Critical phenomena in natural sciences. Chaos, fractals, selforganization and disorder: concepts and tools
type: Item
instance of: scholarly article
title: Critical phenomena in natural sciences. Chaos, fractals, selforganization and disorder: concepts and tools
zbMATH Open document ID: 0977.82001
author: D. Sornette
published in: Springer Series in Synergetics
publication date: 2000-12-10T00:00:00Z
review text: The book introduces into a large variety of topics, most of which belong to or are related to statistical physics. The first six chapters deal with basic concepts, mainly probability, fractals, and statistics, including -- on a heuristic level -- limit theorems, large deviations, and extreme value theorems. Probability distributions on the real line are discussed in some detail, emphasizing power laws and distributions with heavy tails. This introductory part of the book comprises about 160 pages. The following twelve chapters provide brief descriptions of diverse models and results, amongst them long-range correlations, phase transitions, bifurcations, the renormalization group, percolation, rupture models, self-organized criticality, and random spin systems. The amount of material covered in the book is impressive; the list of references comprises 832 entries. The author's goal is to present concepts and results in the simplest and most intuitive way rather than emphasizing mathematical rigor. The global view and the vast amount of topics covered by this book may be of value for engineers, physicists, and for other scientists, in particular from geophysics and meteorology. For mathematicians the book may be useful in order to get an idea about how mathematical results are appreciated from the applications' side, and what mathematics is expected to do for applications.
reviewed by: Hans Crauel
Mathematics Subject Classification ID: 82-01
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 37N10
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 82B26
Mathematics Subject Classification ID: 82B27
Mathematics Subject Classification ID: 82B28
Mathematics Subject Classification ID: 82B31
zbMATH DE Number: 1541845
zbMATH Keywords: probability distributions
zbMATH Keywords: statistical physics
zbMATH Keywords: fractals
zbMATH Keywords: limit theorems
zbMATH Keywords: large deviations
zbMATH Keywords: extreme value theorems
zbMATH Keywords: power laws
zbMATH Keywords: distributions with heavy tails
zbMATH Keywords: long-range correlations
zbMATH Keywords: phase transitions
zbMATH Keywords: bifurcations
zbMATH Keywords: renormalization group
zbMATH Keywords: percolation
zbMATH Keywords: rupture models
zbMATH Keywords: self-organised criticality
zbMATH Keywords: random spin systems
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541845