Ebook: Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools

Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. This is the first textbook written by a well-known expert that provides a modern up-to-date introduction for workers outside statistical physics. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to post-docs in geophysics and meteorology.

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Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. This is the first textbook written by a well-known expert that provides a modern up-to-date introduction for workers outside statistical physics. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to post-docs in geophysics and meteorology.

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Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. This is the first textbook written by a well-known expert that provides a modern up-to-date introduction for workers outside statistical physics. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to post-docs in geophysics and meteorology.
Content:
Front Matter....Pages I-XXII
Useful Notions of Probability Theory....Pages 1-31
Sums of Random Variables, Random Walks and the Central Limit Theorem....Pages 33-57
Large Deviations....Pages 59-91
Power Law Distributions....Pages 93-121
Fractals and Multifractals....Pages 123-161
Rank-Ordering Statistics and Heavy Tails....Pages 163-197
Statistical Mechanics: Probabilistic Point of View and the Concept of “Temperature”....Pages 199-221
Long-Range Correlations....Pages 223-240
Phase Transitions: Critical Phenomena and First-Order Transitions....Pages 241-254
Transitions, Bifurcations and Precursors....Pages 255-266
The Renormalization Group....Pages 267-292
The Percolation Model....Pages 293-311
Rupture Models....Pages 313-344
Mechanisms for Power Laws....Pages 345-394
Self-Organized Criticality....Pages 395-439
Introduction to the Physics of Random Systems....Pages 441-456
Randomness and Long-Range Laplacian Interactions....Pages 457-475
Back Matter....Pages 477-529

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Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. This is the first textbook written by a well-known expert that provides a modern up-to-date introduction for workers outside statistical physics. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to post-docs in geophysics and meteorology.
Content:
Front Matter....Pages I-XXII
Useful Notions of Probability Theory....Pages 1-31
Sums of Random Variables, Random Walks and the Central Limit Theorem....Pages 33-57
Large Deviations....Pages 59-91
Power Law Distributions....Pages 93-121
Fractals and Multifractals....Pages 123-161
Rank-Ordering Statistics and Heavy Tails....Pages 163-197
Statistical Mechanics: Probabilistic Point of View and the Concept of “Temperature”....Pages 199-221
Long-Range Correlations....Pages 223-240
Phase Transitions: Critical Phenomena and First-Order Transitions....Pages 241-254
Transitions, Bifurcations and Precursors....Pages 255-266
The Renormalization Group....Pages 267-292
The Percolation Model....Pages 293-311
Rupture Models....Pages 313-344
Mechanisms for Power Laws....Pages 345-394
Self-Organized Criticality....Pages 395-439
Introduction to the Physics of Random Systems....Pages 441-456
Randomness and Long-Range Laplacian Interactions....Pages 457-475
Back Matter....Pages 477-529
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