Scaling, Self-similarity, and Intermediate Asymptotics PDF Download
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Author: G. I. Barenblatt
Publisher: Cambridge University Press
ISBN: 9780521435222
Category : Mathematics
Languages : en
Pages : 412
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Book Description
Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.
Author: G. I. Barenblatt
Publisher: Cambridge University Press
ISBN: 9780521435222
Category : Mathematics
Languages : en
Pages : 412
Get Book
Book Description
Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.
Author: G. I. Barenblatt
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 248
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Book Description
Author: Grigory Isaakovich Barenblatt
Publisher:
ISBN:
Category :
Languages : en
Pages : 386
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Book Description
Author: G. Barenblatt
Publisher: Springer
ISBN: 9781461585701
Category : Technology & Engineering
Languages : en
Pages : 0
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Book Description
Professor Grigorii Isaakovich Barenblatt has written an outstanding book that contains an attempt to answer the very important questions of how to under stand complex physical processes and how to interpret results obtained by numerical computations. Progress in numerical calculation brings not only great good but also notori ously awkward questions about the role of the human mind. The human partner in the interaction of a man and a computer often turns out to be the weak spot in the relationship. The problem of formulating rules and extracting ideas from vast masses of computational or experimental results remains a matter for our brains, our minds. This problem is closely connected with the recognition of patterns. It is not just a coincidence that in both the Russian and English languages the word "obvious" has two meanings-not only something easily and clearly understood, but also something immediately evident to our eyes. The identification of forms and the search for invariant relations constitute the foundation of pattern recognition; thus, we identify the similarity oflarge and small triangles, etc.
Author: G. I. Barenblatt
Publisher:
ISBN: 9787506247252
Category : Mathematical physics
Languages : en
Pages : 386
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Book Description
Author: G. I. Barenblatt
Publisher: Cambridge University Press
ISBN: 0521826578
Category : Mathematics
Languages : en
Pages : 187
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Book Description
The author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural consequences of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.
Author: G. I. Barenblatt
Publisher:
ISBN: 9781107050242
Category : Differential equations
Languages : en
Pages : 386
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Book Description
Author: G. I. Barenblatt
Publisher: CUP Archive
ISBN: 9780521469203
Category : Mathematics
Languages : en
Pages : 60
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Book Description
This book presents the text of the inaugural lecture of Professor G. I. Barenblatt which deals with a study of scaling phenomena in several topics studied by G. I. Taylor throughout his varied career.
Author: Neil M. Ribe
Publisher: Cambridge University Press
ISBN: 1107174465
Category : Science
Languages : en
Pages : 331
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Book Description
Comprehensive, mathematically advanced treatment of the continuum mechanics of the Earth's mantle and the geodynamic models used to investigate it.
Author: Andrew J. Majda
Publisher: Cambridge University Press
ISBN: 9780521639484
Category : Mathematics
Languages : en
Pages : 562
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Book Description
This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprise a modern applied mathematics graduate course on the weak solution theory for incompressible flow.
