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Exactly solvable sandpile with fractal avalanching
P Helander1, S C Chapman, R O Dendy
1EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon OX14 3DB, United Kingdom.
Summary
This study introduces a simple, solvable one-dimensional sandpile model exhibiting scale-free and fractal properties. The model demonstrates power-law distributions for avalanche energy and time series, offering insights into complex system dynamics.
Area of Science:
- Complex Systems
- Statistical Physics
- Dynamical Systems
Background:
- Sandpile models are used to study self-organized criticality.
- Understanding scale-free behavior and fractal properties is crucial in complex systems.
Purpose of the Study:
- To construct a simple, analytically solvable one-dimensional sandpile model.
- To investigate the emergence of scale-free behavior and fractal properties.
- To analyze avalanche energy and time series distributions.
Main Methods:
- Development of a one-dimensional sandpile model.
- Exact analytical solution applied to the model.
- Analysis of avalanche dynamics and energy distributions.
Main Results:
- The model exhibits exact analytical solvability.
- Scale-free behavior and fractal properties are observed.
- Avalanche energy and time series follow power laws with an index of -1 (1/f spectra).
Conclusions:
- A simple, solvable sandpile model can reproduce complex phenomena like self-organized criticality.
- The model's continuous, nowhere differentiable formula describes its shape and energy.
- The findings contribute to understanding universal properties in complex systems.