{"product_id":"scaling-self-similarity-and-intermediate-asymptotics-grigory-isaakovich-barenblatt-9780521435222","title":"Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics","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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Grigory Isaakovich Barenblatt\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0521435226\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780521435222\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Cambridge University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/12\/1996\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 412\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.60lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 8.98h x 6.04w x 0.76d","brand":"Grigory Isaakovich Barenblatt","offers":[{"title":"Paperback","offer_id":44119803527423,"sku":"9780521435222","price":105.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_574f8b4b-e077-4e80-81b7-5dce59553f46.jpg?v=1687411019","url":"https:\/\/www.whiterainbookhouse.com\/products\/scaling-self-similarity-and-intermediate-asymptotics-grigory-isaakovich-barenblatt-9780521435222","provider":"WR Book House","version":"1.0","type":"link"}