Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics (Cambridge Texts in Applied Mathematics, Series Number 14) - Softcover

Barenblatt, Grigory Isaakovich

Softcover

ISBN 10: 0521435226 ISBN 13: 9780521435222

Publisher: Cambridge University Press, 1996

Synopsis

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.

About this title

Book Description

Beginning from a nontraditional exposition of dimensional analysis, this text uses 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.

About the Author

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1996
• ISBN 10: 0521435226
• ISBN 13: 9780521435222
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 412