Description: Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics by G.I. Barenblatt, Grigory Isaakovich Barenblatt 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Author Biography G. I. Barenblatt is Emeritus G. I. Taylor Professor of Fluid Mechanics at the University of Cambridge, Emeritus Professor at the University of California, Berkeley, and Principal Scientist in the Institute of Oceanology of the Russian Academy of Sciences, Moscow. 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. Review A splendid and very readable work ... Greatly recommended! Sjoerd Rienstra, ITW Nieuws Promotional "Headline" This book deals with a non-traditional exposition of dimensional analysis, physical similarity theory and general theory of scaling phenomena. Description for Bookstore 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. Description for Library 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. Details ISBN0521435226 Author Grigory Isaakovich Barenblatt Short Title SCALING SELF-SIMILARITY & INTE Publisher Cambridge University Press Series Cambridge Texts in Applied Mathematics Language English ISBN-10 0521435226 ISBN-13 9780521435222 Media Book Format Paperback DEWEY 530.15 Series Number 14 Birth 1921 Year 1996 Publication Date 1996-12-31 Imprint Cambridge University Press Subtitle Dimensional Analysis and Intermediate Asymptotics Place of Publication Cambridge Country of Publication United Kingdom Illustrations Illustrations Pages 412 Affiliation University of Cambridge DOI 10.1604/9780521435222 Audience Professional and Scholarly UK Release Date 1996-12-12 AU Release Date 1996-12-12 NZ Release Date 1996-12-12 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:91367481;
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ISBN-13: 9780521435222
Book Title: Scaling, Self-Similarity, and Intermediate Asymptotics: Dimension
Number of Pages: 412 Pages
Language: English
Publication Name: Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics
Publisher: Cambridge University Press
Publication Year: 1996
Subject: Mathematics
Item Height: 229 mm
Item Weight: 600 g
Type: Textbook
Author: Grigory Isaakovich Barenblatt
Item Width: 152 mm
Format: Paperback
