Scaling, Self-Similarity and Intermediate Asymptotics Dimensional Analysis and Intermediate Asymptotics
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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.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $98.00
Copyright year: 1996
Publisher: Cambridge University Press
Publication date: 12/12/1996
Size: 6.25" wide x 9.25" long x 0.75" tall
|Dimensions, dimensional analysis and similarity|
|The application of dimensional analysis to the construction of intermediate asymptotic solutions to problems of mathematical physics|
|Self-similarities of the second kind: first examples|
|Self-similarities of the second kind: further examples|
|Classification of similarity rules and self-similarity solutions|
|Recipe for application of similarity analysis|
|Scaling and transformation groups. Renormalization groups|
|Self-similar solutions and travelling waves|
|Invariant solutions: special problems of the theory|
|Scaling in deformation and fracture in solids|
|Scaling in turbulence|
|Scaling in geophysical fluid dynamics|
|Scaling: miscellaneous special problems|