272 pages, 100 figs
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 10 years after Per Bak and his co-workers presented their seminal idea, more than 2000 papers on this topic appeared. Seismology has been a field in earth sciences where the SOC concept has already deepened the understanding, but there seem to be much more examples in earth sciences where applying the SOC concept may be fruitful. After introducing the reader into the basics of fractals, chaos and SOC, the book presents established and new applications of SOC in earth sciences, namely earthquakes, forest fires, landslides and drainage networks.
From the reviews: "The book by S. Hergarten gives a comprehensive overview on two recently developed approaches in the study of natural phenomenon, namely fractals and SOC. Positive about this book ! is that focuses on geological examples, but it still gives the necessary theoretical background. Hence, the book can be read by geologists as a first contact with the theory of fractals and SOC. Another advantage is that the author looks at these new theories in a self-critical way ! ." (Andre Vervoort, Geologica Belgica, Vol. 7 (3-4), 2004)
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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