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cover of the book Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools

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

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27.01.2024
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Content:
Front Matter....Pages I-XVII
Useful Notions of Probability Theory....Pages 1-22
Sums of Random Variables, Random Walks and the Central Limit Theorem....Pages 23-45
Large Deviations....Pages 47-77
Power Law Distributions....Pages 79-101
Fractals and Multifractals....Pages 103-135
Rank-Ordering Statistics and Heavy Tails....Pages 137-162
Statistical Mechanics: Probabilistic Point of View and the Concept of “Temperature”....Pages 163-181
Long-Range Correlations....Pages 183-198
Phase Transitions: Critical Phenomena and First-Order Transitions....Pages 199-212
Transitions, Bifurcations and Precursors....Pages 213-224
The Renormalization Group....Pages 225-237
The Percolation Model....Pages 239-256
Rupture Models....Pages 257-284
Mechanisms for Power Laws....Pages 285-320
Self-Organized Criticality....Pages 321-360
Introduction to the Physics of Random Systems....Pages 361-374
Randomness and Long-Range Laplacian Interactions....Pages 375-392
Back Matter....Pages 393-434



Content:
Front Matter....Pages I-XVII
Useful Notions of Probability Theory....Pages 1-22
Sums of Random Variables, Random Walks and the Central Limit Theorem....Pages 23-45
Large Deviations....Pages 47-77
Power Law Distributions....Pages 79-101
Fractals and Multifractals....Pages 103-135
Rank-Ordering Statistics and Heavy Tails....Pages 137-162
Statistical Mechanics: Probabilistic Point of View and the Concept of “Temperature”....Pages 163-181
Long-Range Correlations....Pages 183-198
Phase Transitions: Critical Phenomena and First-Order Transitions....Pages 199-212
Transitions, Bifurcations and Precursors....Pages 213-224
The Renormalization Group....Pages 225-237
The Percolation Model....Pages 239-256
Rupture Models....Pages 257-284
Mechanisms for Power Laws....Pages 285-320
Self-Organized Criticality....Pages 321-360
Introduction to the Physics of Random Systems....Pages 361-374
Randomness and Long-Range Laplacian Interactions....Pages 375-392
Back Matter....Pages 393-434
....
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