Nonlinear Waves In Elastic Media
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Nonlinear Waves In Elastic Media
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Author : A.G. Kulikovskii
language : en
Publisher: CRC Press
Release Date : 2021-07-01
Nonlinear Waves In Elastic Media written by A.G. Kulikovskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-01 with Mathematics categories.
Nonlinear Waves in Elastic Media explores the theoretical results of one-dimensional nonlinear waves, including shock waves, in elastic media. It is the first book to provide an in-depth and comprehensive presentation of the nonlinear wave theory while taking anisotropy effects into account. The theory is completely worked out and draws on 15 years of research by the authors, one of whom also wrote the 1965 classic Magnetohydrodynamics. Nonlinear Waves in Elastic Media emphasizes the behavior of quasitransverse waves and analyzes arbitrary discontinuity disintegration problems, illustrating that the solution can be non-unique - a surprising result. The solution is shown to be especially interesting when anisotropy and nonlinearity effects interact, even in small-amplitude waves. In addition, the text contains an independent mathematical chapter describing general methods to study hyperbolic systems expressing the conservation laws. The theoretical results described in Nonlinear Waves in Elastic Media allow, for the first time, discovery and interpretation of many new peculiarities inherent to the general problem of discontinuous solutions and so provide a valuable resource for advanced students and researchers involved with continuum mechanics and partial differential equations.
Nonlinear Waves In Elastic Media
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Author : A.G. Kulikovskii
language : en
Publisher: CRC Press
Release Date : 2021-06-30
Nonlinear Waves In Elastic Media written by A.G. Kulikovskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-30 with Mathematics categories.
Nonlinear Waves in Elastic Media explores the theoretical results of one-dimensional nonlinear waves, including shock waves, in elastic media. It is the first book to provide an in-depth and comprehensive presentation of the nonlinear wave theory while taking anisotropy effects into account. The theory is completely worked out and draws on 15 years of research by the authors, one of whom also wrote the 1965 classic Magnetohydrodynamics. Nonlinear Waves in Elastic Media emphasizes the behavior of quasitransverse waves and analyzes arbitrary discontinuity disintegration problems, illustrating that the solution can be non-unique - a surprising result. The solution is shown to be especially interesting when anisotropy and nonlinearity effects interact, even in small-amplitude waves. In addition, the text contains an independent mathematical chapter describing general methods to study hyperbolic systems expressing the conservation laws. The theoretical results described in Nonlinear Waves in Elastic Media allow, for the first time, discovery and interpretation of many new peculiarities inherent to the general problem of discontinuous solutions and so provide a valuable resource for advanced students and researchers involved with continuum mechanics and partial differential equations.
Questions About Elastic Waves
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Author : Jüri Engelbrecht
language : en
Publisher: Springer
Release Date : 2015-03-05
Questions About Elastic Waves written by Jüri Engelbrecht and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-05 with Mathematics categories.
This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step path towards increased knowledge. The focus is on waves in elastic solids, although some examples also concern non-conservative cases for the sake of completeness. Special attention is paid to the understanding of the influence of microstructure, nonlinearity and internal variables in continua. With the help of many mathematical models for describing waves, physical phenomena concerning wave dispersion, nonlinear effects, emergence of solitary waves, scales and hierarchies of waves as well as the governing physical parameters are analysed. Also, the energy balance in waves and non-conservative models with energy influx are discussed. Finally, all answers are interwoven into the canvas of complexity.
Nonlinear Waves In Elastic Crystals
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Author : Gérard A. Maugin
language : en
Publisher:
Release Date : 1999
Nonlinear Waves In Elastic Crystals written by Gérard A. Maugin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. In this way the student is introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.
Nonlinear Waves In Integrable And Non Integrable Systems
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Author : Jianke Yang
language : en
Publisher: SIAM
Release Date : 2010-12-02
Nonlinear Waves In Integrable And Non Integrable Systems written by Jianke Yang and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-02 with Science categories.
Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).
Nonlinear Waves In Active Media
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Author : Jüri Engelbrecht
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Waves In Active Media written by Jüri Engelbrecht and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
TIlis volume contains the contributions to the Euromech Colloquium No. 241 on Nonlinear Waves in Active Media at the Institute of Cybernetics of the Estonian Academy of Sciences, Tallinn, Estonia, USSR, September 27-30, 1988. The Co-chairmen of the Euromech Colloquium felt that it would be a good service to the community to publish these proceedings. First, the topic itself dealing with various wave processes with energy influx is extremely interesting and attracted a much larger number of participants than usual - a clear sign of its importance to the scientific community. Second, Euromech No. 241 was actually the first Euromech Colloquium held in the Soviet Union and could thus be viewed as a milestone in the extending scientific contacts between East and West. At the colloquium 50 researchers working in very different branches of sci ence met to lecture on their results and to discuss problems of common interest. An introductory paper by I. Engelbrecht presents the common motivation and background of the topics covered. Altogether 36 speakers presented their lectures, of which 30 are gathered here. The remaining six papers which will appear elsewhere are listed on page X. In addition, three contributions by authors who could not attend the colloquium are included. The two lectures given by A.S. Mikhailov, V.S. Davydov and V.S. Zykov are here published as one long paper.
Nonlinear Dispersive Waves
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Author : Mark J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08
Nonlinear Dispersive Waves written by Mark J. Ablowitz 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 2011-09-08 with Mathematics categories.
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.
Nonlinear Wave Processes In Acoustics
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Author : K. Naugolnykh
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-28
Nonlinear Wave Processes In Acoustics written by K. Naugolnykh 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 1998-05-28 with Mathematics categories.
This text considers models of different "acoustic" media as well as equations and behavior of finite-amplitude waves. It also considers the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction on the evolution and interaction of acoustic beams.
Nonlinear Waves
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Author : Lokenath Debnath
language : en
Publisher: CUP Archive
Release Date : 1983-12-30
Nonlinear Waves written by Lokenath Debnath and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-12-30 with Mathematics categories.
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.
Nonlinear Elastic Waves In Materials
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Author : Jeremiah J. Rushchitsky
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-23
Nonlinear Elastic Waves In Materials written by Jeremiah J. Rushchitsky and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-23 with Science categories.
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professionally interesting in waves. But mechanics is understood in the broad sense, when it includes mechanical and other engineering, material science, applied mathematics and physics and so forth. The genesis of this book can be found in author’s years of research and teaching while a head of department at SP Timoshenko Institute of Mechanics (National Academy of Sciences of Ukraine), a member of Center for Micro and Nanomechanics at Engineering School of University of Aberdeen (Scotland) and a professor at Physical-Mathematical Faculty of National Technical University of Ukraine “KPI”. The book comprises 11 chapters. Each chapter is complemented by exercises, which can be used for the next development of the theory of nonlinear waves.