Introduction To Turbulent Dynamical Systems In Complex Systems

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Introduction To Turbulent Dynamical Systems In Complex Systems

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Author : Andrew J. Majda
language : en
Publisher: Springer
Release Date : 2016-09-14

Introduction To Turbulent Dynamical Systems In Complex Systems written by Andrew J. Majda and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-14 with Mathematics categories.

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.

Dynamical Systems Approach To Turbulence

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Author : Tomas Bohr
language : en
Publisher: Cambridge University Press
Release Date : 1998-08-13

Dynamical Systems Approach To Turbulence written by Tomas Bohr 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 1998-08-13 with Science categories.

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.

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

Turbulence And Diffusion

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Author : Oleg G. Bakunin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-15

Turbulence And Diffusion written by Oleg G. Bakunin 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 2008-08-15 with Science categories.

This book is intended to serve as an introduction to the multidisciplinary ?eld of anomalous diffusion in complex systems such as turbulent plasma, convective rolls, zonal ?ow systems, stochastic magnetic ?elds, etc. In spite of its great importance, turbulent transport has received comparatively little treatment in published mo- graphs. This book attempts a comprehensive description of the scaling approach to turbulent diffusion. From the methodological point of view, the book focuses on the general use of correlation estimates, quasilinear equations, and continuous time random walk - proach. I provide a detailed structure of some derivations when they may be useful for more general purposes. Correlation methods are ?exible tools to obtain tra- port scalings that give priority to the richness of ingredients in a physical pr- lem. The mathematical description developed here is not meant to provide a set of “recipes” for hydrodynamical turbulence or plasma turbulence; rather, it serves to develop the reader’s physical intuition and understanding of the correlation mec- nisms involved.

Filtering Complex Turbulent Systems

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Author : Andrew J. Majda
language : en
Publisher: Cambridge University Press
Release Date : 2012-02-23

Filtering Complex Turbulent Systems written by Andrew J. Majda 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 2012-02-23 with Mathematics categories.

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.

Dynamic Mode Decomposition

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Author : J. Nathan Kutz
language : en
Publisher: SIAM
Release Date : 2016-11-23

Dynamic Mode Decomposition written by J. Nathan Kutz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-23 with Science categories.

Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.

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.

Machine Learning Control Taming Nonlinear Dynamics And Turbulence

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Author : Thomas Duriez
language : en
Publisher: Springer
Release Date : 2016-11-02

Machine Learning Control Taming Nonlinear Dynamics And Turbulence written by Thomas Duriez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-02 with Technology & Engineering categories.

This is the first textbook on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading researchers in turbulence control (S. Bagheri, B. Batten, M. Glauser, D. Williams) and machine learning (M. Schoenauer) for a broader perspective. All chapters have exercises and supplemental videos will be available through YouTube.

Multiplicity Of Time Scales In Complex Systems

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Author : Bernhelm Booß-Bavnbek
language : en
Publisher: Springer Nature
Release Date : 2024-04-02

Multiplicity Of Time Scales In Complex Systems written by Bernhelm Booß-Bavnbek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-02 with Science categories.

Note to the interested reader to have a look at the companion to this volume Challenges for Sciences and Communication I | ISBN: 978-3-031-28048-1. This highly interdisciplinary volume brings together a carefully curated set of case studies examining complex systems with multiple time scales (MTS) across a variety of fields: materials science, epidemiology, cell physiology, mathematics, climatology, energy transition planning, ecology, economics, sociology, history, and cultural studies. The book addresses the vast diversity of interacting processes underlying the behaviour of different complex systems, highlighting the multiplicity of characteristic time scales that are a common feature of many and showcases a rich variety of methodologies across disciplinary boundaries. Self-organizing, out-of-equilibrium, ever-evolving systems are ubiquitous in the natural and social world. Examples include the climate, ecosystems, living cells, epidemics, the human brain, and many socio-economic systems across history. Their dynamical behaviour poses great challenges in the pressing context of the climate crisis, since they may involve nonlinearities, feedback loops, and the emergence of spatial-temporal patterns, portrayed by resilience or instability, plasticity or rigidity; bifurcations, thresholds and tipping points; burst-in excitation or slow relaxation, and worlds of other asymptotic behaviour, hysteresis, and resistance to change. Chapters can be read individually by the reader with special interest in such behaviours of particular complex systems or in specific disciplinary perspectives. Read together, however, the case studies, opinion pieces, and meta-studies on MTS systems presented and analysed here combine to give the reader insights that are more than the sum of the book’s individual chapters, as surprising similarities become apparent in seemingly disparate and unconnected systems. MTS systems call into question naïve perceptionsof time and complexity, moving beyond conventional ways of description, analysis, understanding, modelling, numerical prediction, and prescription of the world around us. This edited collection presents new ways of forecasting, introduces new means of control, and – perhaps as the most demanding task – it singles out a sustainable description of an MTS system under observation, offering a more nuanced interpretation of the floods of quantitative data and images made available by high- and low-frequency measurement tools in our unprecedented era of information flows.

Turbulent Flows

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Author : Jean Piquet
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Turbulent Flows written by Jean Piquet 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 2013-04-17 with Technology & Engineering categories.

obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each· chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C~apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied (§1-3). A first detailed study of homogeneous turbulent flows follows (§4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in §5 with the l"Csulting ~alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms (§ 1), their general dynamics (§2) with the particular case of homogeneous, isotropie turbulence (§3) whel"C the so-called Kolmogorov's assumptions are discussed at length.