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Home > Catalog > Scaling, Self-similarity, and Intermediate Asymptotics
Scaling, Self-similarity, and Intermediate Asymptotics
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Details

  • Page extent: 412 pages
  • Size: 228 x 152 mm
  • Weight: 0.6 kg

Library of Congress

  • Dewey number: 530.1/5
  • Dewey version: 20
  • LC Classification: QA401 .B3713 1996
  • LC Subject headings:
    • Mathematical physics
    • Dimensional analysis
    • Differential equations--Asymptotic theory
    • Great Britain--Foreign relations--1660-1688
    • Patriotism--England--History--17th century

Library of Congress Record

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Paperback

 (ISBN-13: 9780521435222 | ISBN-10: 0521435226)

  • There was also a Hardback of this title but it is no longer available
  • Published December 1996

Manufactured on demand: supplied direct from the printer

$98.00 (P)

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.

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.

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