Linear And Nonlinear Wave Propagation

Author : Anonim
Publisher : Elsevier
Page : 322 pages
File Size : 46,8 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080957803

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Non-Linear Wave Propagation With Applications to Physics and Magnetohydrodynamics by A Jeffrey and T Taniuti by Anonim Pdf

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Author : Spencer P Kuo
Publisher : World Scientific
Page : 206 pages
File Size : 54,9 Mb
Release : 2021-04-16
Category : Science
ISBN : 9789811231650

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Linear And Nonlinear Wave Propagation by Spencer P Kuo Pdf

Waves are essential phenomena in most scientific and engineering disciplines, such as electromagnetism and optics, and different mechanics including fluid, solid, structural, quantum, etc. They appear in linear and nonlinear systems. Some can be observed directly and others are not. The features of the waves are usually described by solutions to either linear or nonlinear partial differential equations, which are fundamental to the students and researchers.Generic equations, describing wave and pulse propagation in linear and nonlinear systems, are introduced and analyzed as initial/boundary value problems. These systems cover the general properties of non-dispersive and dispersive, uniform and non-uniform, with/without dissipations. Methods of analyses are introduced and illustrated with analytical solutions. Wave-wave and wave-particle interactions ascribed to the nonlinearity of media (such as plasma) are discussed in the final chapter.This interdisciplinary textbook is essential reading for anyone in above mentioned disciplines. It was prepared to provide students with an understanding of waves and methods of solving wave propagation problems. The presentation is self-contained and should be read without difficulty by those who have adequate preparation in classic mechanics. The selection of topics and the focus given to each provide essential materials for a lecturer to cover the bases in a linear/nonlinear wave course.

Author : Alwyn Scott
Publisher : John Wiley & Sons
Page : 360 pages
File Size : 55,7 Mb
Release : 1970
Category : Mathematics
ISBN : UOM:39015050259376

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Active and Nonlinear Wave Propagation in Electronics by Alwyn Scott Pdf

Author : G. B. Whitham
Publisher : John Wiley & Sons
Page : 660 pages
File Size : 48,7 Mb
Release : 2011-10-18
Category : Science
ISBN : 9781118031209

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Linear and Nonlinear Waves by G. B. Whitham Pdf

Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.

Author : Francesco Romeo,Massimo Ruzzene
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 47,7 Mb
Release : 2013-07-30
Category : Technology & Engineering
ISBN : 9783709113097

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Wave Propagation in Linear and Nonlinear Periodic Media by Francesco Romeo,Massimo Ruzzene Pdf

Waves and defect modes in structures media.- Piezoelectric superlattices and shunted periodic arrays as tunable periodic structures and metamaterials.- Topology optimization.- Map-based approaches for periodic structures.- Methodologies for nonlinear periodic media.​ The contributions in this volume present both the theoretical background and an overview of the state-of-the art in wave propagation in linear and nonlinear periodic media in a consistent format. They combine the material issued from a variety of engineering applications, spanning a wide range of length scale, characterized by structures and materials, both man-made and naturally occurring, featuring geometry, micro-structural and/or materials properties that vary periodically in space, including periodically stiffened plates, shells and beam-like as well as bladed disc assemblies, phononic metamaterials, photonic crystals and ordered granular media. Along with linear models and applications, analytical methodologies for analyzing and exploiting complex dynamical phenomena arising in nonlinear periodic systems are also presented.​

Author : D. S. Drumheller
Publisher : Cambridge University Press
Page : 546 pages
File Size : 40,5 Mb
Release : 1998-02-13
Category : Science
ISBN : 0521587468

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Introduction to Wave Propagation in Nonlinear Fluids and Solids by D. S. Drumheller Pdf

Waves occur widely in nature and have innumerable commercial uses. Pressure waves are responsible for the transmission of speech, bow waves created by meteors can virtually ignite the earth's atmosphere, ultrasonic waves are used for medical imaging, and shock waves are used for the synthesis of new materials. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models. It covers gases, liquids, and solids as integral parts of the subject. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Graduate students, as well as professional engineers and applied physicists, will value this clear, comprehensive introduction to the study of wave phenomena.

Author : K. Murawski
Publisher : World Scientific
Page : 260 pages
File Size : 55,9 Mb
Release : 2002
Category : Science
ISBN : 981277663X

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Analytical and Numerical Methods for Wave Propagation in Fluid Media by K. Murawski Pdf

This book surveys analytical and numerical techniques appropriate to the description of fluid motion with an emphasis on the most widely used techniques exhibiting the best performance.Analytical and numerical solutions to hyperbolic systems of wave equations are the primary focus of the book. In addition, many interesting wave phenomena in fluids are considered using examples such as acoustic waves, the emission of air pollutants, magnetohydrodynamic waves in the solar corona, solar wind interaction with the planet venus, and ion-acoustic solitons.

Author : Satyanad Kichenassamy
Publisher : CRC Press
Page : 297 pages
File Size : 55,9 Mb
Release : 2021-05-30
Category : Mathematics
ISBN : 9781000444728

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Nonlinear Wave Equations by Satyanad Kichenassamy Pdf

This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.

Author : Igor V. Andrianov,Jan Awrejcewicz,Vladyslav Danishevskyy
Publisher : CRC Press
Page : 322 pages
File Size : 53,8 Mb
Release : 2021-04-22
Category : Technology & Engineering
ISBN : 9781000372212

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Linear and Nonlinear Waves in Microstructured Solids by Igor V. Andrianov,Jan Awrejcewicz,Vladyslav Danishevskyy Pdf

This book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics, notably wave processes in heterogeneous materials. Presenting original solutions to common issues within mechanics, this book builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering and material science. Focusing on linear and nonlinear wave phenomena in complex micro-structured solids, the book determines their global characteristics through analysis of their internal structure, using homogenization and asymptotic procedures, in line with the latest thinking within the field. The book’s cutting-edge methodology can be applied to optimal design, non-destructive control and in deep seismic sounding, providing a valuable alternative to widely used numerical methods. Using case studies, the book covers topics such as elastic waves in nonhomogeneous materials, regular and chaotic dynamics based on continualisation and discretization and vibration localization in 1D Linear and Nonlinear lattices. The book will be of interest to students, research engineers, and professionals specialising in mathematics and physics as well as mechanical and civil engineering.

Author : Alan Jeffrey
Publisher : Unknown
Page : 369 pages
File Size : 47,7 Mb
Release : 1964
Category : Electronic
ISBN : OCLC:859841866

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Non-linear Wave Propagation, with Applications to Physics and Magnetohydrodynamics [by] A. Jeffrey [and] T. Taniuti by Alan Jeffrey Pdf

Author : Regional Research Conference on Mathematical Methods in Nonlinear Wave Propagation
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 43,9 Mb
Release : 2005
Category : Nonlinear theories
ISBN : 9780821833490

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Mathematical Studies in Nonlinear Wave Propagation by Regional Research Conference on Mathematical Methods in Nonlinear Wave Propagation Pdf

Lively discussions and stimulating research were part of a five-day conference on Mathematical Methods in Nonlinear Wave Propagation sponsored by the NSF and CBMS. This volume is a collection of lectures and papers stemming from that event. Leading experts present dynamical systems and chaos, scattering and spectral theory, nonlinear wave equations, optimal control, optical waveguide design, and numerical simulation. The book is suitable for a diverse audience of mathematical specialists interested in fiber optic communications and other nonlinear phenomena. It is also suitable for engineers and other scientists interested in the mathematics of nonlinear wave propagation.

Author : Lokenath Debnath
Publisher : CUP Archive
Page : 376 pages
File Size : 41,6 Mb
Release : 1983-12-30
Category : Mathematics
ISBN : 052125468X

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Nonlinear Waves by Lokenath Debnath Pdf

The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

Author : Vladimir Evgenʹevich Zakharov
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 48,8 Mb
Release : 1998
Category : Hamiltonian systems
ISBN : 0821841130

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Nonlinear Waves and Weak Turbulence by Vladimir Evgenʹevich Zakharov Pdf

This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincare normal forms and the inverse scattering method.

Author : P. L. Bhatnagar
Publisher : Oxford University Press, USA
Page : 162 pages
File Size : 40,8 Mb
Release : 1979
Category : Language Arts & Disciplines
ISBN : UOM:39015017342356

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Nonlinear Waves in One-dimensional Dispersive Systems by P. L. Bhatnagar Pdf

Author : Mark J. Ablowitz
Publisher : Cambridge University Press
Page : 363 pages
File Size : 50,7 Mb
Release : 2011-09-08
Category : Mathematics
ISBN : 9781139503488

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Nonlinear Dispersive Waves by Mark J. Ablowitz Pdf

The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.