Scaling Self Similarity And Intermediate Asymptotics Cambridge Texts In Applied Mathematics
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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.
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.
Practical Applied Mathematics
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Author : Sam Howison
language : en
Publisher: Cambridge University Press
Release Date : 2005-03-24
Practical Applied Mathematics written by Sam Howison 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 2005-03-24 with Mathematics categories.
Drawing from a wide variety of mathematical subjects, this book aims to show how mathematics is realised in practice in the everyday world. Dozens of applications are used to show that applied mathematics is much more than a series of academic calculations. Mathematical topics covered include distributions, ordinary and partial differential equations, and asymptotic methods as well as basics of modelling. The range of applications is similarly varied, from the modelling of hair to piano tuning, egg incubation and traffic flow. The style is informal but not superficial. In addition, the text is supplemented by a large number of exercises and sideline discussions, assisting the reader's grasp of the material. Used either in the classroom by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them.
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.
Nonlinear Evolution Equations And Related Topics
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Author : Wolfgang Arendt
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-08-20
Nonlinear Evolution Equations And Related Topics written by Wolfgang Arendt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-20 with Mathematics categories.
Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.
Analytic Combinatorics
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Author : Philippe Flajolet
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-15
Analytic Combinatorics written by Philippe Flajolet 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 2009-01-15 with Mathematics categories.
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Singularities Formation Structure And Propagation
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Author : J. Eggers
language : en
Publisher: Cambridge University Press
Release Date : 2015-09-10
Singularities Formation Structure And Propagation written by J. Eggers 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 2015-09-10 with Mathematics categories.
This book explores a wide range of singular phenomena, providing mathematical tools for understanding them and highlighting their common features.