The Mathematical Theory Of Permanent Progressive Water Waves

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The Mathematical Theory of Permanent Progressive Water-waves

Author : Hisashi Okamoto
Publisher : World Scientific
ISBN 13 : 9789810244507
Total Pages : 248 pages
Book Rating : 4.2/5 (445 download)

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Book Synopsis The Mathematical Theory of Permanent Progressive Water-waves by : Hisashi Okamoto

Download or read book The Mathematical Theory of Permanent Progressive Water-waves written by Hisashi Okamoto and published by World Scientific. This book was released on 2001 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid. The problem of permanent water-waves has attracted a large number of physicists and mathematicians since Stokes' pioneering papers appeared in 1847 and 1880. Among many aspects of the problem, the authors focus on periodic progressive waves, which mean waves traveling at a constant speed with no change of shape. As a consequence, everything about standing waves are excluded and solitary waves are studied only partly. However, even for this restricted problem, quite a number of papers and books, in physics and mathematics, have appeared and more will continue to appear, showing the richness of the subject. In fact, there remain many open questions to be answered.The present book consists of two parts: numerical experiments and normal form analysis of the bifurcation equations. Prerequisite for reading it is an elementary knowledge of the Euler equations for incompressible inviscid fluid and of bifurcation theory. Readers are also expected to know functional analysis at an elementary level. Numerical experiments are reported so that any reader can re-examine the results with minimal labor: the methods used in this book are well-known and are described as clearly as possible. Thus, the reader with an elementary knowledge of numerical computation will have little difficulty in the re-examination.

The Mathematical Theory of Permanent Progressive Water-Waves

Author : Hisashi Okamoto
Publisher : World Scientific Publishing Company
ISBN 13 : 9813102691
Total Pages : 244 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis The Mathematical Theory of Permanent Progressive Water-Waves by : Hisashi Okamoto

Download or read book The Mathematical Theory of Permanent Progressive Water-Waves written by Hisashi Okamoto and published by World Scientific Publishing Company. This book was released on 2001-09-28 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid. The problem of permanent water-waves has attracted a large number of physicists and mathematicians since Stokes' pioneering papers appeared in 1847 and 1880. Among many aspects of the problem, the authors focus on periodic progressive waves, which mean waves traveling at a constant speed with no change of shape. As a consequence, everything about standing waves are excluded and solitary waves are studied only partly. However, even for this restricted problem, quite a number of papers and books, in physics and mathematics, have appeared and more will continue to appear, showing the richness of the subject. In fact, there remain many open questions to be answered. The present book consists of two parts: numerical experiments and normal form analysis of the bifurcation equations. Prerequisite for reading it is an elementary knowledge of the Euler equations for incompressible inviscid fluid and of bifurcation theory. Readers are also expected to know functional analysis at an elementary level. Numerical experiments are reported so that any reader can re-examine the results with minimal labor: the methods used in this book are well-known and are described as clearly as possible. Thus, the reader with an elementary knowledge of numerical computation will have little difficulty in the re-examination.

The Mathematical Theory of Permanent Progressive Water-waves

Author : Hisashi Okamoto
Publisher :
ISBN 13 : 9789812810441
Total Pages : pages
Book Rating : 4.8/5 (14 download)

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Book Synopsis The Mathematical Theory of Permanent Progressive Water-waves by : Hisashi Okamoto

Download or read book The Mathematical Theory of Permanent Progressive Water-waves written by Hisashi Okamoto and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Water Waves

Author : Adrian Constantin
Publisher : Springer
ISBN 13 : 3319314629
Total Pages : 237 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Nonlinear Water Waves by : Adrian Constantin

Download or read book Nonlinear Water Waves written by Adrian Constantin and published by Springer. This book was released on 2016-06-28 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the material can be used by those who are already familiar with one branch of the study of water waves, to learn more about other areas.

Elliptic and Parabolic Equations

Author : Joachim Escher
Publisher : Springer
ISBN 13 : 3319125478
Total Pages : 295 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Elliptic and Parabolic Equations by : Joachim Escher

Download or read book Elliptic and Parabolic Equations written by Joachim Escher and published by Springer. This book was released on 2015-06-04 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations. Particular emphasis was put on the interaction between well-established scientists and emerging young mathematicians, as well as on exploring new connections between pure and applied mathematics. The volume contains material derived after the workshop taking up the impetus to continue collaboration and to incorporate additional new results and insights.

Nonlinear Dispersive Waves

Author : David Henry
Publisher : Springer Nature
ISBN 13 : 3031635124
Total Pages : 288 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Nonlinear Dispersive Waves by : David Henry

Download or read book Nonlinear Dispersive Waves written by David Henry and published by Springer Nature. This book was released on with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis

Author : Adrian Constantin
Publisher : SIAM
ISBN 13 : 1611971861
Total Pages : 325 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis by : Adrian Constantin

Download or read book Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis written by Adrian Constantin and published by SIAM. This book was released on 2011-12-01 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This overview of some of the main results and recent developments in nonlinear water waves presents fundamental aspects of the field and discusses several important topics of current research interest. It contains selected information about water-wave motion for which advanced mathematical study can be pursued, enabling readers to derive conclusions that explain observed phenomena to the greatest extent possible. The author discusses the underlying physical factors of such waves and explores the physical relevance of the mathematical results that are presented. The book is intended for mathematicians, physicists and engineers interested in the interplay between physical concepts and insights and the mathematical ideas and methods that are relevant to specific water-wave phenomena. The material is an expanded version of the author's lectures delivered at the NSF-CBMS Regional Research Conference in the Mathematical Sciences organized by the Mathematics Department of the University of Texas-Pan American in 2010.

Journal of Nonlinear Mathematical Physics

Author :
Publisher : atlantis press
ISBN 13 : 9078677023
Total Pages : 639 pages
Book Rating : 4.0/5 (786 download)

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Book Synopsis Journal of Nonlinear Mathematical Physics by :

Download or read book Journal of Nonlinear Mathematical Physics written by and published by atlantis press. This book was released on with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Resonance Analysis

Author : Elena Kartashova
Publisher : Cambridge University Press
ISBN 13 : 1139493086
Total Pages : 241 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Nonlinear Resonance Analysis by : Elena Kartashova

Download or read book Nonlinear Resonance Analysis written by Elena Kartashova and published by Cambridge University Press. This book was released on 2010-10-21 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780521763608.

Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition)

Author :
Publisher : World Scientific
ISBN 13 : 9814282251
Total Pages : 444 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) by :

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."-

Imperfect Bifurcation in Structures and Materials

Author : Kiyohiro Ikeda
Publisher : Springer Nature
ISBN 13 : 3030214737
Total Pages : 607 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Imperfect Bifurcation in Structures and Materials by : Kiyohiro Ikeda

Download or read book Imperfect Bifurcation in Structures and Materials written by Kiyohiro Ikeda and published by Springer Nature. This book was released on 2019-09-25 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.

Spatio-temporal Chaos & Vacuum Fluctuations Of Quantized Fields

Author : Christian Beck
Publisher : World Scientific
ISBN 13 : 9814489689
Total Pages : 292 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Spatio-temporal Chaos & Vacuum Fluctuations Of Quantized Fields by : Christian Beck

Download or read book Spatio-temporal Chaos & Vacuum Fluctuations Of Quantized Fields written by Christian Beck and published by World Scientific. This book was released on 2002-04-29 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes new applications for spatio-temporal chaotic dynamical systems in elementary particle physics and quantum field theories. The stochastic quantization approach of Parisi and Wu is extended to more general deterministic chaotic processes as generated by coupled map lattices. In particular, so-called chaotic strings are introduced as a suitable small-scale dynamics of vacuum fluctuations. This more general approach to second quantization reduces to the ordinary stochastic quantization scheme on large scales, but it also opens up interesting new perspectives: chaotic strings appear to minimize their vacuum energy for the observed numerical values of the free standard model parameters.

Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics

Author : Rainer Klages
Publisher : World Scientific
ISBN 13 : 9812565078
Total Pages : 458 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics by : Rainer Klages

Download or read book Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics written by Rainer Klages and published by World Scientific. This book was released on 2007 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory.Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity.Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors.The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.

Smooth Particle Applied Mechanics: The State Of The Art

Author : William Graham Hoover
Publisher : World Scientific
ISBN 13 : 9814477184
Total Pages : 315 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Smooth Particle Applied Mechanics: The State Of The Art by : William Graham Hoover

Download or read book Smooth Particle Applied Mechanics: The State Of The Art written by William Graham Hoover and published by World Scientific. This book was released on 2006-11-02 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes readers through all the steps necessary for solving hard problems in continuum mechanics with smooth particle methods. Pedagogical problems clarify the generation of initial conditions, the treatment of boundary conditions, the integration of the equations of motion, and the analysis of the results. Particular attention is paid to the parallel computing necessary for large problems and to the graphic displays, including debugging software, required for the efficient completion of computational projects.The book is self-contained, with summaries of classical particle mechanics and continuum mechanics for both fluids and solids, computer languages, the stability of numerical methods, Lyapunov spectra, and message-passing parallel computing. The main difficulties faced by meshless particle methods are discussed and the means of overcoming them are illustrated with worked examples.

Energy Localisation And Transfer

Author : Thierry Dauxois
Publisher : World Scientific
ISBN 13 : 9814483346
Total Pages : 428 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Energy Localisation And Transfer by : Thierry Dauxois

Download or read book Energy Localisation And Transfer written by Thierry Dauxois and published by World Scientific. This book was released on 2004-02-09 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to localised excitations in spatially discrete systems, from the experimental, numerical and mathematical points of view. Also known as discrete breathers, nonlinear lattice excitations and intrinsic localised modes, these are spatially localised time periodic motions in networks of dynamical units. Examples of such networks are molecular crystals, biomolecules, and arrays of Josephson superconducting junctions. The book also addresses the formation of discrete breathers and their potential role in energy transfer in such systems.

Time Reversibility, Computer Simulation, Algorithms, Chaos (2nd Edition)

Author : William Graham Hoover
Publisher : World Scientific
ISBN 13 : 9814452971
Total Pages : 426 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Time Reversibility, Computer Simulation, Algorithms, Chaos (2nd Edition) by : William Graham Hoover

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.

Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott

Author : William Graham Hoover
Publisher : World Scientific Publishing Company
ISBN 13 : 9814656844
Total Pages : 325 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott by : William Graham Hoover

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.