Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics free ebook download.

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Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics free ebook download

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Mathematics

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Author(s):	aling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptot

Date:	2019	Format:	PDF	Language:	English	ISBN/ASIN:	0521435226
Pages:	1	OCR:		Quality:		ISBN13:
Uploader:	stirkout	Upload Date:	5/18/2019 11:25:50 PM

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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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2497991	Book	http://tezfiles.com/file/9c1ebfa945ce0...		18.00	stirkout

Tags: Analysis Asymptotics Dimensional Intermediate Scaling Self-similarity

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