Selected Topics In Nonlinear Wave Mechanics

Author : C.I. Christov,Arde Guran
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200956

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Selected Topics in Nonlinear Wave Mechanics by C.I. Christov,Arde Guran Pdf

This book gives an overview ofthe current state of nonlinear wave mechanics with emphasis on strong discontinuities (shock waves) and localized self preserving shapes (solitons) in both elastic and fluid media. The exposition is intentionallyat a detailed mathematical and physical level, our expectation being that the reader will enjoy coming to grips in a concrete manner with advances in this fascinating subject. Historically, modern research in nonlinear wave mechanics began with the famous 1858 piston problem paper of Riemann on shock waves and con tinued into the early part of the last century with the work of Hadamard, Rankine, and Hugoniot. After WWII, research into nonlinear propagation of dispersive waves rapidly accelerated with the advent of computers. Works of particular importance in the immediate post-war years include those of von Neumann, Fermi, and Lax. Later, additional contributions were made by Lighthill, Glimm, Strauss, Wendroff, and Bishop. Dispersion alone leads to shock fronts of the propagating waves. That the nonlinearity can com pensate for the dispersion, leading to propagation with a stable wave having constant velocity and shape (solitons) came as a surprise. A solitary wave was first discussed by J. Scott Russell in 1845 in "Report of British Asso ciations for the Advancement of Science. " He had, while horseback riding, observed a solitary wave travelling along a water channel and followed its unbroken progress for over a mile.

Author : Christo I. Christov,Ardéshir Guran
Publisher : Boston : Birkhäuser
Page : 263 pages
File Size : 46,8 Mb
Release : 2002
Category : Nonlinear waves
ISBN : 3764340592

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Selected Topics in Nonlinear Wave Mechanics by Christo I. Christov,Ardéshir Guran Pdf

Author : Arkadi Berezovski,Tarmo Soomere
Publisher : Springer Nature
Page : 376 pages
File Size : 53,9 Mb
Release : 2019-11-16
Category : Mathematics
ISBN : 9783030299514

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Applied Wave Mathematics II by Arkadi Berezovski,Tarmo Soomere Pdf

This book gathers contributions on various aspects of the theory and applications of linear and nonlinear waves and associated phenomena, as well as approaches developed in a global partnership of researchers with the national Centre of Excellence in Nonlinear Studies (CENS) at the Department of Cybernetics of Tallinn University of Technology in Estonia. The papers chiefly focus on the role of mathematics in the analysis of wave phenomena. They highlight the complexity of related topics concerning wave generation, propagation, transformation and impact in solids, gases, fluids and human tissues, while also sharing insights into selected mathematical methods for the analytical and numerical treatment of complex phenomena. In addition, the contributions derive advanced mathematical models, share innovative ideas on computing, and present novel applications for a number of research fields where both linear and nonlinear wave problems play an important role. The papers are written in a tutorial style, intended for non-specialist researchers and students. The authors first describe the basics of a problem that is currently of interest in the scientific community, discuss the state of the art in related research, and then share their own experiences in tackling the problem. Each chapter highlights the importance of applied mathematics for central issues in the study of waves and associated complex phenomena in different media. The topics range from basic principles of wave mechanics up to the mathematics of Planet Earth in the broadest sense, including contemporary challenges in the mathematics of society. In turn, the areas of application range from classic ocean wave mathematics to material science, and to human nerves and tissues. All contributions describe the approaches in a straightforward manner, making them ideal material for educational purposes, e.g. for courses, master class lectures, or seminar presentations.

Author : S.S. Shen
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401121026

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A Course on Nonlinear Waves by S.S. Shen Pdf

The aim of this book is to give a self-contained introduction to the mathe matical analysis and physical explanations of some basic nonlinear wave phe nomena. This volume grew out of lecture notes for graduate courf;!es which I gave at the University of Alberta, the University of Saskatchewan, ·and Texas A&M University. As an introduction it is not intended to be exhaustive iQ its choice of material, but rather to convey to interested readers a basic; yet practical, methodology as well as some of the more important results obtained since the 1950's. Although the primary purpose of this volume is to serve as a textbook, it should be useful to anyone who wishes to understand or conduct research into nonlinear waves. Here, for the first time, materials on X-ray crystallography and the forced Korteweg-de Vries equation are incorporated naturally into a textbook on non linear waves. Another characteristic feature of the book is the inclusion of four symbolic calculation programs written in MATHEMATICA. They emphasize outcomes rather than numerical methods and provide certain symbolic and nu merical results related to solitons. Requiring only one or two commands to run, these programs have user-friendly interfaces. For example, to get the explicit expression of the 2-soliton of the Korteweg-de Vries equation, one only needs to type in soliton[2] when using the program solipac.m.

Author : Gérard A Maugin,Martine Rousseau
Publisher : World Scientific
Page : 252 pages
File Size : 44,9 Mb
Release : 2015-03-26
Category : Science
ISBN : 9789814663809

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Wave Momentum and Quasi-Particles in Physical Acoustics by Gérard A Maugin,Martine Rousseau Pdf

This unique volume presents an original approach to physical acoustics with additional emphasis on the most useful surface acoustic waves on solids. The study is based on foundational work of Léon Brillouin, and application of the celebrated invariance theorem of Emmy Noether to an element of volume that is representative of the wave motion. This approach provides an easy interpretation of typical wave motions of physical acoustics in bulk, at surfaces, and across interfaces, in the form of the motion of associated quasi-particles. This type of motion, Newtonian or not, depends on the wave motion considered, and on the original modeling of the continuum that supports it. After a thoughtful review of Brillouin's fundamental ideas related to radiative stresses, wave momentum and action, and the necessary reminder on modern nonlinear continuum thermomechanics, invariance theory and techniques of asymptotics, a variety of situations and models illustrates the power and richness of the approach and its strong potential in applications. Elasticity, piezoelectricity and new models of continua with nonlinearity, viscosity and some generalized features (microstructure, weak or strong nonlocality) or unusual situations (bounding surface with energy, elastic thin film glued on a surface waveguide), are considered, exhibiting thus the versatility of the approach. This original book offers an innovative vision and treatment of the problems of wave propagation in deformable solids. It opens up new horizons in the theoretical and applied facets of physical acoustics. Contents:Pro;egomena: Wave Momentum and Radiative Stresses in 1D in the Line of BrillouinElements of Continuum ThermomechanicsPseudomomentum and Eshelby StressAction, Phonons and Wave MechanicsTransmission-Reflection ProblemsApplication to Dynamic MaterialsElastic Surface Waves in Terms of Quasi-ParticlesElectroelastic Surface Waves in Terms of Quasi-ParticlesWaves Generalized Elastic ContinuaExamples of Solitonic Systems Readership: Graduate students and researchers in applied physics and mathematics, as well as accousticians. Key Features:Originality of approach to physical acousticsInnovative vision of the problem of wave propagation in deformable solidsEnriching interaction between mathematical physics and wave theoryKeywords:Waves;Physical Acoustics;Surface Waves;Quasi-Particles;Elasticity;Invariance Theorems

Author : Gerard A. Maugin
Publisher : CRC Press
Page : 562 pages
File Size : 42,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 1439846138

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Configurational Forces by Gerard A. Maugin Pdf

Exploring recent developments in continuum mechanics, Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics presents the general framework for configurational forces. It also covers a range of applications in engineering and condensed matter physics. The author presents the fundamentals of accepted standard continuum mechanics, before introducing Eshelby material stress, field theory, variational formulations, Noether’s theorem, and the resulting conservation laws. In the chapter on complex continua, he compares the classical perspective of B.D. Coleman and W. Noll with the viewpoint linked to abstract field theory. He then describes the important notion of local structural rearrangement and its relationship to Eshelby stress. After looking at the relevance of Eshelby stress in the thermodynamic description of singular interfaces, the text focuses on fracture problems, microstructured media, systems with mass exchanges, and electromagnetic deformable media. The concluding chapters discuss the exploitation of the canonical conservation law of momentum in nonlinear wave propagation, the application of canonical-momentum conservation law and material force in numerical schemes, and similarities of fluid mechanics and aerodynamics. Written by a long-time researcher in mechanical engineering, this book provides a detailed treatment of the theory of configurational forces—one of the latest and most fruitful advances in macroscopic field theories. Through many applications, it shows the depth and efficiency of this theory.

Author : Paul Steinmann,Gérard A. Maugin
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 45,7 Mb
Release : 2006-01-20
Category : Technology & Engineering
ISBN : 9780387262611

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Mechanics of Material Forces by Paul Steinmann,Gérard A. Maugin Pdf

The notion dealt with in this volume of proceedings is often traced back to the late 19th-century writings of a rather obscure scientist, C. V. Burton. A probable reason for this is that the painstaking de ciphering of this author's paper in the Philosophical Magazine (Vol. 33, pp. 191-204, 1891) seems to reveal a notion that was introduced in math ematical form much later, that of local structural rearrangement. This notion obviously takes place on the material manifold of modern con tinuum mechanics. It is more or less clear that seemingly different phe nomena - phase transition, local destruction of matter in the form of the loss of local ordering (such as in the appearance of structural defects or of the loss of cohesion by the appearance of damage or the exten sion of cracks), plasticity, material growth in the bulk or at the surface by accretion, wear, and the production of debris - should enter a com mon framework where, by pure logic, the material manifold has to play a prominent role. Finding the mathematical formulation for this was one of the great achievements of J. D. Eshelby. He was led to consider the apparent but true motion or displacement of embedded material inhomogeneities, and thus he began to investigate the "driving force" causing this motion or displacement, something any good mechanician would naturally introduce through the duahty inherent in mechanics since J. L. d'Alembert.

Author : V.K. Kalpakides,G.A. Maugan
Publisher : CRC Press
Page : 184 pages
File Size : 40,9 Mb
Release : 2004-11-23
Category : Technology & Engineering
ISBN : 0203024559

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Configurational Mechanics by V.K. Kalpakides,G.A. Maugan Pdf

This book comprises papers that were presented at the Symposium on Configurational Mechanics, during the 5th EUROMECH Soil Mechanics Conference in Thessaloniki in August 2003. Configurational (or material) mechanics -in contrast to Newtonian mechanics in Euclidean space- concerns any sort of change or "motion" in the material configuration. This framework provides a novel and unifying view on otherwise diverse disciplines like fracture mechanics, phase transitions, plasticity and dislocation theory. In addition, configurational mechanics can be used in computations because it provides a fruitful interpretation of the field equations in the discretized space. This volume contains eleven contributions from specialists from around Europe Articles concern both theoretical and computational mechanics, electroplasticity, magnetoelasticity, elastoplasticity as well as granular, multiphase and micropolar media.

Author : Nizar Abcha,Efim Pelinovsky,Innocent Mutabazi
Publisher : Springer
Page : 229 pages
File Size : 49,7 Mb
Release : 2018-04-20
Category : Science
ISBN : 9783319781938

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Nonlinear Waves and Pattern Dynamics by Nizar Abcha,Efim Pelinovsky,Innocent Mutabazi Pdf

This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physics of the Russian Academy of Sciences in Nizhny Novgorod (Russia). The chapters have been written by leading scientists in Nonlinear Physics, and the topics chosen so as to cover all the fields to which Prof. Ezersky himself contributed, by means of experimental, theoretical and numerical approaches. The volume will appeal to advanced students and researchers studying nonlinear waves and pattern dynamics, as well as other scientists interested in their applications in various natural media.

Author : Johan Dubbeldam,Kirk Green,Daan Lenstra
Publisher : John Wiley & Sons
Page : 261 pages
File Size : 40,7 Mb
Release : 2011-02-21
Category : Science
ISBN : 9783527409310

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The Complexity of Dynamical Systems by Johan Dubbeldam,Kirk Green,Daan Lenstra Pdf

Written by recognized experts, this edited book covers recent theoretical, experimental and applied issues in the growing fi eld of Complex Systems and Nonlinear Dynamics. It is divided into two parts, with the first section application based, incorporating the theory of bifurcation analysis, numerical computations of instabilities in dynamical systems and discussing experimental developments. The second part covers the broad category of statistical mechanics and dynamical systems. Several novel exciting theoretical and mathematical insights and their consequences are conveyed to the reader.

Author : Stanislaw Sieniutycz,Henrik Farkas
Publisher : Elsevier
Page : 810 pages
File Size : 49,5 Mb
Release : 2010-07-07
Category : Science
ISBN : 0080456146

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Variational and Extremum Principles in Macroscopic Systems by Stanislaw Sieniutycz,Henrik Farkas Pdf

Recent years have seen a growing trend to derive models of macroscopic phenomena encountered in the fields of engineering, physics, chemistry, ecology, self-organisation theory and econophysics from various variational or extremum principles. Through the link between the integral extremum of a functional and the local extremum of a function (explicit, for example, in the Pontryagin’s maximum principle variational and extremum principles are mutually related. Thus it makes sense to consider them within a common context. The main goal of Variational and Extremum Principles in Macroscopic Systems is to collect various mathematical formulations and examples of physical reasoning that involve both basic theoretical aspects and applications of variational and extremum approaches to systems of the macroscopic world. The first part of the book is focused on the theory, whereas the second focuses on applications. The unifying variational approach is used to derive the balance or conservation equations, phenomenological equations linking fluxes and forces, equations of change for processes with coupled transfer of energy and substance, and optimal conditions for energy management. A unique multidisciplinary synthesis of variational and extremum principles in theory and application A comprehensive review of current and past achievements in variational formulations for macroscopic processes Uses Lagrangian and Hamiltonian formalisms as a basis for the exposition of novel approaches to transfer and conversion of thermal, solar and chemical energy

Author : Stephen Nettel
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 42,6 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662053171

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Wave Physics by Stephen Nettel Pdf

This textbook gives a detailed explanation of waves and oscillations in classical physics. These classical phenomena are dealt with at a more advanced level than is customary for second-year courses. All aspects of classical wave physics are presented, including the mathematical and physical basis needed for extended understanding. Finally several chapters are devoted to important topics in current wave physics. Special attention is given to nonlinear waves, solitons, chaotic behavior and associated phenomena. The new edition contains improvements such as full development of Greens functions, a broadening of the treatment of wave mechanics and a closer integration with classical mechanics, plus more examples and problems.

Author : Patrick Lynett
Publisher : World Scientific
Page : 314 pages
File Size : 48,9 Mb
Release : 2009
Category : Science
ISBN : 9789812709035

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Nonlinear Wave Dynamics by Patrick Lynett Pdf

In September 2006, research leaders in the field of coastal engineering, fluid mechanics, and wave theory met at Cornell University to celebrate the 60th birthday of Prof. Philip L-F Liu. This volume is a compilation of the research papers presented at the symposium, and includes both review and new research papers. Topics such as nonlinear wave theory, tsunamis, wave-structure interaction, turbulence, and modeling of complex sediment transport are discussed in this volume. All of the contributing authors are research collaborators of Prof. Liu, and include leaders in coastal engineering such as Maarten Dingemans, Hwung-Hweng Hwung, Nobu Kobayashi, Inigo Losada, Hocine Oumeraci, Costas Synolakis, and Harry Yeh.

Author : Stephen Nettel
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 45,6 Mb
Release : 2008-11-21
Category : Science
ISBN : 9783540879084

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Wave Physics by Stephen Nettel Pdf

This textbook gives a detailed explanation of waves and oscillations in classical physics. These classical phenomena are dealt with at a more advanced level than is customary for second-year courses. All aspects of classical wave physics are presented, including the mathematical and physical basis needed for extended understanding. Finally several chapters are devoted to important topics in current wave physics. Special attention is given to nonlinear waves, solitons, chaotic behavior and associated phenomena. The new edition contains improvements such as full development of Greens functions, a broadening of the treatment of wave mechanics and a closer integration with classical mechanics, plus more examples and problems.

Author : Ardéshir Guran,Anders Boström,Oswald Leroy,Gérard Maze
Publisher : World Scientific
Page : 508 pages
File Size : 53,8 Mb
Release : 2002-07-09
Category : Science
ISBN : 9789814493314

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Acoustic Interactions with Submerged Elastic Structures by Ardéshir Guran,Anders Boström,Oswald Leroy,Gérard Maze Pdf

This series of volumes constitutes an outstanding collection of contributions by the most active research workers in the area of acoustics and mechanics. It brings the reader up to date on the status of the various aspects of research in this field. The volumes should preserve their value for a long time, as they represent a monument to the achievements of human research capabilities in the underwater-acoustics aspects of the environment. Contents:Scattering from Elliptical Shells — A Unified Approach Applicable to Both Elastic and Fluid Media (R P Radlinski & M M Simon)On the Systematic Use of Spherical, Cylindrical and Plane Vector Wave Functions in Elastodynamic Scattering Problems (A Boström)Computational Modeling of Transient Acoustic Wavefields — A Structured Approach Based on Reciprocity (A T de Hoop)Linear Viscoelasticity (F Mainardi)Transient Waves in Linear Viscoelastic Media (F Mainardi)Computational Ocean-Seismoacoustic Modeling Using Finite Elements (J E Murphy & S A Chin-Bing)Nonorthogonality of Measured Normal Modes in a Shallow Water Waveguide (G H Rayborn et al.)Nearfield Acoustical Holography (A Sarkissian)Elimination of Internal Resonance Effects in Acoustic Scattering from Cylinders Using Method of Moments (S P Sun & P K Raju)Pulsed Asymmetric Point Force Loading of a Layered Half-Space (P Borejko & F Ziegler)Nonlinear Stability Analysis of Pre-Stressed Elastic Bodies (Y B Fu & R W Ogden) Readership: Nonlinear scientists. Keywords:Reviews:“… Überall's work in acoustic and electromagnetic scattering has evoked much interest, in the US as well as abroad, because of its possible practical applications, as well as the theoretical understanding. Many collaborators have been inspired by it, and have now contributed to this volume. The book is an excellent contribution to the literature of Acoustics and Wave Propagation. Professor Guran is to be congratulated for organizing and editing this volume.”Prof. Hans A Bethe, Nobel Laureate Cornell University “… This is an impressive collection of 45 research and review chapters involving 78 authors. Taking into account the high educational quality and research value of this set of books, it is recommended for purchase by libraries that serves research programs involved with acoustic scattering related to underwater and ultrasonics.”Professor Philip Marston Journal of the Acoustical Society of America