relax slowly following a long time tail. In the present paper a sandpile modelation of the relaxation in complex systems is analysed. Complexity is introduced by a process of avalanches in the Bethe lattice and a feedback mechanism which leads to slower decay with increasing time. In this way, some features of relaxation in complex systems: long time tails relaxation, aging, and fractal distribution of characteristic times, are obtained by simple computer simulations.