{"product_id":"scaling-self-similarity-and-intermediate-asymptotics-dimensional-analysis-and-intermediate-asymptotics-9780521435222","title":"Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics","description":"\u003cp\u003e • Author(s): G. I. Barenblatt | Grigory Isaakovich Barenblatt | Barenblatt Grigory Isaakovich\u003cbr\u003e • Publisher: Cambridge University Press\u003cbr\u003e • Publisher Imprint: Cambridge University Press\u003cbr\u003e • BISAC: Physics - Mathematical \u0026amp; Computational\u003c\/p\u003e\u003cp\u003eScaling (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.\u003c\/p\u003e","brand":"Cambridge University Press","offers":[{"title":"Paperback","offer_id":47614758584471,"sku":"9780521435222","price":10568.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780521435222.webp?v=1775096029","url":"https:\/\/atlanticbooks.com\/products\/scaling-self-similarity-and-intermediate-asymptotics-dimensional-analysis-and-intermediate-asymptotics-9780521435222","provider":"Atlantic Books","version":"1.0","type":"link"}