Scaling Self Similarity And Intermediate Asymptotics

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Scaling Self Similarity And Intermediate Asymptotics

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Author : G. I. Barenblatt
language : en
Publisher: Cambridge University Press
Release Date : 1996-12-12

Scaling Self Similarity And Intermediate Asymptotics written by G. I. Barenblatt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-12 with Mathematics categories.

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.

Scaling Self Similarity And Intermediate Asymptotics

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Author : Grigory Isaakovich Barenblatt
language : en
Publisher:
Release Date : 2005

Scaling Self Similarity And Intermediate Asymptotics written by Grigory Isaakovich Barenblatt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

Scaling Self Similarity And Intermediate Asymptotics Cambridge Texts In Applied Mathematics

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Author : G. I. Barenblatt
language : en
Publisher:
Release Date : 2000

Scaling Self Similarity And Intermediate Asymptotics Cambridge Texts In Applied Mathematics written by G. I. Barenblatt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematical physics categories.

Scaling

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Author : Grigory Isaakovich Barenblatt
language : en
Publisher: Cambridge University Press
Release Date : 2003-11-13

Scaling written by Grigory Isaakovich Barenblatt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-13 with Mathematics categories.

Many phenomena in nature, engineering or society when seen at an intermediate distance, in space or time, exhibit the remarkable property of self-similarity: they reproduce themselves as scales change, subject to so-called scaling laws. It's crucial to know the details of these laws, so that mathematical models can be properly formulated and analysed, and the phenomena in question can be more deeply understood. In this 2003 book, 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 attributes 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.

Similarity Self Similarity And Intermediate Asymptotics

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Author : G. I. Barenblatt
language : en
Publisher:
Release Date : 1979

Similarity Self Similarity And Intermediate Asymptotics written by G. I. Barenblatt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.

Scaling Self Similarity And Intermediate Asymptotics

DOWNLOAD
Author : Grigory Isaakovich Barenblatt
language : en
Publisher: Cambridge University Press
Release Date : 1996-12-12

Scaling Self Similarity And Intermediate Asymptotics written by Grigory Isaakovich Barenblatt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-12 with Mathematics categories.

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.

Scaling Self Similarity And Intermediate Asymptotics

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Author : G. I. Barenblatt
language : en
Publisher:
Release Date : 1996

Scaling Self Similarity And Intermediate Asymptotics written by G. I. Barenblatt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Differential equations categories.

Introduction To Symmetry Analysis Paperback With Cd Rom

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Author : Brian Cantwell
language : en
Publisher: Cambridge University Press
Release Date : 2002-09-23

Introduction To Symmetry Analysis Paperback With Cd Rom written by Brian Cantwell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-23 with Mathematics categories.

An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.

Similarity Self Similarity And Intermediate Asymptotics

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Author : G. I. Barenblatt
language : en
Publisher:
Release Date : 1979

Similarity Self Similarity And Intermediate Asymptotics written by G. I. Barenblatt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.

Applied Asymptotics

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Author : A. R. Brazzale
language : en
Publisher: Cambridge University Press
Release Date : 2007-05-31

Applied Asymptotics written by A. R. Brazzale and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-31 with Mathematics categories.

In fields such as biology, medical sciences, sociology, and economics researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small that approximations based on the normal distribution may be unreliable. Theoretical work over the last quarter-century has led to new likelihood-based methods that lead to very accurate approximations in finite samples, but this work has had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is oriented towards practice and comes with code in the R language (available from the web) which enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap or Bayesian methods.