Download or read book Geometrical Theory Of Dynamical Systems And Fluid Flows Revised Edition written by Tsutomu (Jixin) Kambe and published by World Scientific Publishing Company. This book was released on 2009-12-28 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems.In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics.
Download or read book Geometrical Theory of Dynamical Systems and Fluid Flows revised Edition written by and published by World Scientific. This book was released on 2009 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems. In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics."-
Download or read book Geometrical Theory Of Dynamical Systems And Fluid Flows written by Tsutomu Kambe and published by World Scientific Publishing Company. This book was released on 2004-09-09 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows, and certain integrable systems. The subjects are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The underlying concepts are based on differential geometry and theory of Lie groups in the mathematical aspect, and on transformation symmetries and gauge theory in the physical aspect. A great deal of effort has been directed toward making the description elementary, clear and concise, so that beginners will have an access to the topics.
Download or read book Time Reversibility Computer Simulation Algorithms Chaos 2nd Edition written by William Graham Hoover and published by World Scientific. This book was released on 2012-06-11 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: A small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the “reversibility paradox”, with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the authors' approach to the problem of understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying time-reversible mechanics. Computer simulation has made it possible to probe reversibility from a variety of directions and “chaos theory” or “nonlinear dynamics” has supplied a useful vocabulary and a set of concepts, which allow a fuller explanation of irreversibility than that available to Boltzmann or to Green, Kubo and Onsager. Clear illustration of concepts is emphasized throughout, and reinforced with a glossary of technical terms from the specialized fields which have been combined here to focus on a common theme.The book begins with a discussion, contrasting the idealized reversibility of basic physics against the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory — fractals and Lyapunov instability — are fundamental to the approach.Undergraduate-level physics, calculus, and ordinary differential equations are sufficient background for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers. The generous assortment of examples worked out in the text will stimulate readers to explore the rich and fruitful field of study which links fundamental reversible laws of physics to the irreversibility surrounding us all.This expanded edition stresses and illustrates computer algorithms with many new worked-out examples, and includes considerable new material on shockwaves, Lyapunov instability and fluctuations.
Download or read book Simulation And Control Of Chaotic Nonequilibrium Systems With A Foreword By Julien Clinton Sprott written by William Graham Hoover and published by World Scientific Publishing Company. This book was released on 2015-02-02 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide a lively working knowledge of the thermodynamic control of microscopic simulations, while summarizing the historical development of the subject, along with some personal reminiscences. Many computational examples are described so that they are well-suited to learning by doing. The contents enhance the current understanding of the reversibility paradox and are accessible to advanced undergraduates and researchers in physics, computation, and irreversible thermodynamics.
Download or read book Time Reversability Computer Simulation Algorithms Chaos written by William Graham Hoover and published by World Scientific. This book was released on 2012 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book begins with a discussion, contrasting the idealized reversibility of basic physics against the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory - fractals and Lyapunov instability - are fundamental to the approach. Undergraduate-level physics, calculus, and ordinary differential equations are sufficient background for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers.
Download or read book Differential Dynamical Systems Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.
Download or read book An Introduction to the Geometry and Topology of Fluid Flows written by Renzo L. Ricca and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.
Download or read book Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics written by Tian Ma and published by American Mathematical Soc.. This book was released on 2005 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a geometric theory for incompressible flow and its applications to fluid dynamics. The main objective is to study the stability and transitions of the structure of incompressible flows and its applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications goes well beyond its original motivation of the study of oceanic dynamics. The authors present a substantial advance in the use of geometric and topological methods to analyze and classify incompressible fluid flows. The approach introduces genuinely innovative ideas to the study of the partial differential equations of fluid dynamics. One particularly useful development is a rigorous theory for boundary layer separation of incompressible fluids. The study of incompressible flows has two major interconnected parts. The first is the development of a global geometric theory of divergence-free fields on general two-dimensional compact manifolds. The second is the study of the structure of velocity fields for two-dimensional incompressible fluid flows governed by the Navier-Stokes equations or the Euler equations. Motivated by the study of problems in geophysical fluid dynamics, the program of research in this book seeks to develop a new mathematical theory, maintaining close links to physics along the way. In return, the theory is applied to physical problems, with more problems yet to be explored. The material is suitable for researchers and advanced graduate students interested in nonlinear PDEs and fluid dynamics.
Download or read book Differential Dynamical Systems Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
Download or read book Geometric Theory of Dynamical Systems written by Jacob Palis and published by . This book was released on 1998 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Advances in Computational Fluid Dynamics written by C.C. Chao and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the preface: Fluid dynamics is an excellent example of how recent advances in computational tools and techniques permit the rapid advance of basic and applied science. The development of computational fluid dynamics (CFD) has opened new areas of research and has significantly supplemented information available from experimental measurements. Scientific computing is directly responsible for such recent developments as the secondary instability theory of transition to turbulence, dynamical systems analyses of routes to chaos, ideas on the geometry of turbulence, direct simulations of turbulence, three-dimensional full-aircraft flow analyses, and so on. We believe that CFD has already achieved a status in the tool-kit of fluid mechanicians equal to that of the classical scientific techniques of mathematical analysis and laboratory experiment.
Download or read book Fluid Dynamics written by Z.U.A. Warsi and published by CRC Press. This book was released on 2005-07-26 with total page 874 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many introductions to fluid dynamics offer an illustrative approach that demonstrates some aspects of fluid behavior, but often leave you without the tools necessary to confront new problems. For more than a decade, Fluid Dynamics: Theoretical and Computational Approaches has supplied these missing tools with a constructive approach that made the book a bestseller. Now in its third edition, it supplies even more computational skills in addition to a solid foundation in theory. After laying the groundwork in theoretical fluid dynamics, independent of any particular coordinate system in order to allow coordinate transformation of the equations, the author turns to the technique of writing Navier–Stokes and Euler’s equations, flow of inviscid fluids, laminar viscous flow, and turbulent flow. He also includes requisite mathematics in several “Mathematical Expositions” at the end of the book and provides abundant end-of-chapter problems. What’s New in the Third Edition? New section on free surface flow New section on instability of flows through Chaos and nonlinear dissipative systems New section on formulation of the large eddy simulation (LES) problem New example problems and exercises that reflect new and important topics of current interest By integrating a strong theoretical foundation with practical computational tools, Fluid Dynamics: Theoretical and Computational Approaches, Third Edition is an indispensable guide to the methods needed to solve new and unfamiliar problems in fluid dynamics.
Download or read book Turbulence in Fluid Flows written by George R. Sell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume are based on recent research on the phenomenon of turbulence in fluid flows collected by the Institute for Mathematics and its Applications. This volume looks into the dynamical properties of the solutions of the Navier-Stokes equations, the equations of motion of incompressible, viscous fluid flows, in order to better understand this phenomenon. Although it is a basic issue of science, it has implications over a wide spectrum of modern technological applications. The articles offer a variety of approaches to the Navier-Stokes problems and related issues. This book should be of interest to both applied mathematicians and engineers.
Download or read book Fluid Mechanics written by S. G. Rajeev and published by Oxford University Press. This book was released on 2018-08-23 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid Mechanics: A Geometrical Point of View emphasizes general principles of physics illustrated by simple examples in fluid mechanics. Advanced mathematics (e.g., Riemannian geometry and Lie groups) commonly used in other parts of theoretical physics (e.g. General Relativity or High Energy Physics) are explained and applied to fluid mechanics. This follows on from the author's book Advanced Mechanics (Oxford University Press, 2013). After introducing the fundamental equations (Euler and Navier-Stokes), the book provides particular cases: ideal and viscous flows, shocks, boundary layers, instabilities, and transients. A restrained look at integrable systems (KdV) leads into a formulation of an ideal fluid as a hamiltonian system. Arnold's deep idea, that the instability of a fluid can be understood using the curvature of the diffeomorphism group, will be explained. Leray's work on regularity of Navier-Stokes solutions, and the modern developments arising from it, will be explained in language for physicists. Although this is a book on theoretical physics, readers will learn basic numerical methods: spectral and finite difference methods, geometric integrators for ordinary differential equations. Readers will take a deep dive into chaotic dynamics, using the Smale horse shoe as an example. Aref's work on chaotic advection is explained. The book concludes with a self-contained introduction to renormalization, an idea from high energy physics which is expected to be useful in developing a theory of turbulence.
Download or read book Dynamically Coupled Rigid Body Fluid Flow Systems written by Banavara N. Shashikanth and published by Springer Nature. This book was released on 2021-10-28 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified study of dynamically coupled systems involving a rigid body and an ideal fluid flow from the perspective of Lagrangian and Hamiltonian mechanics. It compiles theoretical investigations on the topic of dynamically coupled systems using a framework grounded in Kirchhoff’s equations. The text achieves a balance between geometric mechanics, or the modern theories of reduction of Lagrangian and Hamiltonian systems, and classical fluid mechanics, with a special focus on the applications of these principles. Following an introduction to Kirchhoff’s equations of motion, the book discusses several extensions of Kirchhoff’s work, particularly related to vortices. It addresses the equations of motions of these systems and their Lagrangian and Hamiltonian formulations. The book is suitable to mathematicians, physicists and engineers with a background in Lagrangian and Hamiltonian mechanics and theoretical fluid mechanics. It includes a brief introductory overview of geometric mechanics in the appendix.
Download or read book Elementary Fluid Mechanics written by Tsutomu Kambe and published by World Scientific. This book was released on 2007 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook describes the fundamental OC physicalOCO aspects of fluid flows for beginners of fluid mechanics in physics, mathematics and engineering, from the point of view of modern physics. It also emphasizes the dynamical aspects of fluid motions rather than the static aspects, illustrating vortex motions, waves, geophysical flows, chaos and turbulence. Beginning with the fundamental concepts of the nature of flows and the properties of fluids, the book presents fundamental conservation equations of mass, momentum and energy, and the equations of motion for both inviscid and viscous fluids. In addition to the fundamentals, this book also covers water waves and sound waves, vortex motions, geophysical flows, nonlinear instability, chaos, and turbulence. Furthermore, it includes the chapters on superfluids and the gauge theory of fluid flows. The material in the book emerged from the lecture notes for an intensive course on Elementary Fluid Mechanics for both undergraduate and postgraduate students of theoretical physics given in 2003 and 2004 at the Nankai Institute of Mathematics (Tianjin) in China. Hence, each chapter may be presented separately as a single lecture."
