The Mathematical Theory Of Permanent Progressive Water Waves
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The Mathematical Theory Of Permanent Progressive Water Waves
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Author : Hisashi Okamoto
language : en
Publisher: World Scientific
Release Date : 2001
The Mathematical Theory Of Permanent Progressive Water Waves written by Hisashi Okamoto and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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
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Author : Hisashi Okamoto
language : en
Publisher:
Release Date : 2001
The Mathematical Theory Of Permanent Progressive Water Waves written by Hisashi Okamoto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Nonlinear Water Waves
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Author : Adrian Constantin
language : en
Publisher: Springer
Release Date : 2016-06-28
Nonlinear Water Waves written by Adrian Constantin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-28 with Mathematics categories.
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.
Nonlinear Dispersive Waves
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Author : David Henry
language : en
Publisher: Springer Nature
Release Date : 2024-08-06
Nonlinear Dispersive Waves written by David Henry and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-06 with Mathematics categories.
This volume explores a number of exciting developments in the field of nonlinear dispersive waves with a particular focus on waves arising in the ocean. Chapters are based on talks given at the workshop “Nonlinear Dispersive Waves” that was held at University College Cork, Ireland, on April 24-25, 2023. Specific topics covered include: The recovery of steady rotational wave surface profiles; Hamiltonian models for the propagation of long gravity waves; Waves propagating at the surface of a fluid covered by floating ice plates; The use of spherical coordinates to describe arctic ocean waves; Boundary value problems related to the Muskat Problem. Nonlinear Dispersive Waves will appeal to researchers as well as graduate students interested in this active area of research.
Elliptic And Parabolic Equations
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Author : Joachim Escher
language : en
Publisher: Springer
Release Date : 2015-06-04
Elliptic And Parabolic Equations written by Joachim Escher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-04 with Mathematics categories.
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 Water Waves With Applications To Wave Current Interactions And Tsunamis
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Author : Adrian Constantin
language : en
Publisher: SIAM
Release Date : 2011-01-01
Nonlinear Water Waves With Applications To Wave Current Interactions And Tsunamis written by Adrian Constantin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
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 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
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Author :
language : en
Publisher: atlantis press
Release Date :
Journal Of Nonlinear Mathematical Physics written by and has been published by atlantis press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Nonlinear Resonance Analysis
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Author : Elena Kartashova
language : en
Publisher: Cambridge University Press
Release Date : 2010-10-21
Nonlinear Resonance Analysis written by Elena Kartashova 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 2010-10-21 with Science categories.
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
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Author :
language : en
Publisher: World Scientific
Release Date : 2009
Geometrical Theory Of Dynamical Systems And Fluid Flows Revised Edition written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Fluid dynamics 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."-
Imperfect Bifurcation In Structures And Materials
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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Nature
Release Date : 2019-09-25
Imperfect Bifurcation In Structures And Materials written by Kiyohiro Ikeda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-25 with Science categories.
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.