Avalanches, Scaling and Coherent Noise

Abstract

We present a simple model of a dynamical system driven by externally-imposed coherent noise. Although the system never becomes critical in the sense of possessing spatial correlations of arbitrarily long range, it does organize into a stationary state characterized by avalanches with a power-law size distribution. We explain the behavior of the model within a time-averaged approximation, and discuss its potential connection to the dynamics of earthquakes, the Gutenberg-Richter law, and to recent experiments on avalanches in rice piles.

17 pages, 4 Postscript figures, written in LaTeX using RevTeX and epsfig.sty

References in corpus (5)

• Avalanche Dynamics in Evolution, Growth, and Depinning Models
• Rank-Ordering Statistics of Extreme Events: Application to the Distribution of Large Earthquakes
• Tracer Dispersion in a Self-Organized Critical System
• Transport in Sand Piles, Interface Depinning, and Earthquake Models
• Mass-extinction: Evolution and the effects of external influences on unfit species

Cited by in corpus (36)

• Power laws and Self-Organized Criticality in Theory and Nature
• Experiments in vortex avalanches
• Universality of Zipf's Law
• Neutral Mutations and Punctuated Equilibrium in Evolving Genetic Networks
• Vortex avalanches and self organized criticality in superconducting niobium
• Unpinning triggers for superfluid vortex avalanches
• Econophysics of adaptive power markets: When a market does not dampen fluctuations but amplifies them
• Coherent noise, scale invariance and intermittency in large systems
• Analysis of return distributions in the coherent noise model
• Knock-on processes in superfluid vortex avalanches and pulsar glitch statistics
• Power law burst and inter-burst interval distributions in the solar wind: turbulence or dissipative SOC ?
• Neutron star glitches have a substantial minimum size
• Aging in coherent noise models and natural time
• Broad distribution of stick-slip events in Slowly Sheared Granular Media: Table-top production of a Gutenberg-Richter-like distribution
• Length Scales and Power Laws in the Two-Dimensional Forest-Fire Model
• A Simple Model of Evolution with Variable System Size
• The Importance of Antipersistence for Traffic Jams
• Extremal dynamics model on evolving networks
• Aftershocks in Coherent-Noise Models
• Diversity waves in collapse-driven population dynamics
• Stretched exponentials and power laws in granular avalanching
• Crossover to Self-Organized Criticality in an Inertial Sandpile Model
• Approaching a large deviation theory for complex systems
• Sensitivity to initial conditions in coherent noise models
• Calculation of the transition matrix and of the occupation probabilities for the states of the Oslo sandpile model
• Long-term statistics of pulsar glitches due to history-dependent avalanches
• Collective effects and synchronization of demand in real-time demand response
• Theoretical and Observational Evidence for Coriolis Effects in Coronal Magnetic Fields Via Direct Current Driven Flaring Events
• Network growth approach to macroevolution
• Hierarchical noise in large systems of independent agents
• Lifetimes of agents under external stress
• Evolutionary ecology in-silico: Does mathematical modelling help in understanding the "generic" trends?
• Defining and finding lifelike entities with a lazy filter
• Exploration-exploitation trade-off features a saltatory search behaviour
• Stochastic and Discrete Time Models of Long-Range Turbulent Transport in the Scrape-Off Layer
• A model of mass extinction