Introduction To Turbulent Dynamical Systems In Complex Systems

Author : Andrew J. Majda
Publisher : Springer
Page : 91 pages
File Size : 46,8 Mb
Release : 2016-09-14
Category : Mathematics
ISBN : 9783319322179

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Introduction to Turbulent Dynamical Systems in Complex Systems by Andrew J. Majda Pdf

This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which are of central importance to the field. The contents cover general framework, concrete examples, and instructive qualitative models. Accessible open problems are mentioned throughout. Topics covered include: · Geophysical flows with rotation, topography, deterministic and random forcing · New statistical energy principles for general turbulent dynamical systems, with applications · Linear statistical response theory combined with information theory to cope with model errors · Reduced low order models · Recent mathematical strategies for online data assimilation of turbulent dynamical systems as well as rigorous results for finite ensemble Kalman filters The volume will appeal to graduate students and researchers working mathematics, physics and engineering and particularly those in the climate, atmospheric and ocean sciences interested in turbulent dynamical as well as other complex systems.

Author : Paul Manneville
Publisher : World Scientific
Page : 456 pages
File Size : 49,9 Mb
Release : 2010-07-21
Category : Science
ISBN : 9781911299400

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Instabilities, Chaos And Turbulence (2nd Edition) by Paul Manneville Pdf

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

Author : Tomas Bohr,Mogens H. Jensen,Giovanni Paladin,Angelo Vulpiani
Publisher : Cambridge University Press
Page : 372 pages
File Size : 47,8 Mb
Release : 2005-08-22
Category : Science
ISBN : 0521017947

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Dynamical Systems Approach to Turbulence by Tomas Bohr,Mogens H. Jensen,Giovanni Paladin,Angelo Vulpiani Pdf

In recent decades, turbulence has evolved into a very active field of theoretical physics. The origin of this development is the approach to turbulence from the point of view of deterministic dynamical systems, and this book shows how concepts developed for low dimensional chaotic systems are applied to turbulent states. This book centers around a number of important simplified models for turbulent behavior in systems ranging from fluid motion (classical turbulence) to chemical reactions and interfaces in disordered systems. The theory of fractals and multifractals now plays a major role in turbulence research, and turbulent states are being studied as important dynamical states of matter occurring also in systems outside the realm of hydrodynamics. The book contains simplified models of turbulent behavior, notably shell models, coupled map lattices, amplitude equations and interface models.

Author : Bernhelm Booß-Bavnbek
Publisher : Springer Nature
Page : 514 pages
File Size : 48,9 Mb
Release : 2024-05-19
Category : Electronic
ISBN : 9783031451058

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Multiplicity of Time Scales in Complex Systems by Bernhelm Booß-Bavnbek Pdf

Author : Andrew J. Majda,John Harlim
Publisher : Cambridge University Press
Page : 368 pages
File Size : 45,5 Mb
Release : 2012-02-23
Category : Mathematics
ISBN : 9781107016668

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Filtering Complex Turbulent Systems by Andrew J. Majda,John Harlim Pdf

The authors develop a systematic applied mathematics perspective on the problems associated with filtering complex turbulent systems. The book contains background material from filtering, turbulence theory and numerical analysis, making it suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required.

Author : Victor Raizer
Publisher : CRC Press
Page : 273 pages
File Size : 52,6 Mb
Release : 2021-10-03
Category : Technology & Engineering
ISBN : 9781000458756

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Remote Sensing of Turbulence by Victor Raizer Pdf

This book offers a unique multidisciplinary integration of the physics of turbulence and remote sensing technology. Remote Sensing of Turbulence provides a new vision on the research of turbulence and summarizes the current and future challenges of monitoring turbulence remotely. The book emphasizes sophisticated geophysical applications, detection, and recognition of complex turbulent flows in oceans and the atmosphere. Through several techniques based on microwave and optical/IR observations, the text explores the technological capabilities and tools for the detection of turbulence, their signatures, and variability. FEATURES Covers the fundamental aspects of turbulence problems with a broad geophysical scope for a wide audience of readers Provides a complete description of remote-sensing capabilities for observing turbulence in the earth’s environment Establishes the state-of-the-art remote-sensing techniques and methods of data analysis for turbulence detection Investigates and evaluates turbulence detection signatures, their properties, and variability Provides cutting-edge remote-sensing applications for space-based monitoring and forecasts of turbulence in oceans and the atmosphere This book is a great resource for applied physicists, the professional remote sensing community, ecologists, geophysicists, and earth scientists.

Author : Leonardo Bacelar Lima Santos,Rogério Galante Negri,Tiago José de Carvalho
Publisher : Springer
Page : 258 pages
File Size : 40,7 Mb
Release : 2019-07-23
Category : Mathematics
ISBN : 9783030212056

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Towards Mathematics, Computers and Environment: A Disasters Perspective by Leonardo Bacelar Lima Santos,Rogério Galante Negri,Tiago José de Carvalho Pdf

With relevant, timely topics, this book gathers carefully selected, peer-reviewed scientific works and offers a glimpse of the state-of-the-art in disaster prevention research, with an emphasis on challenges in Latin America. Topics include studies on surface frost, an extreme meteorological event that occasionally affects parts of Argentina, Bolivia, Peru, and southern Brazil, with serious impacts on local economies; near-ground pollution concentration, which affects many industrial, overpopulated cities within Latin America; disaster risk reduction and management, which are represented by mathematical models designed to assess the potential impact of failures in complex networks; and the intricate dynamics of international armed conflicts, which can be modeled with the help of stochastic theory. The book offers a valuable resource for professors, researchers, and students from both mathematical and environmental sciences, civil defense coordinators, policymakers, and stakeholders.

Author : Andrew J. Majda,Samuel N. Stechmann,Shengqian Chen,H. Reed Ogrosky,Sulian Thual
Publisher : Springer Nature
Page : 123 pages
File Size : 43,7 Mb
Release : 2019-09-24
Category : Mathematics
ISBN : 9783030222475

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Tropical Intraseasonal Variability and the Stochastic Skeleton Method by Andrew J. Majda,Samuel N. Stechmann,Shengqian Chen,H. Reed Ogrosky,Sulian Thual Pdf

In this text, modern applied mathematics and physical insight are used to construct the simplest and first nonlinear dynamical model for the Madden-Julian oscillation (MJO), i.e. the stochastic skeleton model. This model captures the fundamental features of the MJO and offers a theoretical prediction of its structure, leading to new detailed methods to identify it in observational data. The text contributes to understanding and predicting intraseasonal variability, which remains a challenging task in contemporary climate, atmospheric, and oceanic science. In the tropics, the Madden-Julian oscillation (MJO) is the dominant component of intraseasonal variability. One of the strengths of this text is demonstrating how a blend of modern applied mathematical tools, including linear and nonlinear partial differential equations (PDEs), simple stochastic modeling, and numerical algorithms, have been used in conjunction with physical insight to create the model. These tools are also applied in developing several extensions of the model in order to capture additional features of the MJO, including its refined vertical structure and its interactions with the extratropics. This book is of interest to graduate students, postdocs, and senior researchers in pure and applied mathematics, physics, engineering, and climate, atmospheric, and oceanic science interested in turbulent dynamical systems as well as other complex systems.

Author : Philip Holmes,John L. Lumley,Gal Berkooz
Publisher : Cambridge University Press
Page : 438 pages
File Size : 43,5 Mb
Release : 1996-10-10
Category : Science
ISBN : 0521551420

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Turbulence, Coherent Structures, Dynamical Systems and Symmetry by Philip Holmes,John L. Lumley,Gal Berkooz Pdf

For turbulent flows at relatively low speeds there exists an excellent mathematical model in the incompressible Navier-Stokes equations. Why then is the "problem of turbulence" so difficult? One reason is that these nonlinear partial differential equations appear to be insoluble, except through numerical simulations, which offer useful approximations, but little direct understanding. Three recent developments offer new hope. First, the discovery by experimentalists of coherent structures in certain turbulent flows. Secondly, the suggestion that strange attractors and other ideas from finite dimensional dynamical systems theory might play a role in the analysis of the governing equations. And, finally, the introduction of the Karhunen Loève or proper orthogonal decomposition. This book introduces these developments and describes how they may be combined to create low-dimensional models of turbulence, resolving only the coherent structures. This book will interest engineers, especially in the aerospace, chemical, civil, environmental and geophysical areas, as well as physicists and applied mathematicians concerned with turbulence.

Author : Philip Holmes,John L. Lumley,Gahl Berkooz,Clarence W. Rowley
Publisher : Unknown
Page : 386 pages
File Size : 46,8 Mb
Release : 2012
Category : Differentiable dynamical systems
ISBN : 1107227895

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Turbulence, Coherent Structures, Dynamical Systems and Symmetry by Philip Holmes,John L. Lumley,Gahl Berkooz,Clarence W. Rowley Pdf

"This book describes methods that reveal its structures and dynamics. Building on the existence of coherent structures - recurrent patterns - in turbulent flows, it describes mathematical methods that reduce the governing (Navier-Stokes) equations to simpler forms that can be understood more easily. This second edition contains a new chapter on the balanced proper orthogonal decomposition: a method derived from control theory that is especially useful for flows equipped with sensors and actuators. It also reviews relevant work carried out since 1995"--

Author : Tomas Bohr
Publisher : Cambridge University Press
Page : 373 pages
File Size : 46,7 Mb
Release : 1998-08-13
Category : Science
ISBN : 9780521475143

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Dynamical Systems Approach to Turbulence by Tomas Bohr Pdf

This book treats turbulence from the point of view of dynamical systems. In recent decades, turbulence has evolved into a very active field of theoretical physics. The modern theory of fractals and multifractals now plays a major role in turbulence research, and turbulent states are being studied as important dynamical states of matter, in a much broader context than hydrodynamics. The origin of this development is the approach to turbulence from the point of view of deterministic dynamical systems, and in this book it is shown how concepts developed for low dimensional chaotic systems can be applied to turbulent states.

Author : G. C. Layek
Publisher : Springer Nature
Page : 701 pages
File Size : 48,6 Mb
Release : 2024-05-19
Category : Electronic
ISBN : 9789819976959

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An Introduction to Dynamical Systems and Chaos by G. C. Layek Pdf

Author : Tapan K. Sengupta
Publisher : Cambridge University Press
Page : 643 pages
File Size : 53,5 Mb
Release : 2021-09-30
Category : Technology & Engineering
ISBN : 9781108490412

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Transition to Turbulence by Tapan K. Sengupta Pdf

"Present understanding of transition to turbulence has now been studied over one hundred and fifty years. The path the studies have taken posed it as a modal eigenvalue problem. Some researchers have suggested alternative models without being specific. First-principle based approach of receptivity is the route to build bridges among ideas for solving the Navier-Stokes equation for specific canonical problems. This book highlights the mathematical physics, scientific computing, and new ideas and theories for nonlinear analyses of fluid flows, for which vorticity dynamics remain central. This book is a blend of classic with distinctly new ideas, which establish different dynamics of flows, from genesis to evolution of disturbance fields with rigorously developed methods to tracing coherent structures amidst the seemingly random and chaotic fluid dynamics of transitional and turbulent flows"--

Author : Michael Shats,Horst Punzmann
Publisher : World Scientific
Page : 397 pages
File Size : 46,6 Mb
Release : 2006
Category : Science
ISBN : 9789812566980

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Lecture Notes on Turbulence and Coherent Structures in Fluids, Plasmas and Nonlinear Media by Michael Shats,Horst Punzmann Pdf

This book is based on the lectures delivered at the 19th Canberra International Physics Summer School held at the Australian National University in Canberra (Australia) in January 2006.The problem of turbulence and coherent structures is of key importance in many fields of science and engineering. It is an area which is vigorously researched across a diverse range of disciplines such as theoretical physics, oceanography, atmospheric science, magnetically confined plasma, nonlinear optics, etc. Modern studies in turbulence and coherent structures are based on a variety of theoretical concepts, numerical simulation techniques and experimental methods, which cannot be reviewed effectively by a single expert.The main goal of these lecture notes is to introduce state-of-the-art turbulence research in a variety of approaches (theoretical, numerical simulations and experiments) and applications (fluids, plasmas, geophysics, nonlinear optical media) by several experts. A smooth introduction is presented to readers who are not familiar with the field, while reviewing the most recent advances in the area. This collection of lectures will provide a useful review for both postgraduate students and researchers new to the advancements in this field, as well as specialists seeking to expand their knowledge across different areas of turbulence research.

Author : Bhimsen K. Shivamoggi
Publisher : Springer
Page : 375 pages
File Size : 47,5 Mb
Release : 2014-05-14
Category : Technology & Engineering
ISBN : 9789400770942

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Nonlinear Dynamics and Chaotic Phenomena: An Introduction by Bhimsen K. Shivamoggi Pdf

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.