Share
Scaling, Self-Similarity, and Intermediate Asymptotics Paperback: Dimensional Analysis and Intermediate Asymptotics (Cambridge Texts in Applied Mathematics)
Grigory Isaakovich Barenblatt
(Author)
·
Cambridge University Press
· Paperback
Scaling, Self-Similarity, and Intermediate Asymptotics Paperback: Dimensional Analysis and Intermediate Asymptotics (Cambridge Texts in Applied Mathematics) - Barenblatt, Grigory Isaakovich
Choose the list to add your product or create one New List
✓ Product added successfully to the Wishlist.
Go to My Wishlists
Origin: U.S.A.
(Import costs included in the price)
It will be shipped from our warehouse between
Friday, July 19 and
Friday, July 26.
You will receive it anywhere in United Kingdom between 1 and 3 business days after shipment.
Synopsis "Scaling, Self-Similarity, and Intermediate Asymptotics Paperback: Dimensional Analysis and Intermediate Asymptotics (Cambridge Texts in Applied Mathematics)"
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.