Localization And Solitary Waves In Solid Mechanics

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Localization and Solitary Waves in Solid Mechanics

Author : A. R. Champneys
Publisher : World Scientific
ISBN 13 : 9789810239152
Total Pages : 400 pages
Book Rating : 4.2/5 (391 download)

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Book Synopsis Localization and Solitary Waves in Solid Mechanics by : A. R. Champneys

Download or read book Localization and Solitary Waves in Solid Mechanics written by A. R. Champneys and published by World Scientific. This book was released on 1999 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classical problems such as the buckling of cylindrical shells, twisted rods and pipelines, to the folding of geological strata, the failure of sandwich structures and the propagation of solitary waves in suspended beam systems.

Localization and Solitary Waves in Solid Mechanics

Author : A. R. Champneys
Publisher :
ISBN 13 :
Total Pages : 141 pages
Book Rating : 4.:/5 (382 download)

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Book Synopsis Localization and Solitary Waves in Solid Mechanics by : A. R. Champneys

Download or read book Localization and Solitary Waves in Solid Mechanics written by A. R. Champneys and published by . This book was released on 1997 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Localization And Solitary Waves In Solid Mechanics

Author : Alan R Champneys
Publisher : World Scientific
ISBN 13 : 9814494623
Total Pages : 398 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Localization And Solitary Waves In Solid Mechanics by : Alan R Champneys

Download or read book Localization And Solitary Waves In Solid Mechanics written by Alan R Champneys and published by World Scientific. This book was released on 1999-11-30 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classical problems such as the buckling of cylindrical shells, twisted rods and pipelines, to the folding of geological strata, the failure of sandwich structures and the propagation of solitary waves in suspended beam systems.

Normal Modes and Localization in Nonlinear Systems

Author : Alexander F. Vakakis
Publisher : John Wiley & Sons
ISBN 13 : 3527617876
Total Pages : 552 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Normal Modes and Localization in Nonlinear Systems by : Alexander F. Vakakis

Download or read book Normal Modes and Localization in Nonlinear Systems written by Alexander F. Vakakis and published by John Wiley & Sons. This book was released on 2008-07-11 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.

Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena

Author : Ping Sheng
Publisher : Elsevier
ISBN 13 : 9780080535067
Total Pages : 339 pages
Book Rating : 4.5/5 (35 download)

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Book Synopsis Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena by : Ping Sheng

Download or read book Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena written by Ping Sheng and published by Elsevier. This book was released on 1995-04-04 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives readers a coherent picture of waves in disordered media, including multiple scattered waves. The book is intended to be self-contained, with illustrated problems and solutions at the end of each chapter to serve the double purpose of filling out the technical and mathematical details and giving the students exercises if used as a course textbook. The study of wave behavior in disordered media has applications in: Condensed matter physics (semi and superconductor nanostructures and mesoscopic phenomena) Materials science/analytical chemistry (analysis of composite and crystalline structures and properties) Optics and electronics (microelectronic and optoelectronic devices) Geology (seismic exploration of Earths subsurface)

The Mathematical Theory of Permanent Progressive Water-Waves

Author : Hisashi Okamoto
Publisher : World Scientific Publishing Company
ISBN 13 : 9813102691
Total Pages : 244 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis The Mathematical Theory of Permanent Progressive Water-Waves by : Hisashi Okamoto

Download or read book The Mathematical Theory of Permanent Progressive Water-Waves written by Hisashi Okamoto and published by World Scientific Publishing Company. This book was released on 2001-09-28 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid. The problem of permanent water-waves has attracted a large number of physicists and mathematicians since Stokes' pioneering papers appeared in 1847 and 1880. Among many aspects of the problem, the authors focus on periodic progressive waves, which mean waves traveling at a constant speed with no change of shape. As a consequence, everything about standing waves are excluded and solitary waves are studied only partly. However, even for this restricted problem, quite a number of papers and books, in physics and mathematics, have appeared and more will continue to appear, showing the richness of the subject. In fact, there remain many open questions to be answered. The present book consists of two parts: numerical experiments and normal form analysis of the bifurcation equations. Prerequisite for reading it is an elementary knowledge of the Euler equations for incompressible inviscid fluid and of bifurcation theory. Readers are also expected to know functional analysis at an elementary level. Numerical experiments are reported so that any reader can re-examine the results with minimal labor: the methods used in this book are well-known and are described as clearly as possible. Thus, the reader with an elementary knowledge of numerical computation will have little difficulty in the re-examination.

Resolution Of The Twentieth Century Conundrum In Elastic Stability

Author : Isaac E Elishakoff
Publisher : World Scientific
ISBN 13 : 9814583553
Total Pages : 352 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Resolution Of The Twentieth Century Conundrum In Elastic Stability by : Isaac E Elishakoff

Download or read book Resolution Of The Twentieth Century Conundrum In Elastic Stability written by Isaac E Elishakoff and published by World Scientific. This book was released on 2014-05-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been stability theories developed for beams, plates and shells — the most significant elements in mechanical, aerospace, ocean and marine engineering. For beams and plates, the theoretical and experimental values of buckling loads are in close vicinity. However for thin shells, the experimental predictions do not conform with the theory, due to presence of small geometric imperfections that are deviations from the ideal shape.This fact has been referred to in the literature as ‘embarrassing’, ‘paradoxical’ and ‘perplexing’. Indeed, the popular adage, “In theory there is no difference between theory and practice. In practice there is”, very much applies to thin shells whose experimental buckling loads may constitute a small fraction of the theoretical prediction based on classical linear theory; because in practice, engineers use knockdown factors that are not theoretically substantiated.This book presents a uniform approach that tames this prima-donna-like and capricious behavior of structures that has been dubbed the ‘imperfection sensitivity’ — thus resolving the conundrum that has occupied the best minds of elastic stability throughout the twentieth century.

Spatio-Temporal Chaos and Vacuum Fluctuations of Quantized Fields

Author : Christian Beck
Publisher : World Scientific
ISBN 13 : 9814489689
Total Pages : 292 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Spatio-Temporal Chaos and Vacuum Fluctuations of Quantized Fields by : Christian Beck

Download or read book Spatio-Temporal Chaos and Vacuum Fluctuations of Quantized Fields written by Christian Beck and published by World Scientific. This book was released on 2002-04-29 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes new applications for spatio-temporal chaotic dynamical systems in elementary particle physics and quantum field theories. The stochastic quantization approach of Parisi and Wu is extended to more general deterministic chaotic processes as generated by coupled map lattices. In particular, so-called chaotic strings are introduced as a suitable small-scale dynamics of vacuum fluctuations. This more general approach to second quantization reduces to the ordinary stochastic quantization scheme on large scales, but it also opens up interesting new perspectives: chaotic strings appear to minimize their vacuum energy for the observed numerical values of the free standard model parameters. Contents:Chaotic Quantization of Field TheoriesChaotic StringsVacuum Energy of Chaotic StringsPhase Transitions and Spontaneous Symmetry BreakingStochastic Interpretation of the Uncertainty RelationGeneralized Statistical Mechanics ApproachInteraction Energy of Chaotic StringsSelf Energy of Chaotic StringsTotal Vacuum Energy of Chaotic StringsGrand Unification11-Dimensional Space-Time and Quantum GravitySummary Readership: Graduate students, researchers and academics involved in dynamical systems, statistical physics and high energy physics. Keywords:

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 888 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Integrability and Nonintegrability of Dynamical Systems

Author : Alain Goriely
Publisher : World Scientific
ISBN 13 : 9789812811943
Total Pages : 438 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Integrability and Nonintegrability of Dynamical Systems by : Alain Goriely

Download or read book Integrability and Nonintegrability of Dynamical Systems written by Alain Goriely and published by World Scientific. This book was released on 2001 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, its geometrical relevance and dynamical consequences. Integrability theory is approached from different perspectives, first in terms of differential algebra, then in terms of complex time singularities and finally from the viewpoint of phase geometry (for both Hamiltonian and non-Hamiltonian systems). As generic systems of differential equations cannot be exactly solved, the book reviews the different notions of nonintegrability and shows how to prove the nonexistence of exact solutions and/or a constant of motion. Finally, nonintegrability theory is linked to dynamical systems theory by showing how the property of complete integrability, partial integrability or nonintegrability can be related to regular and irregular dynamics in phase space. Contents: Integrability: An Algebraic Approach; Integrability: An Analytic Approach; Polynomial and Quasi-Polynomial Vector Fields; Nonintegrability; Hamiltonian Systems; Nearly Integrable Dynamical Systems; Open Problems. Readership: Mathematical and theoretical physicists and astronomers and engineers interested in dynamical systems.

Time Reversibility, Computer Simulation, And Chaos

Author : William Graham Hoover
Publisher : World Scientific
ISBN 13 : 9814494283
Total Pages : 288 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Time Reversibility, Computer Simulation, And Chaos by : William Graham Hoover

Download or read book Time Reversibility, Computer Simulation, And Chaos written by William Graham Hoover and published by World Scientific. This book was released on 1999-11-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: A small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the “reversibility paradox”, with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the author's approach to the problem of understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying time-reversible mechanics. Computer simulation has made it possible to probe reversibility from a variety of directions and “chaos theory” or “nonlinear dynamics” has supplied a useful vocabulary and set of concepts, which allow a fuller explanation of irreversibility than that available to Boltzmann or to Green and Kubo and Onsager. Clear illustration of concepts is emphasized throughout, and reinforced with a glossary of technical terms from the specialized fields which have been combined here to focus on a common theme.The book begins with a discussion contrasting the idealized reversibility of basic physics and the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory — fractals and Lyapunov instability — are fundamental to the approach.Undergraduate-level physics, calculus, and ordinary differential equations are sufficient background for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers. The generous assortment of examples worked out in the text will stimulate readers to explore the rich and fruitful field of study which links fundamental reversible laws of physics to the irreversibility surrounding us all.

Rayleigh-Bénard Convection

Author : A V Getling
Publisher : World Scientific
ISBN 13 : 9814498971
Total Pages : 256 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Rayleigh-Bénard Convection by : A V Getling

Download or read book Rayleigh-Bénard Convection written by A V Getling and published by World Scientific. This book was released on 1998-03-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book presents a concise but systematic account of the formation of spatial flow structures in a horizontal fluid layer heated from below. Flows of this type, known as Rayleigh-Bénard convection, show important features of behaviour inherent not only in various hydrodynamic-instability phenomena but also in nonlinear pattern-forming processes in other contexts. The book describes the basic methods of investigating convection patterns, and the types of two- and three-dimensional flows, pattern defects, and sequences of convection-regime changes. The author pays special attention to the question of how various factors (mainly reducible to initial and boundary conditions) determine the shapes and sizes of the structures which develop. In this way, the role of order and disorder in flow patterns, as a factor strongly affecting the character of the evolution of structures, is revealed. The presentation emphasizes the physical picture of these phenomena, without excessive mathematical detail. Contents:Basic Concepts:The Boussinesq ApproximationThe Rayleigh-Bénard ProblemLinear AnalysisNonlinear Regimes and BifurcationsPlanforms of Convection CellsInvestigation Tools:ExperimentTheoretical ApproachesBasic Types of Convective-Flow Structures:Two-Dimensional Rolls and Three-Dimensional CellsPatterns of Quasi-Two-Dimensional RollsConvection Textures. Roll-Pattern DefectsConvection-Regimes:Regime DiagramPhase TurbulenceSpiral-Defect ChaosSelection of the Wavenumbers of Convection Rolls:Wavenumbers in Experiments with Random Initial DisturbancesSearches for Universal Selection CriteriaStability of Two-Dimensional Roll FlowsLyapunov Functional and Selection“Selection Mechanisms”Peculiarities of Stratification and Vertical Structure of Convection:Effects of Strong Temperature Dependence of ViscosityPenetrative ConvectionSmall-Scale Motions in a Globally Unstable LayerAstro- and Geophysical Applications Readership: Specialists in nonlinear phenomena, hydrodynamic stability, thermophysics, astrophysics, atmospheric and oceanic physics, applied science and technology; graduate students in physics, mechanics and mathematics. keywords:Rayleigh-BÃ©nard Convection;Thermal Convection;Horizontal Layer;Structures;Patterns;Regimes;Wavenumber Selection “There are no other texts covering similar ground and … this book will be especially useful to any graduate student who wishes to understand modern developments in the theory of convection.” Journal of Fluid Mechanics “… there is no denying that the convective regime of moderate amplitude, where pattern theory works well, is well worth a book of its own, and Getling's is of about the right thickness.” Physics Today “…written competently and authoritatively … by far the best available monograph on Rayleigh-Bénard convection.” European Journal of Mechanics

Topics in Nonlinear Time Series Analysis

Author : Andreas Galka
Publisher : World Scientific
ISBN 13 : 9789810241483
Total Pages : 368 pages
Book Rating : 4.2/5 (414 download)

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Book Synopsis Topics in Nonlinear Time Series Analysis by : Andreas Galka

Download or read book Topics in Nonlinear Time Series Analysis written by Andreas Galka and published by World Scientific. This book was released on 2000 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough review of a class of powerful algorithms for the numerical analysis of complex time series data which were obtained from dynamical systems. These algorithms are based on the concept of state space representations of the underlying dynamics, as introduced by nonlinear dynamics. In particular, current algorithms for state space reconstruction, correlation dimension estimation, testing for determinism and surrogate data testing are presented ? algorithms which have been playing a central role in the investigation of deterministic chaos and related phenomena since 1980. Special emphasis is given to the much-disputed issue whether these algorithms can be successfully employed for the analysis of the human electroencephalogram.

Smooth Dynamical Systems

Author : M C Irwin
Publisher : World Scientific
ISBN 13 : 9814491209
Total Pages : 272 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Smooth Dynamical Systems by : M C Irwin

Download or read book Smooth Dynamical Systems written by M C Irwin and published by World Scientific. This book was released on 2001-04-30 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reprint of M C Irwin's beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area. Request Inspection Copy Contents: Some Simple ExamplesEquivalent SystemsIntegration of Vector FieldsLinear Systems, Linearization, Stable ManifoldsStable SystemsAppendices Readership: Graduate students in mathematics. Keywords:

Positive Transfer Operators And Decay Of Correlations

Author : Viviane Baladi
Publisher : World Scientific
ISBN 13 : 9814496669
Total Pages : 326 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Positive Transfer Operators And Decay Of Correlations by : Viviane Baladi

Download or read book Positive Transfer Operators And Decay Of Correlations written by Viviane Baladi and published by World Scientific. This book was released on 2000-07-12 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description. Indeed, there often exist ergodic invariant measures with special additional features. For a given invariant measure, and a class of observables, the correlation functions tell whether (and how fast) the system “mixes”, i.e. “forgets” its initial conditions.This book, addressed to mathematicians and mathematical (or mathematically inclined) physicists, shows how the powerful technology of transfer operators, imported from statistical physics, has been used recently to construct relevant invariant measures, and to study the speed of decay of their correlation functions, for many chaotic systems. Links with dynamical zeta functions are explained.The book is intended for graduate students or researchers entering the field, and the technical prerequisites have been kept to a minimum.

Symplectic Twist Maps: Global Variational Techniques

Author : Christophe Gole
Publisher : World Scientific
ISBN 13 : 9814506338
Total Pages : 325 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Symplectic Twist Maps: Global Variational Techniques by : Christophe Gole

Download or read book Symplectic Twist Maps: Global Variational Techniques written by Christophe Gole and published by World Scientific. This book was released on 2001-11-22 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates mainly on the theorem of existence of periodic orbits for higher dimensional analogs of Twist maps. The setting is that of a discrete variational calculus and the techniques involve Conley-Zehnder-Morse Theory. They give rise to the concept of ghost tori which are of interest in the dimension 2 case (ghost circles). The debate is oriented somewhat toward the open problem of finding orbits of all (in particular, irrational) rotation vectors.

Combinatorial Dynamics and Entropy in Dimension One

Author : LluÃs AlsedÃ
Publisher : World Scientific Publishing Company
ISBN 13 : 9813105593
Total Pages : 432 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Combinatorial Dynamics and Entropy in Dimension One by : LluÃs AlsedÃ

Download or read book Combinatorial Dynamics and Entropy in Dimension One written by LluÃs AlsedÃ and published by World Scientific Publishing Company. This book was released on 2000-10-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (periodic orbits) of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.; it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of “chaos” present in it; for that the topological entropy is used. The book analyzes the combinatorial dynamics and topological entropy for the continuous maps of either an interval or the circle into itself.