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 Here
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: 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: Grigory Isaakovich Barenblatt
Publisher:
ISBN:
Category :
Languages : en
Pages : 386
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Book Description
Author: G. I. Barenblatt
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 248
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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: G. I. Barenblatt
Publisher:
ISBN: 9787506247252
Category : Mathematical physics
Languages : en
Pages : 386
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Book Description
Author: P. A. Martin
Publisher: Cambridge University Press
ISBN: 9780521414142
Category : Mathematics
Languages : en
Pages : 262
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Book Description
This volume contains papers by distinguished researchers in fluid mechanics and asymptotics. The papers collected here outline the development of these topics.
Author: Robert W. Batterman
Publisher: Oxford University Press
ISBN: 0198033478
Category : Philosophy
Languages : en
Pages : 156
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Book Description
Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines.
Author: Brian Cantwell
Publisher: Cambridge University Press
ISBN: 9780521777407
Category : Mathematics
Languages : en
Pages : 660
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Book Description
An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.
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.
