Nonlinear Instability Chaos And Turbulence
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Nonlinear Instability Chaos And Turbulence
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Author : Lokenath Debnath
language : en
Publisher: Computational Mechanics
Release Date : 1998
Nonlinear Instability Chaos And Turbulence written by Lokenath Debnath and has been published by Computational Mechanics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Medical categories.
The second volume in a study of nonlinear stability, chaos and turbulence. It demonstrates the importance of mathematical, computational and experimental techniques to the advancement of research in nonlinear instability, chaotic motions and turbulent flow systems.
Nonlinear Instability Chaos And Turbulence
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Author : Lokenath Debnath
language : en
Publisher: Computational Mechanics
Release Date : 1998
Nonlinear Instability Chaos And Turbulence written by Lokenath Debnath and has been published by Computational Mechanics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.
This is a collection of research and research-expository articles written by leading experts who have made important contributions to the areas of non-linear instability, chaos and turbulence. It brings together developments in the theory and applications of the subjects and related topics which are likely to determine fruitful directions for further study and research. It is also intended as a reference guide for the readers interested in advance study and research in non-linear phenomena.
Instabilities Chaos And Turbulence
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Author : Paul Manneville
language : en
Publisher: World Scientific
Release Date : 2010
Instabilities Chaos And Turbulence written by Paul Manneville and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.
From Instability To Intelligence
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Author : Michail Zak
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-11
From Instability To Intelligence written by Michail Zak 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 2008-12-11 with Science categories.
So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. -A. Einstein The word "instability" in day-to-day language is associated with some thing going wrong or being abnormal: exponential growth of cancer cells, irrational behavior of a patient, collapse of a structure, etc. This book, however, is about "good" instabilities, which lead to change, evolution, progress, creativity, and intelligence; they explain the paradox of irreversi bility in thermodynamics, the phenomena of chaos and turbulence in clas sical mechanics, and non-deterministic (multi-choice) behavior in biological and social systems. The concept of instability is an attribute of dynamical models that de scribe change in time of physical parameters, biological or social events, etc. Each dynamical model has a certain sensitivity to small changes or "errors" in initial values of its variables. These errors may grow in time, and if such growth is of an exponential rate, the behavior of the variable is defined as unstable. However, the overall effect of an unstable variable upon the dynamical system is not necessarily destructive. Indeed, there al ways exists such a group of variables that do not contribute to the energy of the system. In mechanics such variables are called ignorable or cyclic.
Nonlinear Dynamics And Chaos
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Author : Steven H. Strogatz
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Nonlinear Dynamics And Chaos written by Steven H. Strogatz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Continuum Mechanics And Applications In Geophysics And The Environment
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Author : Brian Straughan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Continuum Mechanics And Applications In Geophysics And The Environment written by Brian Straughan 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 2013-03-09 with Science categories.
This book is dedicated to Professor Kolumban Hutter of the Darmstadt Univer sity of Technology on the occasion of his 60th birthday on 22 January 200l. Professor Hutter graduated in Civil Engineering from the ETH Zurich, and then worked in industry-related consulting at the Institute of Mechanics and the Laboratory of Hydraulics and Soil Mechanics at the ETH, before embark ing on a PhD in Theoretical and Applied Mechanics in Cornell University. He duly completed his PhD under the supervision of Professor Y. H. Pao, working in the field of the electrodynamics of continuous media. After his PhD, Professor Hutter returned to Europe where he worked as a senior scientist at the Labor atory for Hydraulics, Hydrology and Glaciology, ETH Zurich, being involved in glacier flow, physical limnology, avalanche research and granular media. At the same time he maintained scientific contact with the Mechanics Institute of the Vienna University of Technology. In both European cities he received a habil itation degree: In Vienna for Mechanics, in Zurich for Theoretical Glaciology and Limnology. Since 1987 Professor Hutter has been the successor to Professor Becker at the Department of Mechanics, Darmstadt University of Technology. Professor Hutter's work has always been relevant to reallife, and a feature of the man is his attention to experiments and matching theory. He has built up an internationally respected laboratory in Darmstadt which concentrates on both experimental and theoretical aspects.
Physics Of Buoyant Flows From Instabilities To Turbulence
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Author : Mahendra Kumar Verma
language : en
Publisher: World Scientific
Release Date : 2018-05-30
Physics Of Buoyant Flows From Instabilities To Turbulence written by Mahendra Kumar Verma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-30 with Science categories.
Gravity pervades the whole universe; hence buoyancy drives fluids everywhere including those in the atmospheres and interiors of planets and stars. Prime examples of such flows are mantle convection, atmospheric flows, solar convection, dynamo process, heat exchangers, airships and hot air balloons. In this book we present fundamentals and applications of thermal convection and stratified flows.Buoyancy brings in extremely rich phenomena including waves and instabilities, patterns, chaos, and turbulence. In this book we present these topics in a systematic manner. First we present a unified treatment of linear theory that yields waves and thermal instability for stably and unstably-stratified flows respectively. We extend this analysis to include rotation and magnetic field. We also describe nonlinear saturation and pattern formation in Rayleigh-Bénard convection.The second half of the book is dedicated to buoyancy-driven turbulence, both in stably-stratified flow and in thermal convection. We describe the spectral theory including energy flux and show that the thermally-driven turbulence is similar to hydrodynamic turbulence. We also describe large-scale quantities like Reynolds and Nusselt numbers, flow anisotropy, and the dynamics of flow structures, namely flow reversals. Thus, this book presents all the major aspects of the buoyancy-driven flows in a coherent manner that would appeal to advanced graduate students and researchers.
Nonlinear Dynamics And Chaotic Phenomena An Introduction
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Author : Bhimsen K. Shivamoggi
language : en
Publisher: Springer
Release Date : 2014-05-14
Nonlinear Dynamics And Chaotic Phenomena An Introduction written by Bhimsen K. Shivamoggi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Technology & Engineering categories.
This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special emphasis on some aspects of fluid dynamics and plasma physics reflecting the author’s involvement in these areas of physics. A few exercises have been provided that range from simple applications to occasional considerable extension of the theory. Finally, the list of references given at the end of the book contains primarily books and papers used in developing the lecture material this volume is based on. This book has grown out of the author’s lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism has been kept to a minimum. This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theoretically inclined researcher in the physical sciences and engineering. This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity and precision, updating and amplification of several sections, addition of new material like theory of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and critical phenomena perspectives on the fluid turbulence problem and many new exercises.
An Informal Introduction To Turbulence
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Author : A. Tsinober
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
An Informal Introduction To Turbulence written by A. Tsinober 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 2006-04-11 with Science categories.
To Turbulence by ARKADY TSINOBER Department of Fluid Mechanics, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBookISBN: 0-306-48384-X Print ISBN: 1-4020-0110-X ©2004 Kluwer Academic Publishers NewYork, Boston, Dordrecht, London, Moscow Print ©2001 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook maybe reproducedor transmitted inanyform or byanymeans, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://kluweronline. com and Kluwer's eBookstoreat: http://ebooks. kluweronline. com TO My WITS TABLE OF CONTENTS 1 INTRODUCTION 1 Brief history 1 1. 1 1. 2 Nature and major qualitative universal features of turbulent flows 2 1. 2. 1 Representative examples of turbulent flows 2 1. 2. 2 In lieu of definition: major qualitative universal f- tures of turbulent flows 15 1. 3 Why turbulence is so impossibly difficult? The three N's 19 On the Navier-Stokes equations 19 1. 3. 1 1. 3. 2 On the nature of the problem 21 1. 3. 3 Nonlinearity 22 1. 3. 4 Noninegrability 22 Nonlocality 1. 3. 5 23 1. 3. 6 On physics of turbulence 24 1. 3. 7 On statistical theories 24 1. 4 Outline of the following material 25 1. 5 In lieu of summary 26 2 ORIGINS OF TURBULENCE 27 2. 1 Instability 27 2. 2 Transition to turbulence versus routes to chaos 29 2.
Sir James Lighthill And Modern Fluid Mechanics
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Author : Lokenath Debnath
language : en
Publisher: World Scientific
Release Date : 2008
Sir James Lighthill And Modern Fluid Mechanics written by Lokenath Debnath and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Biography & Autobiography categories.
This is perhaps the first book containing biographical information of Sir James Lighthill and his major scientific contributions to the different areas of fluid mechanics, applied mathematics, aerodynamics, linear and nonlinear waves in fluids, geophysical fluid dynamics, biofluiddynamics, aeroelasticity, boundary layer theory, generalized functions, and Fourier series and integrals. Special efforts is made to present Lighthill's scientific work in a simple and concise manner, and generally intelligible to readers who have some introduction to fluid mechanics. The book also includes a list of Lighthill's significant papers.Written for the mathematically literate reader, this book also provides a glimpse of Sir James' serious attempt to stimulate interest in mathematics and its diverse applications among the general public of the world, his profound influence on teaching of mathematics and science with newer applications, and his deep and enduring concern on enormous loss of human lives, economic and marine resources by natural hazards. By providing detailed background information and knowledge, sufficient to start interdisciplinary research, it is intended to serve as a ready reference guide for readers interested in advanced study and research in modern fluid mechanics.