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

Scaling, Self-similarity, And Intermediate Asymptotics: Dimensional Analysis and Intermediate…

byGrigory Isaakovich Barenblatt

Paperback | December 28, 1996

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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.
Title:Scaling, Self-similarity, And Intermediate Asymptotics: Dimensional Analysis and Intermediate…Format:PaperbackDimensions:412 pages, 8.98 × 5.98 × 0.91 inPublished:December 28, 1996Publisher:Cambridge University Press

The following ISBNs are associated with this title:

ISBN - 10:0521435226

ISBN - 13:9780521435222


Table of Contents

Preface; Introduction; 1. Dimensions, dimensional analysis and similarity; 2. The application of dimensional analysis to the construction of intermediate asymptotic solutions to problems of mathematical physics. Self-similar solutions; 3. Self-similarities of the second kind: first examples; 4. Self-similarities of the second kind: further examples; 5. Classification of similarity rules and self-similarity solutions. Recipe for application of similarity analysis; 6. Scaling and transformation groups. Renormalization groups. 7. Self-similar solutions and travelling waves; 8. Invariant solutions: special problems of the theory; 9. Scaling in deformation and fracture in solids; 10. Scaling in turbulence; 11. Scaling in geophysical fluid dynamics; 12. Scaling: miscellaneous special problems.

Editorial Reviews

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