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: 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: 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: Annick LESNE
Publisher: Springer Science & Business Media
ISBN: 364215123X
Category : Science
Languages : en
Pages : 406
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Book Description
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.
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.
