This book presents an overview of the current understanding of gravitation, with a focus on the current efforts to test its theory, especially general relativity. It shows how the quest for a deeper theory, which would possibly incorporate gravity in the quantum realm, is more than ever an open field. The majority of the contributions deals with the manifold facets of "experimental gravitation", but the book goes beyond this and covers a broad range of subjects from the foundations of gravitational theories to astrophysics and cosmology. The book is divided into three parts. The first part deals with foundations and Solar System tests. An introductory pedagogical chapter reviews first Newtonian gravitational theory, special relativity, the equivalence principle and the basics of general relativity. Then it focuses on approximation methods, mainly the post-Newtonian formalism and the relaxed Einstein equations, with a discussion on how they are used in treating experimental tests and in the problem of generation and detection of gravitational waves. Following this is a set of chapters describing the most recent experiments, techniques and observations on the testing of gravity theories in the laboratory, around the Earth and in the Solar System. The second part is dedicated to astrophysical topics deeply linked with the study of gravitation, namely binary pulsars and the perspective of direct detection of gravitational waves. These cases are paradigmatic in that the gravitational signals act at the same time as messengers helping us to understand the properties of important and wide classes of astrophysical objects. The third part explores the many open issues in current knowledge of gravitation machinery, especially related to astrophysical and cosmological problems and the way possible solutions to them impact the quest for a quantum theory of gravitation and unified theory. Included is a selection of the many possible paths, giving a hint to the subtleties one is called upon. Whenever possible, a close link to observational constraints and possible experimental tests is provided. In selecting the topics of the various contributions, particular care has been devoted to ensure their fit in a coherent representation of our understanding of gravitational phenomena. The book is aimed at graduate level students and will form a valuable reference for those working in the field.

Summary This bookis an introdU(;tion to the three numerical methodsmost commonly used for the mechanical analysisof deformable solids, namely: * the finite element method(FEM), a particularcaseofGalerkin's method, for the spatial discretisationofsolids; * the linear iteration method(LIM), a generalizationofNewton's method, for solving geometricandmaterial nonlinearities; * the finite difference method (FDM), in fact Newmark's method, for the temporal discretisation oftheproblem. The main reason for this selection is the degree of generality reached by the computerprograms basedon the combinationofthese methods. The originalityofthepresentation lies in the comparable emphasisputon the spatial, temporal and nonlinear dimensions of problem solving. For each dimension, there corresponds one method whose basic principle is exposed. It is then shown how they can be combined in a compact and flexible fonn. Thisjoint investigationofthe three methods leads to a particularly neat global algorithm. It is with this double objectiveof simplicity and unity in mind that this book has been designed. An outline of the book follows. A one-dimensional bar model problem, including all the ingredients necessary for acompletepresentationofthe addressed methods, isdefined in Chapter1. Emphasis is placedon the virtual work principle as an alternative to the.differentialequation ofmotion. Chapters 2, 3 and 4 present the three numerical methods: FEM, LIM and FDM, respectively. Although the presentation relies on a one-dimensional model problem, the fonnalism used is general and directly extendible to two- and three-dimensional situations. The compact combination of the three methods is discussed in detail in Chapter 5, which also contains several sections concerning their computer implementation.

This book examines the study of mechanical systems as well as its links to other sciences of nature. It presents the fundamentals behind how mechanical theories are constructed and details the solving methodology and mathematical tools used: vectors, tensors and notions of field theory. It also offers continuous and discontinuous phenomena as well as various mechanical magnitudes in a unitary form by means of the theory of distributions.

A profusion of research and results on the mechanical behaviour of crystalline solids has followed the discovery of dislocations in the early thirties. This trend has been enhanced by the development of powerful experimental techniques. particularly X ray diffraction. transmission and scanning electron microscopy. microanalysis. The technological advancement has given rise to the study of various and complex materials. not to speak of those recently invented. whose mechanical properties need to be mastered. either for their lise as structural materials. or more simply for detenllining their fonnability processes. As is often the case this fast growth has been diverted both by the burial of early fundamental results which are rediscovered more or less accurately. and by the too fast publication of inaccurate results. which propagate widely. and are accepted without criticism. Examples of these statements abound. and will not be quoted here for the sake of dispassionateness. Understanding the mechanical properties of materials implies the use of various experimental techniques. combined with a good theoretical knowledge of elasticity. thermodynamics and solid state physics. The recent development of various computer techniques (simulation. ab initio calculations) has added to the difficulty of gathering the experimental information. and mastering the theoretical understanding. No laboratory is equipped with all the possible experimental settings. almost no scientist masters all this theoretical kno\vledge. Therefore. cooperation between scientists is needed more than even before.

This book is based upon the lectures delivered from 18 to 22 June 2007 at the INFN-LaboratoriNazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci, with the participation of prestigious lecturers, including S. Ferrara, M. Gnaydin, P. Levay, T. Mohaupt, and A. Zichichi. All lectures were given at a pedagogical, introductory level, a feature which is re?ected in the s- ci?c "?avor" of this volume, which has also bene?ted much from the extensive discussions and related reworking of the various contributions. This is the fourth volume in a series of books on the general topics of sup- symmetry, supergravity, black holes, and the attractor mechanism. Indeed, based on previous meetings, three volumes have already been published: BELLUCCI S. (2006). Supersymmetric Mechanics - Vol. 1: Supersymmetry, NoncommutativityandMatrixModels.(vol.698, pp.1-229).ISBN:3-540-33313-4. Berlin, Heidelberg: Springer Verlag (Germany). Springer Lecture Notes in Physics Vol. 698. BELLUCCIS., S.FERRARA, A.MARRANI.(2006).SupersymmetricMech- ics - Vol. 2: The Attractor Mechanism and Space Time Singularities. (vol. 701, pp. 1-242). ISBN-13: 9783540341567. Berlin, Heidelberg: Springer Verlag (G- many). Springer Lecture Notes in Physics Vol. 701. BELLUCCIS.(2008).SupersymmetricMechanics-Vol.3: AttractorsandBlack HolesinSupersymmetricGravity.(vol.755, pp.1-373).ISBN-13:9783540795223. Berlin, Heidelberg: Springer Verlag (Germany). Springer Lecture Notes in Physics 755. In this volume, we have included two contributions originating from short p- sentations of recent original results given by participants, i.e., Wei Li and Filipe Moura.

The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.

Underactuated multibody systems are intriguing mechatronic systems, as they posses fewer control inputs than degrees of freedom. Some examples are modern light-weight flexible robots and articulated manipulators with passive joints. This book investigates such underactuated multibody systems from an integrated perspective. This includes all major steps from the modeling of rigid and flexible multibody systems, through nonlinear control theory, to optimal system design. The underlying theories and techniques from these different fields are presented using a self-contained and unified approach and notation system. Subsequently, the book focuses on applications to large multibody systems with multiple degrees of freedom, which require a combination of symbolical and numerical procedures. Finally, an integrated, optimization-based design procedure is proposed, whereby both structural and control design are considered concurrently. Each chapter is supplemented by illustrated examples.

Co-integration of sensors with their associated electronics on a single silicon chip may provide many significant benefits regarding performance, reliability, miniaturization and process simplicity without significantly increasing the total cost.

Micromachined Thin-Film Sensors for SOI-CMOS Co-integration covers the challenges and interests and demonstrates the successful co-integration of gas-flow sensors on dielectric membrane, with their associated electronics, in CMOS-SOI technology.

We firstly investigate the extraction of residual stress in thin layers and in their stacking and the release, in post-processing, of a 1 Am-thick robust and flat dielectric multilayered membrane using Tetramethyl Ammonium Hydroxide (TMAH) silicon micromachining solution. The optimization of its selectivity towards aluminum is largely demonstrated.

The second part focuses on sensors design and characteristics. A novel loop-shape polysilicon microheater is designed and built in a CMOS-SOI standard process. High thermal uniformity, low power consumption and high working temperature are confirmed by extensive measurements. The additional gas flow sensing layers are judiciously chosen and implemented. Measurements in the presence of a nitrogen flow and gas reveal fair sensitivity on a large flow velocity range as well as good response to many gases. Finally, MOS transistors suspended on released dielectric membranes are presented and fully characterized as a concluding demonstrator of the co-integration in SOI technology.

This book contains a systematical analysis of geometrical situations leading to contact pairs -- point-to-surface, surface-to-surface, point-to-curve, curve-to-curve and curve-to-surface. Each contact pair is inherited with a special coordinate system based on its geometrical properties such as a Gaussian surface coordinate system or a Serret-Frenet curve coordinate system. The formulation in a covariant form allows in a straightforward fashion to consider various constitutive relations for a certain pair such as anisotropy for both frictional and structural parts. Then standard methods well known in computational contact mechanics such as penalty, Lagrange multiplier methods, combination of both and others are formulated in these coordinate systems. Such formulations require then the powerful apparatus of differential geometry of surfaces and curves as well as of convex analysis. The final goals of such transformations are then ready-for-implementation numerical algorithms within the finite element method including any arbitrary discretization techniques such as high order and isogeometric finite elements, which are most convenient for the considered geometrical situation. The book proposes a consistent study of geometry and kinematics, variational formulations, constitutive relations for surfaces and discretization techniques for all considered geometrical pairs and contains the associated numerical analysis as well as some new analytical results in contact mechanics.

The Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Goettingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. The Theory of the Top: Volume IV. Technical Applications of the Theory of the Top is the fourth and final installment in a series of self-contained English translations that provide insights into kinetic theory and kinematics.

Over the last quarter of this century, revolutionary advances have been made both in kind and in precision in the application of particle traps to the study of thephysics of charged particles, leading to intensi?ed interest in, and wide proliferation of, this topic. This book is intended as a timely addition to the literature, providing a systematic uni?ed treatment of the subject, from the point of view of the application of these devices to fundamental atomic and particle physics. Thetechniqueofusingelectromagnetic?eldstocon?neandisolateatomic particles in vacuo, rather than by material walls of a container, was initially conceivedbyW.Paulintheformofa3Dversionoftheoriginalrfquadrupole mass ?lter, for which he shared the 1989 Nobel Prize in physics [1], whereas H.G. Dehmelt who also shared the 1989 Nobel Prize [2] saw these devices (including the Penning trap) as a way of isolating electrons and ions, for the purposes of high resolution spectroscopy. These two broad areas of appli- tion have developed more or less independently, each attaining a remarkable degree of sophistication and generating widespread interest and experimental activity.

This book develops a unified mathematical framework for treating a wide variety of diffusion-related periodic phenomena in such areas as heat transfer, electrical conduction, and light scattering. Deriving and using Green functions in one and higher dimensions to provide a unified approach, the author develops the properties of diffusion-wave fields first for the well-studied case of thermal-wave fields and then applies the methods to nonthermal fields. The presentation, largely in the form of case studies directly applicable in a wide range of experimental methodologies, is intended for graduate students, professional scientists and engineers working in fields that involve diffusion waves, including thermal-wave, photothermal and photoacoustic spectroscopies, non-destructive evaluation, semiconductor and electronic device carrier plasma-wave characterization, and biomedical laser tissue diffuse photon density-wave diagnostics. The treatment requires no more mathematical background than a course in advanced calculus and mathematical analysis. Problems at the ends of each chapter complement the main text and some serve to extend the material to current research.

As any human activity needs goals, mathematical research needs problems -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the ben eficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a du ality gap between the two partners, and this gap is growing wider. Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications which fall into the two following complementary categories: 1. An annual book dedicated to the latest developments in mechanics and mathematics; 2. Monographs, advanced textbooks, handbooks, edited vol umes and selected conference proceedings. The AMMA annual book publishes invited and contributed compre hensive reviews, research and survey articles within the broad area of modern mechanics and applied mathematics. Mechanics is understood here in the most general sense of the word, and is taken to embrace relevant physical and biological phenomena involving electromagnetic, thermal and quantum effects and biomechanics, as well as general dy namical systems. Especially encouraged are articles on mathematical and computational models and methods based on mechanics and their interactions with other fields. All contributions will be reviewed so as to guarantee the highest possible scientific standards."

This book presents a broad view of the current state of the art regarding the dynamic response of composite and sandwich structures subjected to impacts and explosions. Each chapter combines a thorough assessment of the literature with original contributions made by the authors. The first section deals with fluid-structure interactions in marine structures. The first chapter focuses on hull slamming and particularly cases in which the deformation of the structure affects the motion of the fluid during the water entry of flexible hulls. Chapter 2 presents an extensive series of tests underwater and in the air to determine the effects of explosions on composite and sandwich structures. Full-scale structures were subjected to significant explosive charges, and such results are extremely rare in the open literature. Chapter 3 describes a simple geometrical theory of diffraction for describing the interaction of an underwater blast wave with submerged structures. The second section addresses the problem of impact on laminated composite structures with chapters devoted to ballistic impacts on pre-stressed composite structures, tests developed to simulate dynamic failure in marine structures, damage mechanisms and energy absorption in low velocity impacts, perforation, the numerical simulation of intra and inter-ply damage during impact, and hail impact on laminated composites. Sandwich structures with laminated facings are considered in Section 3 with chapters dealing with the discrete modeling of honeycomb core during the indentation of sandwich structures, the behavior of fold core sandwich structures during impact, and impact on helicopter blades. The fourth section consists of two chapters presenting experimental results and numerical simulation of composite structures subjected to crash. This volume is intended for advanced undergraduate and graduate students, researchers, and engineers interested and involved in analysis and design of composite structures.

This book gives an overview of recent advances in the fracture mechanics of polymers (experimental and alternative methods), morphology property correlations (homopolymers, copolymers, blends), hybrid methods for polymer testing and polymer diagnostics, and biocompatible materials and medical prostheses, as well as application examples and limits. The investigation of deformation and fracture behaviour using the experimental methods of fracture mechanics has been the subject of intense research during the last decade. In a systematic manner, each chapter of this book gives a review of the particular aspects. This book will be of great value to scientists, engineers and graduates in polymer materials science.

Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics. The outstanding points of these proceedings are Coherent compendium of the current state of modelling and analysis of non-linear stochastic systems from engineering, applied mathematics and physics point of view. Subject areas include: Multiscale phenomena, stability and bifurcations, control and estimation, computational methods and modelling. For the Engineering and Physics communities, this book will provide first-hand information on recent mathematical developments. The applied mathematics community will benefit from the modelling and information on various possible applications.

Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.

Adaptive structural systems in conjunction with multifunctional materials facilitate technical solutions with a wide spectrum of applications and a high degree of integration. By virtue of combining the actuation and sensing capabilities of piezoelectric materials with the advantages of fiber composites, the anisotropic constitutive properties may be tailored according to requirements and the failure behavior can be improved. Such adaptive fiber composites are very well-suited for the task of noise and vibration reduction. In this respect the helicopter rotor system represents a very interesting and widely perceptible field of application. The occurring oscillations can be reduced with aid of aerodynamic couplings via fast manipulation of the angle of attack, being induced by twist actuation of the rotor blade. On the one hand the sensing properties may be used to determine the current state of deformation, while on the other hand the actuation properties may be used to attain the required state of deformation. The implementation of such concepts requires comprehensive knowledge of the theoretical context, which shall be illuminated in the work at hand from the examination of the material behavior to the simulation of the rotating structure.

This work investigates the theoretical and cosmological implications of modifying Einstein's theory of general relativity. It explores two classes of modifications to gravity: those in which the graviton is given a small mass, and those in which Lorentz invariance is spontaneously broken. It elucidates the nature of cosmological perturbations in theories of massive bimetric gravity, including a potentially deadly instability. Theories of gravity beyond general relativity could explain why the expansion of the Universe is accelerating, obviating the need for a dark energy, and can also affect the evolution of the early Universe. Next, it investigates the nature of spacetime in massive gravity theories that contain two different spacetime metrics. Lastly, the strongest constraints to date are placed on the size of Lorentz-violating effects in the gravity sector during inflation.

This book presents a general classical field theory, incorporating continuum mechanics, electrodynamics, and thermodynamics. The continuum equations of material behavior are derived from the principles of Onsager's non-equilibrium thermodynamics supplemented with dynamic degrees of freedom. The book contains the basic principles and methods of modern continuum mechanics and of rheology. Non-equilibrium thermodynamics is discussed in detail. Applications include elasticity, thermoelasticity, viscoelasticity, plasticity, rheooptics, etc. The models of rheology are developed within a consistent thermodynamic framework. Viscoelastic and plastic response, Ostwald's curve of generalized Newtonian fluids, creep, elasticity preceding plastic flow, the rules of rheooptics, etc., are discussed, and the empirical Cox-Merz rule is proved. The thermodynamic results are compared to the results of microscopic theories. Several kinds of colloids, polymers, and liquid crystals are studied. The technical level of the book is high. It is designed for engineers, physicists, natural scientists and applied mathematicians.

This book examines the theoretical foundations underpinning the field of strength of materials/theory of elasticity, beginning from the origins of the modern theory of elasticity. While the focus is on the advances made within Italy during the nineteenth century, these achievements are framed within the overall European context. The vital contributions of Italian mathematicians, mathematical physicists and engineers in respect of the theory of elasticity, continuum mechanics, structural mechanics, the principle of least work and graphical methods in engineering are carefully explained and discussed. The book represents a work of historical research that primarily comprises original contributions and summaries of work published in journals. It is directed at those graduates in engineering, but also in architecture, who wish to achieve a more global and critical view of the discipline and will also be invaluable for all scholars of the history of mechanics.