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Published on: August 1, 2011
1/f(alpha) noise from correlations between avalanches in self-organized criticality
1Department of Mathematics, Imperial College of Science, Technology, and Medicine, London, SW7 2BZ, United Kingdom. davidsen@theo-physik.uni-kiel.de
Summary
Large, slowly driven systems can reach a self-organized critical state, generating 1/f(alpha) noise from correlated avalanches. This phenomenon, observed in sandpile models, links noise characteristics to avalanche power-law distributions.
Area of Science:
- Complex systems science
- Statistical physics
- Nonlinear dynamics
Background:
- Many natural and artificial systems exhibit complex emergent behaviors.
- Self-organized criticality (SOC) is a hypothesized mechanism for generating power-law statistics and 1/f noise in such systems.
- Understanding the emergence of low-frequency noise (1/f noise) is crucial in various scientific fields.
Purpose of the Study:
- To demonstrate that large, slowly driven systems can naturally evolve into a self-organized critical state.
- To investigate the relationship between temporal correlations of bursts and the generation of 1/f(alpha) noise.
- To analyze the statistical properties of avalanches and their connection to noise characteristics.
Main Methods:
- Theoretical analysis of driven complex systems.
- Numerical simulations of a deterministic sandpile model.
- Statistical analysis of avalanche event distributions and temporal correlations.
Main Results:
- Large, slowly driven systems can spontaneously reach a self-organized critical state.
- This critical state is characterized by long-range temporal correlations between avalanches.
- These correlations produce low-frequency 1/f(alpha) noise, with avalanches exhibiting power-law statistics.
- A scaling relation was identified between the noise exponent (alpha) and the avalanche power-law exponent in the sandpile model.
Conclusions:
- Self-organized criticality provides a viable mechanism for generating 1/f noise in driven systems.
- The observed power-law distributions and temporal correlations are key signatures of SOC.
- The sandpile model serves as a concrete example illustrating these principles and their interrelations.
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