This volume presents a carefully written introduction to nonlinear waves in the natural sciences and engineering. It contains many classical results as well as more recent results, dealing with topics such as the forced Korteweg--de Vries equation and material relating to X-ray crystallography. The volume contains nine chapters. Chapter 1 concerns asymptotics and nonlinear ordinary differential equations. Conservation laws are discussed in Chapter 2, and Chapter 3 considers water waves. The scattering and inverse scattering method is described in Chapter 4, which also contains a full explanation of using the inverse scattering method for finding 1-, 2- and 3-soliton solutions of the Korteweg--de Vries equation. After dealing with the Burgers equation in Chapter 5, Chapter 6 discusses the forced Korteweg--de Vries equations. Here the emphasis is on steady-state bifurcations and unsteady-state periodic soliton generation. The Sine--Gordon and nonlinear SchrAdinger equations are the subject of Chapter 7. The final two chapters consider wave instability and resonance. Every chapter contains problems and exercises, together with guidance for their solution. The volume concludes with some appendices which describe symbolic derivations of certain results on solitons. Several user-friendly MATHEMATICA packages are included. The prerequisite for using this book is a background knowledge of basic physics, linear algebra and differential equations. For graduates and researchers in mathematics, physics and engineering wishing to have a good introduction to nonlinear wave theory and its applications. This volume is also highly recommended as a course book.

Among the many books on Galileo Galilei only very few deal directly and in depth with his scientific accomplishments proper. This is one of them and among the correspondingly sparse literature the author of this work distinguishes himself by focusing on mechanics, in particular on the fundamental concept of motion and percussion - having performed crucial original experiments and in Galileos spirit. Indeed, while the author lets Galilei speak for himself when he explains his experiments and findings, he also makes full use of our present day knowledge of physics to make the reader better understand the perspective.

The result of this very fine understanding is an unsurpassingly authoritative account on some of the foundations of preclassical mechanics as laid down by the great Pisan scientist, widely regarded as the first experimental physicist in the modern sense.

This book will not only be an indispensable source of reference for historians of sciences but appeal to anyone interested in the foundations of experimental physics in general and of mechanics in particular."

Papers of the Paris meeting in June 1990 on Local Group Galaxies, molecules in early-type galaxies, observations of spiral structure in molecular clouds, a comparison with other gaseous components and IR emission, interacting galaxies and starbursts, gas and star dynamics, galaxy evolution, IRAS ult

This volume of proceedings contains the papers from the third in a successful series of conferences organized by the Deutscher Verband fur Materialforschung undprufung DVM]. The purpose of the conference was to review methods of improving the performance of materials and structures and to extend working life, especially under complex loading conditions such as environmental attack and high temperature degradation as well as providing a comprehensive evaluation of recent progress in low cycle fatigue and elasto-plastic behaviour of materials. Safe design and effective operation of highly stressed structures rely on the extensive use of mechanical approaches and micromechanics analysis to predict the deformation and fracture response of materials in service. Because of the need to create greater confidence in the engineering world in advanced materials as efficient replacements for conventional materials, many of the papers emphasize the role of new materials and emerging technology.

Advances in technology are demanding ever-increasing mastery over the materials being used: the challenge is to gain a better understanding of their behaviour, and more particularly of the relations between their microstructure and their macroscopic properties.

This work, of which this is the first volume, aims to provide the means by which this challenge may be met. Starting from the mechanics of deformation, it develops the laws governing macroscopic behaviour expressed as the constitutive equations always taking account of the physical phenomena which underlie rheological behaviour. The most recent developments are presented, in particular those concerning

heterogeneous materials such as metallic alloys, polymers and composites. Each chapter is devoted to one of the major classes of material behaviour.

As the subtitles indicate, Volume 1 deals with micro- and macroscopic constitutive behaviour and Volume 2 with damage and fracture mechanics. A third volume will be devoted to exercises and their full solutions complementing the content of these two first volumes.

Most of the chapters end with a set of exercises, to many of which either the full solution or hints on how to obtain this are given; each volume is profusely illustrated with explanatory diagrams and with electron-microscope photographs.

This book, now in its second edition, has been rigorously re-written, updated and modernised for a new generation. The authors improved the existing material, in particular in modifying the organisation, and added new up-to-date content. Understanding the subject matter requires a good knowledge of solid mechanics and materials science; the main elements of these fields are given in a set of annexes at the

end of the first volume. The authors also thought it interesting for the readers to give as footnotes some information about the many scientists whose names are attached to theories and formulae and whose memories must be celebrated.

Whilst the present book, as well as Volume 2, is addressed primarily to graduate students, part of it can be used in undergraduate courses; and it is hoped that practising engineers and scientists will find the information it conveys useful. It is the authors hope also that English-speaking readers will want to learn about the aspects of French

culture, and more particularly of the French school of micromechanics of materials, which this treatment undoubtedly displays.

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IAU Symposium 172 Dynamics, Ephemerides and Astrometry of the Solar System was held in Paris in July, 1995. 250 scientists from 33 countries attended the symposium; 24 invited lectures and 165 contributed papers were presented (117 of which were posters). The papers covered topics on celestial mechanics (chaos and evolution of the solar system, asteroids, theories of the motion of the planets, the moon and the natural satellites), methods (symplectic mappings and elliptic functions), astrometry (CCD observations, VLBI and radar observations), ephemerides (representation and numerical integration) and on the history of celestial mechanics.

The emergence of flow control as an attractive new field is owed to breakthroughs in MEMS (micro-electromechanical systems) and related technologies. The instrumentation of fluid flows on extremely short length and short time scales requires the practical tool of control algorithms with provable performance guarantees. Dedicated to this problem, Flow Control by Feedback, brings together controller design and fluid mechanics expertise in an exposition of the latest research results. Featuring: Exhaustive treatment of flow control core areas including stabilization and mixing control techniques; self-contained introductory sections on Navier-Stokes equations, linear and nonlinear control and sensors and MEMS to facilitate accessibility to this cross-disciplinary subject; a comprehensive survey of feedback algorithms for flow control that are currently available. In response to the intense interest in flow control, this volume will be an essential addition to the library of researchers and graduate students in control theory, fluid mechanics, mathematics and physics. Content structure is ideal for instruction on flow control modules or as supplementary reading on fluid dynamics and infinite dimensional systems courses.

This work is a detailed study of both the theoretical and phenomenological consequences of a massive graviton, within the ghost-free theory of massive gravity, the de Rham-Gabadadze-Tolley (dRGT) theory. Its aim is to test the physical viability of the theory. It begins by putting constraints on the parameters of the theory in the decoupling limit based on purely theoretical grounds, like classical stability in the cosmological evolution of self-accelerating and degravitating solutions. The author then constructs a proxy theory to massive gravity from the decoupling limit resulting in non-minimally coupled scalar-tensor interactions as an example of a subclass of Horndeski theories. Lastly, she addresses the natural question of whether the parameters introduced in the dRGT theory are subject to strong renormalization by quantum loops and shows how the non-renormalization theorem protects the graviton mass from quantum corrections. Beyond the decoupling limit the quantum corrections are found to be proportional to the graviton mass, proving its technical naturalness.

The papers included in this volume were presented at the Symposium on Advances in the Continuum Mechanics and Thermodynamics of Material Behavior, held as part of the 1999 Joint ASME Applied Mechanics and Materials Summer Conference at Virginia Tech on June 27-30, 1999. The Symposium was held in honor of Professor Roger L. Fosdick on his 60th birthday. The papers are written by prominent researchers in the fields of mechanics, thermodynamics, materials modeling, and applied mathematics. They address open questions and present the latest development in these and related areas. This volume is a valuable reference for researchers and graduate students in universities and research laboratories.

This book is intended as a historical and critical study on the origin of the equations of motion as established in Newton's Principia. The central question that it aims to answer is whether it is indeed correct to ascribe to Galileo the inertia principle and the law of falling bodies. In order to accomplish this task, the study begins by considering theories on the motion of bodies from classical antiquity, and especially those of Aristotle. The theories developed during the Middle Ages and the Renaissance are then reviewed, with careful analysis of the contributions of, for example, the Merton and Parisian Schools and Galileo's immediate predecessors, Tartaglia and Benedetti. Finally, Galileo's work is examined in detail, starting from the early writings. Excerpts from individual works are presented, to allow the texts to speak for themselves, and then commented upon. The book provides historical evidence both for Galileo's dependence on his forerunners and for the major breakthroughs that he achieved. It will satisfy the curiosity of all who wish to know when and why certain laws have been credited to Galileo.

Modern concepts of fracture mechanics are presented consecutively. Homogeneous and structured models, where microstructure plays an essential role, are considered for fracture and phase transition. Firstly, one-dimensional models are comprehensively studied allowing one to retrace the main phenomena without technical difficulties. More realistic models are then used as linear and nonlinear elastic mediums, such as elastic plates with crack closure, viscoelastic discrete lattices, chains and cohesive zone models. Also considered are, crack origination, equilibrium, slow and fast growth. Sub- and super critical crack speed regimes and transition from one regime to another are studied. Fourier transform and related topics, including a version of the Wiener-Hopf technique dealing with originals are presented, as well as required topics from wave theory. This book is targeted at researchers of materials and structures, also at lecturers and advanced students.

As the name implies, Intermediate Dynamics: A Linear Algebraic Approach views intermediate dynamics - Newtonian 3-D rigid body dynamics and analytical mechanics - from the perspective of the mathematical field. This is particularly useful in the former: the inertia matrix can be determined through simple translation (via the Parallel Axis Theorem) and rotation of axes using rotation matrices. The inertia matrix can then be determined for simple bodies from tabulated moments of inertia in the principal axes; even for bodies whose moments of inertia can be found only numerically, this procedure allows the inertia tensor to be expressed in arbitrary axes - something particularly important in the analysis of machines, where different bodies' principal axes are virtually never parallel. To understand these principal axes (in which the real, symmetric inertia tensor assumes a diagonalized normal form), virtually all of Linear Algebra comes into play.

The book presents a unified and well-developed approach to the dynamics of angular motions of rigid bodies subjected to perturbation torques of different physical nature. It contains both the basic foundations of the rigid body dynamics and of the asymptotic method of averaging. The rigorous approach based on the averaging procedure is applicable to bodies with arbitrary ellipsoids of inertia. Action of various perturbation torques, both external (gravitational, aerodynamical, solar pressure) and internal (due to viscous fluid in tanks, elastic and visco-elastic properties of a body) is considered in detail. The book can be used by researchers, engineers and students working in attitude dynamics of spacecraft.

Solar Thermal Conversion Technologies for Industrial Process Heating presents a comprehensive look at the use of solar thermal energy in industrial applications, such as textiles, chemical processing, and food. The successful projects implemented in a variety of industries are shown in case studies, alongside performance assessment methodologies. The book will be useful for researchers, graduate students, and industry professionals with an aim to promote mutual understanding between sectors dealing with solar thermal energy. The book includes various solar thermal energy conversion technologies and new techniques and applications of solar collectors in industrial sectors. Features: Covers the key designs and novel technologies employed in the processing industries. Discusses challenges in the incorporation of the solar thermal system in industrial applications. Explores the techno-economic, environmental impact, and life cycle analysis, with government policies for promoting the system. Includes real-world case studies. Presents chapters written by global experts in the field. The book will be useful for researchers, graduate students, and industry professionals with an aim to promote mutual understanding between sectors dealing with solar thermal energy.

This volume contains selected papers presented at the Symposium on "Recent Developments in Non-linear Oscillations of Mechanical Systems," held in Hanoi, Vietnam, from 2 - 5 March 1999. This Symposium was initiated and sponsored by the International Union of Theoretical and Applied Mechanics (lUI AM) and organised in conjunction with Vietnam National University, Hanoi. Ihe purpose of the Symposium was to bring together scientists active in different fields of oscillations with the aim to review the recent progress in theory of oscillations and engineering applications and to outline the prospects in its further achievements to then co-ordinate and direct research in this field to further co-operation between scientists and various scientific institutions. An International Scientific Committee was appointed by the Bureau of IUI AM with the following members: Nguyen Van Dao (Vietnam, Co-Chairman) E.J. Kreuzer (Germany, Co-Chairman) D.H. van Campen (The Netherlands) F.L. Chernousko (Russia) A.H. Nayfeh (U.S.A) Nguyen Xuan Hung (Vietnam) W.O. Schiehlen (Germany) J.M.T. Thompson (U.K) Y. Veda (Japan). This Committee selected the participants to be invited and the papers to be presented at the Symposium. As a result of this procedure, 52 active scientists from 16 countries responded to the invitation, and 42 papers were presented in lecture and poster discussion sessions.

The aim of this book is to provide an account of the state of the art in Com putational Kinematics. We understand here under this term, that branch of kinematics research involving intensive computations not only of the numer ical type, but also of a symbolic nature. Research in kinematics over the last decade has been remarkably ori ented towards the computational aspects of kinematics problems. In fact, this work has been prompted by the need to answer fundamental question s such as the number of solutions, whether real or complex, that a given problem can admit. Problems of this kind occur frequently in the analysis and synthesis of kinematic chains, when finite displacements are considered. The associated models, that are derived from kinematic relations known as closure equations, lead to systems of nonlinear algebraic equations in the variables or parameters sought. What we mean by algebraic equations here is equations whereby the unknowns are numbers, as opposed to differen tial equations, where the unknowns are functions. The algebraic equations at hand can take on the form of multivariate polynomials or may involve trigonometric functions of unknown angles. Because of the nonlinear nature of the underlying kinematic models, purely numerical methods turn out to be too restrictive, for they involve iterative procedures whose convergence cannot, in general, be guaranteed. Additionally, when these methods converge, they do so to only isolated solu tions, and the question as to the number of solutions to expect still remains."

From the reviews: "The book is excellent, and covers a very broad area (usually treated as separate topics) from a unified perspective. [ ] It will be very useful for both mathematicians and physicists." EMS Newsletter

This graduate level textbook is devoted to understanding, prediction and control of high dimensional chaotic and attractor systems of real life. The objective is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high dimensional chaotic and attractor dynamics. From introductory material on low-dimensional attractors and chaos, the text explores concepts including Poincare s 3-body problem, high-tech Josephson junctions, and more.

Present developments in materials science, mechanics and engineering, as well as the demands of modern technology, result in a new and growing interest in plasticity and in bordering domains of the mechanical behavior of materials. This growing interest is attested to by the success of both The International Journal of Plasticity, which after its inception rapidly became the leading journal for plasticity research, and the series ofInternational Symposia on Plasticity and Its Current Applications, which is now the premier international forum for plasticity research dissemination. The First International Symposium on Plasticity and Its Current Applications was conceived and organized by Professor Akhtar S. Khan, and was held at the University of Oklahoma (Norman, Oklahoma, USA) from July 30 to August 3, 1984. It was attended by over one hundred scientists from fifteen countries. "Plasticity '89: the Second International Symposium on Plasticity and Its Current Applications" was held at Mie University (Tsu, Japan) from July 31 to August 4, 1989; this symposium was co-chaired by Professors Khan and Tokuda. The main emphasis of this meeting was on dynamic plasticity and micromechanics, although it included other aspects of plasticity as well. It was attended by over two hundred researchers from twenty-three nations.

The scientific description of processes involved in the powerful release of energy from high explosive materials remains one of the most complex problems confronting modern science. In spite of fifty years of concentrated research built upon careful and precise experiments and the massive use of modern computers, the problem remains a major challenge. Anatoliy N. Dremin is recognized as perhaps the most innovative contributor to detonation science and this book provides unique insights into the physics, chemistry, and mechanics relevant to initiation and sustenance of detonation processes. The book presents theories, both conventional and unusual, for describing the processes as well as the experimental challenges to theory and modeling. An unusually valuable contribution to modern science, it will be required reading for any serious student of energetic materials and powerful, high-energy processes.

Mechanics plays a central role in determining form and function in biology. This holds at the cellular, molecular and tissue scales. At the cellular scale, mechanics in?uences cell adhesion, cytoskeletal dynamics and the traction that the cell can generate on a given substrate. All of these in turn - fect the cellular functions of migration, mitosis, phagocytosis, endocytosis and stem cell differentiation among others. Indeed, if cells do not develop the appropriate stresses, they are unviable and die. These aspects of cell mechanics are frequently used by mainstream biologists, as traditional mechanicians may be surprised to learn. There is a growing view that many functions of the cell are mechanical in nature even though chemical signals play crucial roles in the processes. Free energy barriers control transitions between different conformations of vir- ally every macromolecule including DNA, RNA, the adhesion protein integrin, the motor protein myosin, and the proteins vinculin and talin that link the cytoskeleton to focal adhesions. The strain energy can be a signi?cant component of the total free energy barrier. For binding to take place, the macromolecules need to be in conf- mational states that expose chemical groups without steric hinderance. The kinetics of chemical reactions are therefore strongly in?uenced by the conformational strain energy.

This textbook offers a clear and comprehensive introduction to analytical mechanics, one of the core components of undergraduate physics courses. The book starts with a thorough introduction into Lagrangian mechanics, detailing the d'Alembert principle, Hamilton's principle and conservation laws. It continues with an in-depth explanation of Hamiltonian mechanics, illustrated by canonical and Legendre transformation, the generalization to quantum mechanics through Poisson brackets and all relevant variational principles. Finally, the Hamilton-Jacobi theory and the transition to wave mechanics are presented in detail. Ideally suited to undergraduate students with some grounding in classical mechanics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successful German editions, the eight volumes of this series cover the complete core curriculum of theoretical physics at undergraduate level. Each volume is self-contained and provides all the material necessary for the individual course topic. Numerous problems with detailed solutions support a deeper understanding. Wolfgang Nolting is famous for his refined didactical style and has been referred to as the "German Feynman" in reviews.

The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999. One of the conference days was dedicated to Professor V. Lakshmikantham in th honor of his 75 birthday. 50 well established professionals (in differential equations, nonlinear analysis, numerical analysis, and nonlinear mechanics) attended the conference from 13 countries. Twelve of the attendees delivered hour long invited talks and remaining thirty-eight presented invited forty-five minute talks. In each of these talks, the focus was on the recent developments in differential equations and nonlinear mechanics and their applications. This book consists of 29 papers based on the invited lectures, and I believe that it provides a good selection of advanced topics of current interest in differential equations and nonlinear mechanics. I am indebted to the Department of Mathematics, College of Arts and Sciences, Department of Mechanical, Materials and Aerospace Engineering, and the Office of International Studies (of the University of Central Florida) for the financial support of the conference. Also, to the Mathematics Department of the University of Central Florida for providing secretarial and administrative assistance. I would like to thank the members of the local organizing committee, Jeanne Blank, Jackie Callahan, John Cannon, Holly Carley, Brad Pyle, Pete Rautenstrauch, and June Wingler for their assistance. Thanks are also due to the conference organizing committee, F. H. Busse, J. R. Cannon, V. Girault, R. H. J. Grimshaw, P. N. Kaloni, V.