Geometrical Theory Of Dynamical Systems And Fluid Flows Revised Edition
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Geometrical Theory Of Dynamical Systems And Fluid Flows
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Author : Tsutomu Kambe
language : en
Publisher: World Scientific
Release Date : 2004
Geometrical Theory Of Dynamical Systems And Fluid Flows written by Tsutomu Kambe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
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.
Geometrical Theory Of Dynamical Systems And Fluid Flows Revised Edition
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Author : Tsutomu (Jixin) Kambe
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009-12-28
Geometrical Theory Of Dynamical Systems And Fluid Flows Revised Edition written by Tsutomu (Jixin) Kambe and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-28 with Science categories.
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.
New Trends In Intuitive Geometry
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Author : Gergely Ambrus
language : en
Publisher: Springer
Release Date : 2018-11-03
New Trends In Intuitive Geometry written by Gergely Ambrus and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.
This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.
Theory And Practice Of Finite Elements
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Author : Alexandre Ern
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Theory And Practice Of Finite Elements written by Alexandre Ern 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 2013-03-09 with Mathematics categories.
The origins of the finite element method can be traced back to the 1950s when engineers started to solve numerically structural mechanics problems in aeronautics. Since then, the field of applications has widened steadily and nowadays encompasses nonlinear solid mechanics, fluid/structure interactions, flows in industrial or geophysical settings, multicomponent reactive turbulent flows, mass transfer in porous media, viscoelastic flows in medical sciences, electromagnetism, wave scattering problems, and option pricing (to cite a few examples). Numerous commercial and academic codes based on the finite element method have been developed over the years. The method has been so successful to solve Partial Differential Equations (PDEs) that the term "Finite Element Method" nowadays refers not only to the mere interpolation technique it is, but also to a fuzzy set of PDEs and approximation techniques. The efficiency of the finite element method relies on two distinct ingredi ents: the interpolation capability of finite elements (referred to as the approx imability property in this book) and the ability of the user to approximate his model (mostly a set of PDEs) in a proper mathematical setting (thus guar anteeing continuity, stability, and consistency properties). Experience shows that failure to produce an approximate solution with an acceptable accuracy is almost invariably linked to departure from the mathematical foundations. Typical examples include non-physical oscillations, spurious modes, and lock ing effects. In most cases, a remedy can be designed if the mathematical framework is properly set up.
Discrete And Continuous Dynamical Systems
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Author :
language : en
Publisher:
Release Date : 2006
Discrete And Continuous Dynamical Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differentiable dynamical systems categories.
Bifurcation Theory And Applications
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Author : Tian Ma
language : en
Publisher: World Scientific
Release Date : 2005
Bifurcation Theory And Applications written by Tian Ma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
- Provides a comprehensive and intuitive review of existing bifurcation theories - New theories for bifurcations from eigenvalues with even multiplicity - General recipes for applications
Incompressible Bipolar And Non Newtonian Viscous Fluid Flow
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Author : Hamid Bellout
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-19
Incompressible Bipolar And Non Newtonian Viscous Fluid Flow written by Hamid Bellout 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 2013-11-19 with Science categories.
The theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The Navier-Stokes model of fluid flow is based on the Stokes hypothesis, which a priori simplifies and restricts the relationship between the stress tensor and the velocity. By relaxing the constraints of the Stokes hypothesis, the mathematical theory of multipolar viscous fluids generalizes the standard Navier-Stokes model. The rigorous theory of multipolar viscous fluids is compatible with all known thermodynamical processes and the principle of material frame indifference; this is in contrast with the formulation of most non-Newtonian fluid flow models which result from ad hoc assumptions about the relation between the stress tensor and the velocity. The higher-order boundary conditions, which must be formulated for multipolar viscous flow problems, are a rigorous consequence of the principle of virtual work; this is in stark contrast to the approach employed by authors who have studied the regularizing effects of adding artificial viscosity, in the form of higher order spatial derivatives, to the Navier-Stokes model. A number of research groups, primarily in the United States, Germany, Eastern Europe, and China, have explored the consequences of multipolar viscous fluid models; these efforts, and those of the authors, which are described in this book, have focused on the solution of problems in the context of specific geometries, on the existence of weak and classical solutions, and on dynamical systems aspects of the theory. This volume will be a valuable resource for mathematicians interested in solutions to systems of nonlinear partial differential equations, as well as to applied mathematicians, fluid dynamicists, and mechanical engineers with an interest in the problems of fluid mechanics.
Simulation And Control Of Chaotic Nonequilibrium Systems With A Foreword By Julien Clinton Sprott
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Author : William Graham Hoover
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-02-02
Simulation And Control Of Chaotic Nonequilibrium Systems With A Foreword By Julien Clinton Sprott written by William Graham Hoover and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-02 with Science categories.
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.
Vortex Dominated Flows
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Author : Lu Ting
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-05
Vortex Dominated Flows written by Lu Ting 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 2007-07-05 with Science categories.
This monograph provides in-depth analyses of vortex dominated flows via matched and multiscale asymptotics, and demonstrates how insight gained through these analyses can be exploited in the construction of robust, efficient, and accurate numerical techniques. The book explores the dynamics of slender vortex filaments in detail, including fundamental derivations, compressible core structure, weakly non-linear limit regimes, and associated numerical methods. Similarly, the volume covers asymptotic analysis and computational techniques for weakly compressible flows involving vortex-generated sound and thermoacoustics. The book is addressed to both graduate students and researchers.
Piecewise Smooth Dynamical Systems
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Author : Mario Bernardo
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-01
Piecewise Smooth Dynamical Systems written by Mario Bernardo 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 2008-01-01 with Mathematics categories.
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.