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Scaling, Self-similarity, and Intermediate Asymptotics : Dimensional Analysis and Intermediate Asymptotics - Grigory Isaakovich Barenblatt

Scaling, Self-similarity, and Intermediate Asymptotics

Dimensional Analysis and Intermediate Asymptotics

Paperback Published: 10th February 1997
ISBN: 9780521435222
Number Of Pages: 412

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Scaling (power-type) laws reveal the fundamental property of the phenomena--self similarity. Self-similar (scaling) phenomena repeat themselves in time and/or space. The property of self-similarity simplifies substantially the mathematical modeling of phenomena and its analysis--experimental, analytical and computational. The book begins from a non-traditional exposition of dimensional analysis, physical similarity theory and general theory of scaling phenomena. Classical examples of scaling phenomena are presented. It is demonstrated that scaling comes on a stage when the influence of fine details of initial and/or boundary conditions disappeared but the system is still far from ultimate equilibrium state (intermediate asymptotics). It is explained why the dimensional analysis as a rule is insufficient for establishing self-similarity and constructing scaling variables. Important examples of scaling phenomena for which the dimensional analysis is insufficient (self-similarities of the second kind) are presented and discussed. A close connection of intermediate asymptotics and self-similarities of the second kind with a fundamental concept of theoretical physics, the renormalization group, is explained and discussed. Numerous examples from various fields--from theoretical biology to fracture mechanics, turbulence, flame propagation, flow in porous strata, atmospheric and oceanic phenomena are presented for which the ideas of scaling, intermediate asymptotics, self-similarity and renormalization group were of decisive value in modeling.

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

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.

ISBN: 9780521435222
ISBN-10: 0521435226
Series: Cambridge Texts in Applied Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 412
Published: 10th February 1997
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.81 x 15.34  x 1.93
Weight (kg): 0.73

Earn 188 Qantas Points
on this Book