Turbulent Motion And The Structure Of Chaos
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Turbulent Motion And The Structure Of Chaos
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Author : Yu.L. Klimontovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Turbulent Motion And The Structure Of Chaos written by Yu.L. Klimontovich 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 2012-12-06 with Science categories.
analyzing the experimental data and constructing math.ematical models of the processes under study, one has to rely rather on the physical intuition than on the strict calculations. Now let us go one step higher and explain the main title of the book. The concepts of "laminary" and "turbulent" motions were first introduced in hydrodynamics. Since the old days these concepts have considerably broadened; now the laminar and the turbulent motions have been discovered and investigated at all levels of description of nonequilibrium processes in the open systems, from kinetics to reaction diffusion. In any case, one of the principal characteristics of the turbulent motion is the existence of a large number of well-developed macroscopic degrees of freedom. For this reason the turbulent motion is extremely complicated and to a large extent unpredictable. As the laminar and the turbulent flows play an important role in the processes of evolution in the open systems, and in particular, in the processes of self-organization, the need arises for assessing the relative degree of order of laminar and turbulent motions, and also for comparing the degree of order of various turbulent motions. Without being able to make such estimates it will be impossible to determine whether the evolution is going towards higher or towards lower organization when one turbulent state is replaced by another.
Turbulent Motion And The Structure Of Chaos
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Author : Yu.L. Klimontovich
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-09-30
Turbulent Motion And The Structure Of Chaos written by Yu.L. Klimontovich 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 1991-09-30 with Science categories.
analyzing the experimental data and constructing math.ematical models of the processes under study, one has to rely rather on the physical intuition than on the strict calculations. Now let us go one step higher and explain the main title of the book. The concepts of "laminary" and "turbulent" motions were first introduced in hydrodynamics. Since the old days these concepts have considerably broadened; now the laminar and the turbulent motions have been discovered and investigated at all levels of description of nonequilibrium processes in the open systems, from kinetics to reaction diffusion. In any case, one of the principal characteristics of the turbulent motion is the existence of a large number of well-developed macroscopic degrees of freedom. For this reason the turbulent motion is extremely complicated and to a large extent unpredictable. As the laminar and the turbulent flows play an important role in the processes of evolution in the open systems, and in particular, in the processes of self-organization, the need arises for assessing the relative degree of order of laminar and turbulent motions, and also for comparing the degree of order of various turbulent motions. Without being able to make such estimates it will be impossible to determine whether the evolution is going towards higher or towards lower organization when one turbulent state is replaced by another.
Instabilities Chaos And Turbulence 2nd Edition
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Author : Paul Manneville
language : en
Publisher: World Scientific
Release Date : 2010-07-21
Instabilities Chaos And Turbulence 2nd Edition 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 2010-07-21 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./a
Turbulent Motion And The Structure Of Chaos
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Author : Yu.L. Klimontovich
language : en
Publisher: Springer
Release Date : 2012-09-27
Turbulent Motion And The Structure Of Chaos written by Yu.L. Klimontovich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-27 with Science categories.
analyzing the experimental data and constructing math.ematical models of the processes under study, one has to rely rather on the physical intuition than on the strict calculations. Now let us go one step higher and explain the main title of the book. The concepts of "laminary" and "turbulent" motions were first introduced in hydrodynamics. Since the old days these concepts have considerably broadened; now the laminar and the turbulent motions have been discovered and investigated at all levels of description of nonequilibrium processes in the open systems, from kinetics to reaction diffusion. In any case, one of the principal characteristics of the turbulent motion is the existence of a large number of well-developed macroscopic degrees of freedom. For this reason the turbulent motion is extremely complicated and to a large extent unpredictable. As the laminar and the turbulent flows play an important role in the processes of evolution in the open systems, and in particular, in the processes of self-organization, the need arises for assessing the relative degree of order of laminar and turbulent motions, and also for comparing the degree of order of various turbulent motions. Without being able to make such estimates it will be impossible to determine whether the evolution is going towards higher or towards lower organization when one turbulent state is replaced by another.
Engineering Applications Of Dynamics Of Chaos
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Author : W. Szemplinska-Stupnicka
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-12-18
Engineering Applications Of Dynamics Of Chaos written by W. Szemplinska-Stupnicka 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 1991-12-18 with Mathematics categories.
The treatment of chaotic dynamics in mathematics and physics during last two decades has led to a number of new concepts for the investigation of complex behavior in nonlinear dynamical processes. The aim the CISM course Engineering Applications of Dynamics of Chaos of which this is the proceedings volume was to make these concepts available to engineers and applied scientists possessing only such modest knowledges in mathematics which are usual for engineers, for example graduating from a Technical University. The contents of the articles contributed by leading experts in this field cover not only theoretical foundations and algorithmic and computational aspects but also applications to engineering problems. In the first article an introduction into the basic concepts for the investigation of chaotic behavior of dynamical systems is given which is followed in the second article by an extensive treatment of approximative analytical methods to determine the critical parameter values describing the onset of chaos. The important relation between chaotic dynamics and the phenomenon of turbulence is treated in the third article by studying instabilities various fluid flows. In this contribution also an introduction into interesting phenomenon of pattern formation is given. The fourth and fifth articles present various applications to nonlinear oscillations including roll motions of ships, rattling oscillations in gear boxes, tumbling oscillations of satellites, flutter motions of fluid carrying pipes and vibrations of robot arms. In the final article a short treatment of hyperchaos is given.
An Introduction To Dynamical Systems And Chaos
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Author : G. C. Layek
language : en
Publisher: Springer Nature
Release Date : 2024-02-23
An Introduction To Dynamical Systems And Chaos written by G. C. Layek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-23 with Mathematics categories.
This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes to chaos and multistable coexisting attractors. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, featuring a multitude of detailed worked-out examples alongside comprehensive exercises. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate, graduate and research students in mathematics, physics and engineering. The second edition of the book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillations, Bogdanov–Takens, periodbubbling and Neimark–Sacker bifurcations, and dynamics on circle. The organized structures in bi-parameter plane for transitional and chaotic regimes are new active research interest and explored thoroughly. The connections of complex chaotic attractors with fractals cascades are explored in many physical systems. Chaotic attractors may attain multiple scaling factors and show scale invariance property. Finally, the ideas of multifractals and global spectrum for quantifying inhomogeneous chaotic attractors are discussed.
Dissipative Structures And Chaos
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Author : Hazime Mori
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Dissipative Structures And Chaos written by Hazime Mori 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 2013-11-11 with Science categories.
This book consists of two parts, the first dealing with dissipative structures and the second with the structure and physics of chaos. The first part was written by Y. Kuramoto and the second part by H. Mori. Throughout the book, emphasis is laid on fundamental concepts and methods rather than applications, which are too numerous to be treated here. Typical physical examples, however, including nonlinear forced oscilla tors, chemical reactions with diffusion, and Benard convection in horizontal fluid layers, are discussed explicitly. Our consideration of dissipative structures is based on a phenomenolog ical reduction theory in which universal aspects of the phenomena under consideration are emphasized, while the theory of chaos is developed to treat transport phenomena, such as the mixing and diffusion of chaotic orbits, from the viewpoint of the geometrical phase space structure of chaos. The title of the original, Japanese version of the book is Sanitsu Kozo to Kaosu (Dissipative Structures and Chaos). It is part of the Iwanami Koza Gendai no Butsurigaku (Iwanami Series on Modern Physics). The first Japanese edition was published in March 1994 and the second in August 1997. We are pleased that this book has been translated into English and that it can now have an audience outside of Japan. We would like to express our gratitude to Glenn Paquette for his English translation, which has made this book more understandable than the original in many respects.
Self Organization Of Complex Structures
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Author : Frank Schweitzer
language : en
Publisher: CRC Press
Release Date : 1997-07-16
Self Organization Of Complex Structures written by Frank Schweitzer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-16 with Computers categories.
During the past twenty years, a broad spectrum of theories and methods have been developed in physics, chemistry and molecular biology to explain structure formation in complex systems. These methods have been applied to many different fields such as economics, sociology and town planning, and this book reflects the interdisciplinary nature of complexity and self-organisation. The main focus is on the emergence of collective phenomena from individual or microscopic interactions. Presents a wide-ranging overview from fundamental aspects of the evolution of complexity, to applications in biology, ecology, sociology, economics, and urban structure formation.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1986
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mechanics, Applied categories.