Download or read book A Variational Principle for Periodic Waves of Infinite Depth Classic Reprint written by Ellen R. Gottlieb and published by Forgotten Books. This book was released on 2018-02-05 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A Variational Principle for Periodic Waves of Infinite Depth Most of the results in this paper rest upon the investi gation of properties of M. Formulas for the first and second variations of M will be derived. The functional M and its first variation 6m will be important in showing the impossibility of the existence of certain asymmetric periodic waves. In the special case in which the wave is almost flat, we indicate in Chapter 4 how M might be used to set up an existence proof for periodic waves on an ocean of infinite depth. In particular we show that for a fixed area and a certain fixed potential energy. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book A Variational Principle for Periodic Waves of Infinite Depth written by Ellen Ruth Gottlieb and published by . This book was released on 1969 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper deals with periodic waves on an ocean of infinite depth. The flow is assumed to be two-dimensional, incompressible, steady, and irrotational. The impossibility of the existence of an asymmetric wave is proved. This is accomplished through an application of Steiner symmetrization. Also discussed is the shape of possible periodic waves. Using the calculus of variations, an extremal problem is set up involving the kinetic energy, an area integral, and the potential energy. For waves of small amplitude the kinetic energy is shown to be a minimum if one fixes the area and the potential energy. This is accomplished by showing the first variation to be zero and the second variation to be positive. Since the kinetic energy is closely related to the Dirichlet integral, this is a generalization of the Dirichlet principle. This result is applicable in showing the existence of periodic surface waves. (Author).
Download or read book A Variational Principle for Periodic Waves of Infinite Depth written by Ellen Ruth Gottlieb and published by . This book was released on 1969 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper deals with periodic waves on an ocean of infinite depth. The flow is assumed to be two-dimensional, incompressible, steady, and irrotational. The impossibility of the existence of an asymmetric wave is proved. This is accomplished through an application of Steiner symmetrization. Also discussed is the shape of possible periodic waves. Using the calculus of variations, an extremal problem is set up involving the kinetic energy, an area integral, and the potential energy. For waves of small amplitude the kinetic energy is shown to be a minimum if one fixes the area and the potential energy. This is accomplished by showing the first variation to be zero and the second variation to be positive. Since the kinetic energy is closely related to the Dirichlet integral, this is a generalization of the Dirichlet principle. This result is applicable in showing the existence of periodic surface waves. (Author).
Download or read book A Variational Principle for Periodic Waves of Infinite Depth Primary Source Edition written by Ellen R. Gottlieb and published by . This book was released on 2013-10 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1990 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Problems in the Theory of Water Waves written by Frederic Dias and published by American Mathematical Soc.. This book was released on 1996 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings featured in this book grew out of a conference attended by 40 applied mathematicians and physicists which was held at the International Center for Research in Mathematics in Luminy, France, in May 1995. This volume reviews recent developments in the mathematical theory of water waves. The following aspects are considered: modeling of various wave systems, mathematical and numerical analysis of the full water wave problem (the Euler equations with a free surface) and of asymptotic models (Korteweg-de Vries, Boussinesq, Benjamin-Ono, Davey-Stewartson, Kadomtsev-Petviashvili, etc.), and existence and stability of solitary waves.
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.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quasi Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity written by Roberto Feola and published by American Mathematical Society. This book was released on 2024-04-17 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book A Variational Approach to Surface Solitary Waves written by R. E. L. Turner and published by . This book was released on 1983 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research in experimental and theoretical hydrodynamics in the las few decades has indicated that solitary waves play a special role in the evolution of general disturbances in fluids. Still, the investigation of solitary waves and, in particular, the use of variational principles associated with these waves is far from complete. While variational principles for surface waves in fluids of constant density have been discussed in the literature, the existence proofs given here appear to be the first rigorous use of critical point theory to obtain surface waves. Moreover, we treat a class of density profiles not heretofore included in an exact theory. In this report we treat a two-dimensional flow fo an incompressible, inviscid fluid in a region with a horizontal bottom of infinite extent and a free upper surface. The fluid is acted on by gravity and has a non-diffusive, variable density which may be discontinuous. It is shown by means of a variational principle that the governing equations allow both periodic and single-crested progressing waves of permanent form, the analogues, respectively, of the classical cnoidal and solitary waves. The solitary waves are obtained from periodic ones as the periods grow unboundedly. All of the waves obtained have elevated streamlines and have speds greater than the critical speed associated withthe ambient density. Further, the amplitudes are shown to be exponentially decreasing away from the crest.
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.
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.
Download or read book Scaling Limits and Models in Physical Processes written by Carlo Cercignani and published by Birkhäuser. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory text, in two parts, on scaling limits and modelling in equations of mathematical physics. The first part is concerned with basic concepts of the kinetic theory of gases which is not only important in its own right but also as a prototype of a mathematical construct central to the theory of non-equilibrium phenomena in large systems. It also features a very readable historic survey of the field. The second part dwells on the role of integrable systems for modelling weakly nonlinear equations which contain the effects of both dispersion and nonlinearity. Starting with a historical introduction to the subject and a description of numerical techniques, it proceeds to a discussion of the derivation of the Korteweg de Vries and nonlinear Schrödinger equations, followed by a careful treatment of the inverse scattering theory for the Schrödinger operator. The book provides an up-to-date and detailed overview to this very active area of research and is intended as an accessible introduction for non-specialists and graduate students in mathematics, physics and engineering.
Download or read book New Trends In Differential Equations Control Theory And Optimization Proceedings Of The 8th Congress Of Romanian Mathematicians written by Viorel Barbu and published by World Scientific. This book was released on 2016-06-17 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains a collection of original papers and surveys in various areas of Differential Equations, Control Theory and Optimization written by well-known specialists and is thus useful for PhD students and researchers in applied mathematics.
Download or read book U S Government Research Development Reports written by and published by . This book was released on 1969 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book U S Government Research and Development Reports written by and published by . This book was released on 1969-10 with total page 1340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 2011-01-01 with total page 333 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 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.
