Editorial Reviews
Review
'A splendid and very readable work ... Greatly recommended!' Sjoerd Rienstra, ITW Nieuws
Book Description
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.
Scaling, Self-similarity, and Intermediate Asymptotics : Dimensional Analysis and Intermediate Asymptotics (Cambridge Texts in Applied Mathematics)
Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics (Cambridge Texts in Applied Mathematics),Grigory Isaakovich Barenblatt,M. J. Ablowitz,S. H. Davis,E. J. Hinch,A. Iserles,J. Ockendon,P. J. Olver,Cambridge University Press,0521435226,Applied,Asymptotic theory,Differential equations,Dimensional analysis,Mathematical Analysis,Mathematical Physics,Mathematics,Science/Mathematics,Applied mathematics,Mathematics / Graphic Methods,Probability & statistics
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