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| Author | : Lewis Madison Hull |
| Publisher | : |
| Total Pages | : 18 |
| Release | : 1920 |
| Genre | : Modulation (Electronics) |
| ISBN | : |
| Author | : Lev A. Ostrovsky |
| Publisher | : Johns Hopkins University Press |
| Total Pages | : 0 |
| Release | : 2003-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780801873256 |
Waves occur naturally in a vast number of scientific or engineering situations. Ripples on a pond, the light we see, and the oscillations of bridges and buildings can often be described as solitary or interacting waves. Wave theory is therefore one of the most important branches of pure and applied science. In Modulated Waves: Theory and Applications Lev Ostrovsky and Alexander Potapov consider linear and nonlinear waves such as solitons, waves in inhomogeneous media, and many others. They discuss modulated waves—those characterized by a slow variation of the macroscopic parameters of amplitude, frequency, and profile. Most of the fundamentals of wave theory may be understood by considering this class of waves. Theoretical analysis is supported by examples from different branches of physics: electrodynamics, fluid mechanics, acoustics, optics, and the mechanics of solids.
| Author | : A. Doelman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 122 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 0821842935 |
The authors investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg-Landau equation, they establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, they show that the viscous shock profiles in the Burgers equation for the wave number can be found as genuine modulated waves in the underlying reaction-diffusion system. In other words, they establish the existence and stability of waves that are time-periodic in appropriately moving coordinate frames which separate regions in physical space that are occupied by wave trains of different, but almost identical, wave number. The speed of these shocks is determined by the Rankine-Hugoniot condition where the flux is given by the nonlinear dispersion relation of the wave trains. The group velocities of the wave trains in a frame moving with the interface are directed toward the interface. Using pulse-interaction theory, the authors also consider similar shock profiles for wave trains with large wave number, that is, for an infinite sequence of widely separated pulses. The results presented here are applied to the FitzHugh-Nagumo equation and to hydrodynamic stability problems.
| Author | : Franklin Chung-chi Lei |
| Publisher | : |
| Total Pages | : 128 |
| Release | : 1971 |
| Genre | : |
| ISBN | : |
| Author | : G.J. Komen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 265 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9400923090 |
Ten years ago, de Loor and co-workers at TNO, The Netherlands, were the first to report bottom topography patterns in real aperture radar (RAR) images of the southern North Sea. At that time, this was a real puzzle. The skin depth of microwaves for sea water is only of the order of centimeters while the sea bottom is about 20 meters below the surface. Electromagnetic radiation therefore cannot probe the bottom directly. Similar phenomena were found in radar imagery from SEASAT and SIR-AlB synthetic aperture radars (SAR's) of Nantucket Shoals, the English Channel and many other coastal areas. Since then theory and ocean field experiments (Le., Phelps Bank, Georgia Straits, SARSEX, TOWARD, FASINEX, etc.) have advanced our understanding considerably. We now know that these surface signatures are the results of surface currents, perturbed by the bottom topography, which refract the propagation and modulate the energy of (short) surface waves so as to cause microwave backscatter power variations. Hence, any large scale ocean features containing nonuniform surface currents (i.e. internal waves, eddies, fronts, etc.) will cause similar manifestations in the radar imagery by means of current-wave-microwave interactions. Observations confirm this.
| Author | : Julian L. Davis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 303 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461232848 |
This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical tech niques, and on showing how these methods of mathematical physics can be effective in unifying the physics of wave propagation in electromagnetic media. Chapter 1 presents the theory of time-varying electromagnetic fields, which involves a discussion of Faraday's laws, Maxwell's equations, and their appli cations to electromagnetic wave propagation under a variety of conditions.
| Author | : Emmanuel Kengne |
| Publisher | : Springer Nature |
| Total Pages | : 525 |
| Release | : 2023-02-23 |
| Genre | : Science |
| ISBN | : 981196744X |
This book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose–Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross–Pitaevskii equations. Based on the Heisenberg model of spin–spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.
| Author | : James Leland Weblemoe |
| Publisher | : |
| Total Pages | : 58 |
| Release | : 1948 |
| Genre | : |
| ISBN | : |
| Author | : Yu.Z. Miropol'sky |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 413 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 9401713251 |
This monograph creates a systematic interpretation of the theoretical and the most actual experimental aspects of the internal wave dynamics in the ocean. Firstly, it draws attention to the important physical effects from an oceanographical point of view which are presented in mathematical descriptions. Secondly, the book serves as an introduction to the range of modern ideas and the methods in the study of wave processes in dispersive media. The book is meant for specialists in physics of the ocean, oceanography, geophysics, hydroacoustics.
| Author | : Michel Remoissenet |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 353 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 3662037904 |
Written for an interdisciplinary readership, this book is a practical guide to the fascinating world of solitons. The author approaches the subject from the standpoint of applications in optics, hydrodynamics, and electrical and chemical engineering. This third edition has been thoroughly revised and updated.
