Geometrical Theory Of Dynamical Systems And Fluid Flows (Revised Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometrical Theory Of Dynamical Systems And Fluid Flows (Revised Edition) write by Tsutomu (Jixin) Kambe. This book was released on 2009-12-28. Geometrical Theory Of Dynamical Systems And Fluid Flows (Revised Edition) available in PDF, EPUB and Kindle. 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.
Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition)
Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) write by . This book was released on 2009. Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) available in PDF, EPUB and Kindle. "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."-
Geometrical Theory Of Dynamical Systems And Fluid Flows
Geometrical Theory Of Dynamical Systems And Fluid Flows - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometrical Theory Of Dynamical Systems And Fluid Flows write by Tsutomu Kambe. This book was released on 2004-09-09. Geometrical Theory Of Dynamical Systems And Fluid Flows available in PDF, EPUB and Kindle. 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.
Time Reversibility, Computer Simulation, Algorithms, Chaos (2nd Edition)
Time Reversibility, Computer Simulation, Algorithms, Chaos (2nd Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Time Reversibility, Computer Simulation, Algorithms, Chaos (2nd Edition) write by William Graham Hoover. This book was released on 2012-06-11. Time Reversibility, Computer Simulation, Algorithms, Chaos (2nd Edition) available in PDF, EPUB and Kindle. 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.
Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott
Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott write by William Graham Hoover. This book was released on 2015-02-02. Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott available in PDF, EPUB and Kindle. 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.
