Titlebook: Critical Phenomena in Natural Sciences; Chaos, Fractals, Sel Didier Sornette Textbook 20001st edition Springer-Verlag Berlin Heidelberg 200

Osmosis

Encephalitis

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,Statistical Mechanics: Probabilistic Point of View and the Concept of “Temperature”,d within the thermodynamic theory of systems at equilibrium, as the inverse of the variation . of the entropy with respect to a variation of the energy ., at fixed system volume. If the variation of entropy . is large for a given variation of energy ., the temperature is small: the system has few ex

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Long-Range Correlations,viously the general situation and we will encounter it in different guises when dealing with the collective behavior of systems made up of many interacting elements. Studying the correlations and their consequences is an essential part of the analysis of a system since the correlations are the signa

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The Renormalization Group,m previously introduced in Chap. 2. The RG analysis, introduced in field theory and in critical phase transitions, is a very general mathematical (and conceptual) tool, which allows one to decompose the problem of finding the “macroscopic” behavior of a large number of interacting parts into a succe

Atrium

CORE

Rupture Models,na like the cracking of glass, aging of concrete, the failure of fiber networks in the formation of paper and the breaking of a metal bar subject to an external load. Failure of composite systems are of utmost importance in naval, aeronautics and space industries [596]. By the term composite, we ref

cavity

Mechanisms for Power Laws,tural phenomena have power law size distributions reading, in the notation of Chap. 4, . up to some large limiting cut-off [463, 7, 607]. In expression (14.1), .(.)d. is the probability to observe the variable in the range between . and . + d.. Power laws seem to also describe a large ensemble of so

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