Point-occurrence self-similarity in crackling-noise systems and in other complex systems

Abstract

It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is fulfilled, signaling the existence on those systems of self-similarity in time-size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not fulfill a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double power-law waiting-time densities. This is somehow reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.

arXiv commentSubmitted to J. Stat. Mech. for the proceedings of UPON 2008 (Lyon), topic: crackling noise

References in corpus (21)

• Crackling Noise
• Unified Scaling Law for Earthquakes
• Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes
• Critical phenomena in atmospheric precipitation
• A Complexity View of Rainfall
• Scaling and universality in rock fracture
• "Universal" Distribution of Inter-Earthquake Times Explained
• Signature of effective mass in crackling noise asymmetry
• Universality in solar flare and earthquake occurrence
• Universal Earthquake-Occurrence Jumps, Correlations with Time, and Anomalous Diffusion
• Interevent time distribution in seismicity: a theoretical approach
• Inter-occurrence Times in the Bak-Tang-Wiesenfeld Sandpile Model: A Comparison with the Turbulent Statistics of Solar Flares
• How far away is the next earthquake?
• Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares
• Correlations and invariance of seismicity under renormalization-group transformations
• The effect of thresholding on temporal avalanche statistics
• Time-Decreasing Hazard and Increasing Time until the Next Earthquake
• Fracture Processes Observed with A Cryogenic Detector
• Scaling and correlations in the dynamics of forest-fire occurrence
• Vere-Jones' Self-Similar Branching Model
• Epileptic Seizures: Quakes of the brain?

Cited by in corpus (7)

• Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator
• Power-law size distributions in geoscience revisited
• The effect of thresholding on temporal avalanche statistics
• Scaling in the Timing of Extreme Events
• The perils of thresholding
• Testing Universality in Critical Exponents: the Case of Rainfall
• Are Triggering Rates of Labquakes Universal? Inferring Triggering Rates From Incomplete Information