Scaling, Self-similarity, and Intermediate Asymptotics

Dimensional Analysis and Intermediate Asymptotics

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Paperback | 10 February 1997

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412 Pages

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22.86 x 15.24 x 2.34

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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.

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'A splendid and very readable work ... Greatly recommended!' Sjoerd Rienstra, ITW Nieuws

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Non-Fiction Science Physics Mathematics Calculus & Mathematical Analysis Probability & Statistics Applied Mathematics

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
Table of Contents provided by Publisher. All Rights Reserved.

Scaling, Self-similarity, and Intermediate Asymptotics

Dimensional Analysis and Intermediate Asymptotics

At a Glance

Paperback

Industry Reviews

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How to return your order

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