Fractals - Fractal distributions Is the Earth's Surface Fractal?- Recognizing Power-Law Distributions - Do Cumulative Size Distributions Tell the Truth? - Binning - Censoring -- Self-Affine Time Series - Brownian Motion - Persistence, Stationarity, and Predictability -- Deterministic Chaos - Linear and Non-Linear Systems - Limit Sysles and Strange Attractors -- Self-Organized Criticality - Critical-Point Phenomena - Universality -- Earthquakes and Stick-Slip Motion - The Fractal Character of Earthquakes - Efficient Simulation of the OFC Model -- Landslides - Triggering Mechanisms and Driving Forces - On Predicting Slope Stability -- Drainage Networks - Fractal Properties of Drainage Networks - Optimization by Permanent Reorganization?- Where do we stand? - Some Fractal Size Distributions - Tools for Data Analysis - The Lorenz Equations - Numerics of Ordinary Differential Equations.
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Text of Note
Self-organized criticality (SOC) has become a magic word in various scientific disciplines, it provides a framework for understanding complexity and scale invariance in systems showing irregular fluctuations. In the first years since Per Bak and his co-workers presented their seminal idea, more than 2000 papers on this topic have been published. Seismology has been a rich field in earth sciences where the SOC concept has already deepened understanding, but there seem to be many more examples in earth sciences where applying the SOC concept may be fruitful. After introducing the reader to the basics of fractals, chaos and SOC the book presents established and new applications of SOC in the earth sciences: earthquakes, forest fires, landslides and drainage networks.