Scaling, Self-similarity, and Intermediate Asymptotics

Dimensional Analysis and Intermediate Asymptotics

G. I. Barenblatt - Collection Cambridge Texts in Applied Mathematics

386 pages, parution le 01/12/1996

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Résumé

Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.

Sommaire

Preface
Introduction
Dimensions, dimensional analysis and similarity
The application of dimensional analysis to the construction of intermediate asymptotic solutions to problems of mathematical physics. Self-similar solutions
Self-similarities of the second kind: first examples
Self-similarities of the second kind: further examples
Classification of similarity rules and self-similarity solutions. Recipe for application of similarity analysis
Scaling and transformation groups. Renormalization groups
Self-similar solutions and travelling waves
Invariant solutions: special problems of the theory
Scaling in deformation and fracture in solids
Scaling in turbulence
Scaling in geophysical fluid dynamics
Scaling: miscellaneous special problems

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	G. I. Barenblatt
Collection	Cambridge Texts in Applied Mathematics
Parution	01/12/1996
Nb. de pages	386
Couverture	Broché
Poids	540g
Intérieur	Noir et Blanc
EAN13	9780521435222
ISBN13	978-0-521-43522-2