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Author: J. Engelbrecht Publisher: Springer Science & Business Media ISBN: 9401588910 Category : Technology & Engineering Languages : en Pages : 197
Book Description
At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.
Author: J. Engelbrecht Publisher: Springer Science & Business Media ISBN: 9401588910 Category : Technology & Engineering Languages : en Pages : 197
Book Description
At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.
Author: Patrick Lynett Publisher: World Scientific ISBN: 9812709037 Category : Science Languages : en Pages : 314
Book Description
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: G. B. Whitham Publisher: John Wiley & Sons ISBN: 1118031202 Category : Science Languages : en Pages : 660
Book Description
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: A.I. Maimistov Publisher: Springer Science & Business Media ISBN: 9401724482 Category : Science Languages : en Pages : 668
Book Description
A non-linear wave is one of the fundamental objects of nature. They are inherent to aerodynamics and hydrodynamics, solid state physics and plasma physics, optics and field theory, chemistry reaction kinetics and population dynamics, nuclear physics and gravity. All non-linear waves can be divided into two parts: dispersive waves and dissipative ones. The history of investigation of these waves has been lasting about two centuries. In 1834 J. S. Russell discovered the extraordinary type of waves without the dispersive broadening. In 1965 N. J. Zabusky and M. D. Kruskal found that the Korteweg-de Vries equation has solutions of the solitary wave form. This solitary wave demonstrates the particle-like properties, i. e. , stability under propagation and the elastic interaction under collision of the solitary waves. These waves were named solitons. In succeeding years there has been a great deal of progress in understanding of soliton nature. Now solitons have become the primary components in many important problems of nonlinear wave dynamics. It should be noted that non-linear optics is the field, where all soliton features are exhibited to a great extent. This book had been designed as the tutorial to the theory of non-linear waves in optics. The first version was projected as the book covering all the problems in this field, both analytical and numerical methods, and results as well. However, it became evident in the process of work that this was not a real task.
Author: Maged Marghany Publisher: Elsevier ISBN: 0128209259 Category : Science Languages : en Pages : 464
Book Description
Nonlinear Ocean Dynamics: Synthetic Aperture Radar delivers the critical tools needed to understand the latest technology surrounding the radar imaging of nonlinear waves, particularly microwave radar, as a main source to understand, analyze and apply concepts in the field of ocean dynamic surface. Filling the gap between modern physics quantum theory and applications of radar imaging of ocean dynamic surface, this reference is packed with technical details associated with the potentiality of synthetic aperture radar (SAR). The book also includes key methods needed to extract the value-added information necessary, such as wave spectra energy, current pattern velocity, internal waves, and more. This book also reveals novel speculation of a shallow coastal front: named as Quantized Marghany's Front. Rounding out with practical simulations of 4-D wave-current interaction patterns using using radar images, the book brings an effective new source of technology and applications for today’s coastal scientists and engineers. Solves specific problems surrounding the nonlinearity of ocean surface dynamics in synthetic aperture radar data Helps develop new algorithms for retrieving ocean wave spectra and ocean current movements from synthetic aperture radar Includes over 100 equations that illustrate how to follow examples in the book
Author: Santo Banerjee Publisher: CRC Press ISBN: 1000404757 Category : Science Languages : en Pages : 218
Book Description
Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media. It provides an introduction to the background of dynamical systems, waves, oscillations and plasmas. Basic concepts of dynamical systems and phase plane analysis for the study of dynamical properties of nonlinear waves in plasmas are presented. Different kinds of waves in plasmas are introduced. Reductive perturbative technique and its applications to derive different kinds of nonlinear evolution equations in plasmas are discussed. Analytical wave solutions of these nonlinear evolution equations are presented using the concept of bifurcation theory of planar dynamical systems in a very simple way. Bifurcations of both small and arbitrary amplitudes of various nonlinear acoustic waves in plasmas are presented using phase plots and time-series plots. Super nonlinear waves and its bifurcation behaviour are discussed for various plasma systems. Multiperiodic, quasiperiodic and chaotic motions of nonlinear plasma waves are discussed in presence of external periodic force. Multistability of plasma waves is investigated. Stable oscillation of plasma waves is also presented in dissipative plasmas. The book is meant for undergraduate and postgraduate students studying plasma physics. It will also serve a reference to the researchers, scientists and faculties to pursue the dynamics of nonlinear waves and its properties in plasmas. It describes the concept of dynamical systems and is useful in understanding exciting features, such as solitary wave, periodic wave, supernonlinear wave, chaotic, quasiperiodic and coexisting structures of nonlinear waves in plasmas. The concepts and approaches, discussed in the book, will also help the students and professionals to study such features in other nonlinear media.
Author: P.S Landa Publisher: Springer Science & Business Media ISBN: 9401587639 Category : Mathematics Languages : en Pages : 550
Book Description
A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
Author: Holm Altenbach Publisher: Springer Nature ISBN: 3030387089 Category : Technology & Engineering Languages : en Pages : 473
Book Description
This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.
Author: Patrick Lynett Publisher: World Scientific ISBN: 9812709045 Category : Science Languages : en Pages : 314
Book Description
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: Alexander G. Bagdoev Publisher: Springer ISBN: 3642372678 Category : Science Languages : en Pages : 274
Book Description
This monograph is devoted to problems of propagation and stability of linear and nonlinear waves in continuous media with complex structure. It considers the different media, such as solid with cavities, preliminary deformed disperse medium, solid with porosity filled by the electrically conductive and non-conductive liquid, magnetoelastic, piezo-semiconductors, crystals with dislocations, composites with inclusions, an electrically conductive asymmetrical liquid, a mixture of gas with a drop liquid. The book also considers the propagation of a laser beam through a two-level medium. The presented results are based on methods of evolution and modulation equations that were developed by the authors. The book is intended for scientific and technical researchers, students and post-graduate students specializing in mechanics of continuous media, physical acoustics, and physics of the solid state.
Author: J. Engelbrecht
Author: J. Engelbrecht
Author: Patrick Lynett
Author: G. B. Whitham
Author: A.I. Maimistov
Author: Maged Marghany
Author: Santo Banerjee
Author: P.S Landa
Author: Holm Altenbach
Author: Patrick Lynett
Author: Alexander G. Bagdoev