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

• Main Author: Sornette, Didier (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Edition: Second Edition.
• Series: Springer Series in Synergetics,
• Subjects: Physics.; Earth sciences.; Game theory.; Statistical physics.; Dynamical systems.; Statistical Physics, Dynamical Systems and Complexity.; Earth Sciences, general.; Game Theory, Economics, Social and Behav. Sciences.

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 fi...

Table of Contents:

• Useful Notions of Probability Theory
• Sums of Random Variables, Random Walks and the Central Limit Theorem
• Large Deviations
• Power Law Distributions
• Fractals and Multifractals
• Rank-Ordering Statistics and Heavy Tails
• Statistical Mechanics: Probabilistic Point of View and the Concept of “Temperature”
• Long-Range Correlations
• Phase Transitions: Critical Phenomena and First-Order Transitions
• Transitions, Bifurcations and Precursors
• The Renormalization Group
• The Percolation Model
• Rupture Models
• Mechanisms for Power Laws
• Self-Organized Criticality
• to the Physics of Random Systems
• Randomness and Long-Range Laplacian Interactions.