In this short book, renowned theoretical physicist and author Carlo Rovelli gives a straightforward introduction to Einstein's General Relativity, our current theory of gravitation. Focusing on conceptual clarity, he derives all the basic results in the simplest way, taking care to explain the physical, philosophical and mathematical ideas at the heart of "the most beautiful of all scientific theories". Some of the main applications of General Relativity are also explored, for example, black holes, gravitational waves and cosmology, and the book concludes with a brief introduction to quantum gravity. Written by an author well known for the clarity of his presentation of scientific ideas, this concise book will appeal to university students looking to improve their understanding of the principal concepts, as well as science-literate readers who are curious about the real theory of General Relativity, at a level beyond a popular science treatment.

The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).

An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Not many disciplines can c1aim the richness of creative ideas that make up the subject of analytical mechanics. This is not surprising since the beginnings of analyti cal mechanics mark also the beginnings of the theoretical treatment of other physical sciences, and contributors to analytical mechanics have been many, inc1uding the most brilliant mathematicians and theoreticians in the history of mankind. As the foundation for theoretical physics and the associated branches of the engineering sciences, an adequate command of analytical mechanics is an essential tool for any engineer, physicist, and mathematician active in dynamics. A fascinating dis cipline, analytical mechanics is not only indispensable for the solution of certain mechanics problems but also contributes so effectively towards a fundamental under standing of the subject of mechanics and its applications. In analytical mechanics the fundamental laws are expressed in terms of work done and energy exchanged. The extensive use of mathematics is a consequence of the fact that in analytical mechanics problems can be expressed by variational State ments, thus giving rise to the employment of variational methods. Further it can be shown that the independent variables may be either displacements or impulses, thus providing in principle the possibility of two complementary formulations, i.e. a dis placement formulation and an impulse formulation, for each problem. This duality is an important characteristic of mechanics problems and is given special emphasis in the present book."

The overwhelming focus of this 2nd volume of "Physics of Lakes" is adequately expressed by its subtitle "Lakes as Oscillators". It deals with barotropic and baroclinic waves in homogeneous and stratified lakes on the rotating Earth and comprises 12 chapters, starting with rotating shallow-water waves, demonstrating their classification into gravity and Rossby waves for homogeneous and stratified water bodies. This leads to gravity waves in bounded domains of constant depth, Kelvin, Poincare and Sverdrup waves, reflection of such waves in gulfs and rectangles and their description in sealed basins as barotropic 'inertial waves proper'. The particular application to gravity waves in circular and elliptical basins of constant depth leads to the description of Kelvin-type and Poincare-type waves and their balanced description in basins of arbitrary geometry on the rotating Earth. Consideration of two-, three- and n-layer fluids with sharp interfaces give rise to the description of gravity waves of higher order baroclinicity with experimental corroboration in a laboratory flume and e.g. in Lake of Lugano, Lake Banyoles and Lake Biwa. Barotropic wave modes in Lake Onega with complex geometry show that data and computational output require careful interpretation. Moreover, a summer field campaign in Lake of Lugano and its two-layer modal analysis show that careful statistical analyses of the data are requested to match data with computational results. Three chapters are devoted to topographic Rossby waves. Conditions are outlined for which these waves are negligibly affected by baroclinicity. Three classes of these large period modes are identified: channel modes, so-called Ball modes and bay modes, often with periods which lie very close together. The last chapter deals with an entire class of Chrystal-type equations for barotropic waves in elongated basins which incorporate the effects of the rotation of the Earth.

Divided into four parts, this book covers recent developments in topics pertaining to gravity theories, including discussions on the presence of scalar fields. Part One is devoted to exact solutions in general relativity, and is mainly concerned with the results of rotating null dust beams and fluids. Also included is a panoramic vision of new research directions in this area, which would require revising certain theorems and their possible extensions within gravity theories, new aspects concerning the Ernst potentials, double Kerr spacetimes, and rotating configurations. In particular, there is a detailed discussion of totally symmetric and totally geodesic spaces, in which a method for generating (2+1)-dimensional solutions from (3+1)-dimensional solutions is given. Part Two deals with alternative theories of gravity, all of which include scalar fields and gauge fields. Here, quantum and cosmological effects, which arise from both gravity theories in four and higher dimensions and from metric-affine theories, are investigated. Part Three is devoted to cosmological and inflationary scenarios. Local effects, such as the influence of scalar fields in protogalactic interactions, numerical studies of the collapse of molecular cores, as well as the inverse inflationary problem and the blue eigenvalue spectrum of it, are considered. Moreover, the role of scalar fields as dark matter and quantum cosmology in the Bergman-Wagoner and Gowdy theories, together with the relation of the conformal symmetry and deflationary gas universe, are likewise presented. The last part of the book includes some mixed topics which are still in the experimental stage. Among them are the foundation of the Maxwell theory, a discussion on electromagnetic Thirring problems, a note on the staticity of black holes with non-minimally coupled scalar fields, and a study of the Lorentz force free charged fluids in general relativity. Thus, this book is the most up-to-date, comprehensive collection of papers on the subject of exact solutions and scalar fields in gravity and is a valuable tool for researchers in the area.

This book is an experimental physics textbook on classical mechanics focusing on the development of experimental skills by means of discussion of different aspects of the experimental setup and the assessment of common issues such as accuracy and graphical representation. The most important topics of an experimental physics course on mechanics are covered and the main concepts are explored in detail. Each chapter didactically connects the experiment and the theoretical models available to explain it. Real data from the proposed experiments are presented and a clear discussion over the theoretical models is given. Special attention is also dedicated to the experimental uncertainty of measurements and graphical representation of the results. In many of the experiments, the application of video analysis is proposed and compared with traditional methods.

A concise introduction to the greatest questions of modern cosmology. What came before the big bang? How will the universe evolve into the future? Will there be a big crunch? Questions like these have no definitive answers, but there are many contending theories. In A Little Book about the Big Bang, physicist and writer Tony Rothman guides expert and uninitiated readers alike through the most compelling mysteries surrounding the nature and origin of the universe. Cosmologists are busy these days, actively researching dark energy, dark matter, and quantum gravity, all at the foundation of our understanding of space, time, and the laws governing the universe. Enlisting thoughtful analogies and a step-by-step approach, Rothman breaks down what is known and what isn't and details the pioneering experimental techniques scientists are bringing to bear on riddles of nature at once utterly basic and stunningly complex. In Rothman's telling, modern cosmology proves to be an intricate web of theoretical predictions confirmed by exquisitely precise observations, all of which make the theory of the big bang one of the most solid edifices ever constructed in the history of science. At the same time, Rothman is careful to distinguish established physics from speculation, and in doing so highlights current controversies and avenues of future exploration. The idea of the big bang is now almost a century old, yet with each new year comes a fresh enigma. That is scientific progress in a nutshell: every groundbreaking discovery, every creative explanation, provokes new and more fundamental questions. Rothman takes stock of what we have learned and encourages readers to ponder the mysteries to come.

The mathematical theory of contact mechanics is a growing field in engineering and scientific computing. This book is intended as a unified and readily accessible source for mathematicians, applied mathematicians, mechanicians, engineers and scientists, as well as advanced students. The first part describes models of the processes involved like friction, heat generation and thermal effects, wear, adhesion and damage. The second part presents many mathematical models of practical interest and demonstrates the close interaction and cross-fertilization between contact mechanics and the theory of variational inequalities. The last part reviews further results, gives many references to current research and discusses open problems and future developments. The book can be read by mechanical engineers interested in applications. In addition, some theorems and their proofs are given as examples for the mathematical tools used in the models.

Discusses the concepts of mechanical, thermal, and thermodynamic equilibrium and their applications. Covers the molecular basis for internal energy, entropy, thermodynamic equilibrium, and reversibility. Enables the reader to model irreversibility and determine the net loss in performance of a thermal system compared to an idealized system and approach an ideal one. Demonstrates entropy as a path independent property by use of reversible heat engines and reversible heat pumps interacting with a process between two states, the environment and the reservoir. Covers the role of reversibility from a thermodynamics standpoint and relates it to other areas, such as gas dynamics, combustion, propulsion, power plant engineering, and engines.

A cognitive journey towards the reliable simulation of scattering problems using finite element methods, with the pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forming the core of this book. Starting from the basic physical assumptions, the author methodically develops both the strong and weak forms of the governing equations, while the main chapter on finite element analysis is preceded by a systematic treatment of Galerkin methods for indefinite sesquilinear forms. In the final chapter, three dimensional computational simulations are presented and compared with experimental data. The author also includes broad reference material on numerical methods for the Helmholtz equation in unbounded domains, including Dirichlet-to-Neumann methods, absorbing boundary conditions, infinite elements and the perfectly matched layer. A self-contained and easily readable work.

In addition to expanding and clarifying a number of sections of the first edition, it generalizes the analysis that eliminates the noncausal pre-acceleration so that it applies to removing any pre-deceleration as well. It also introduces a robust power series solution to the equation of motion that produces an extremely accurate solution to problems such as the motion of electrons in uniform magnetic fields.

Now in an updated new edition, this textbook explains mechanical vibrations concepts in detail, concentrating on their practical use. This second edition includes the new chapter Multi-Degree-of-Freedom (MDOF) Time Response, as well as new sections covering superposition, music and vibrations, generalized coordinates and degrees-of-freedom, and first-order systems. Related theorems and formal proofs are provided, as are real-life applications. Students, researchers, and practicing engineers alike will appreciate the user-friendly presentation of a wealth of topics, including practical optimization for designing vibration isolators and transient and harmonic excitations. Advanced Vibrations: Theory and Application is an ideal text for students of engineering, designers, and practicing engineers.

Elastomers are found in many applications ranging from technology to daily life applications for example in tires, drive systems, sealings and print rollers. Dynamical operation conditions put extremely high demands on the performance and stability of these materials and their elastic and flow properties can be easily adjusted by simple manipulations on their elastic and viscous properties. However, the required service life suffers often from material damage as a result of wear processes such as abrasion and wear fatigue, mostly caused by crack formation and propagation. This book covers interdisciplinary research between physics, physical chemistry, material sciences and engineering of elastomers within the range from nanometres to millimetres and connects these aspects with the constitutive material properties. The different chapters describe reliable lifetime and durability predictions based on new fracture mechanical testing concepts and advanced material-theoretical methods which are finally implemented in the finite element method for structural simulations. The use of this approach allows a realistic description of complex geometrical and loading conditions which includes the peculiarities of the mechanical behaviour of elastomeric materials in detail. Furthermore, this approach demonstrates how multi-scale research concepts provide an ambitious interdisciplinary challenge at the interface between engineering and natural sciences. This book covers the interests of academic researchers, graduate students and professionals working in polymer science, rubber and tire technology and in materials science at the interface of academic and industrial research.

The petrochemical industry is a scientific and engineering field that encompasses the production of a wide range of chemicals and polymers. The purpose of this book is not only to provide a follow-on to form the later chapters of the highly successful Chemistry and Technology of Petroleum 5th Edition but also provides a simplified approach to a very diverse chemical subject dealing with the chemistry and technology of various petroleum and petrochemical process. Following from the introductory chapters, this book provides the readers with a valuable source of information containing insights into petrochemical reactions and products, process technology, and polymer synthesis. Provides readers with a valuable source of information containing insights into petrochemical reactions and products, process technology, and polymer synthesis Introduces the reader to the various petrochemical intermediates are generally produced by chemical conversion of primary petrochemicals to form more complicated derivative products The reactions and processes involved in transforming petroleum-based hydrocarbons into the chemicals that form the basis of the multi-billion dollar petrochemical industry are reviewed and described The book includes information on new process developments for the production of raw materials and intermediates for petrochemicals Includes a description of the origin of the raw materials for the petrochemicals industry - including an overview of the coal chemicals industry

21st Century Kinematics focuses on algebraic problems in the analysis and synthesis of mechanisms and robots, compliant mechanisms, cable-driven systems and protein kinematics. The specialist contributors provide the background for a series of presentations at the 2012 NSF Workshop. The text shows how the analysis and design of innovative mechanical systems yield increasingly complex systems of polynomials, characteristic of those systems. In doing so, it takes advantage of increasingly sophisticated computational tools developed for numerical algebraic geometry and demonstrates the now routine derivation of polynomial systems dwarfing the landmark problems of even the recent past. The 21st Century Kinematics workshop echoes the NSF-supported 1963 Yale Mechanisms Teachers Conference that taught a generation of university educators the fundamental principles of kinematic theory. As such these proceedings will provide admirable supporting theory for a graduate course in modern kinematics and should be of considerable interest to researchers in mechanical design, robotics or protein kinematics or who have a broader interest in algebraic geometry and its applications.

This book covers different topics of nonlinear mechanics in complex structures, such as the appearance of new nonlinear phenomena and the behavior of finite-dimensional and distributed nonlinear systems, including numerous systems directly connected with important technological problems.

This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.

This book discusses how and why animals evolved into particular shapes. The book identifies the physical laws which decide over the evolutionary (selective) value of body shape and morphological characters. Comparing the mechanical necessities with morphological details, the author attempts to understand how evolution works, and which sorts of limitations are set by selection. The book explains morphological traits in more biomechanical detail without getting lost in physics, or in methods. Most emphasis is placed on the proximate question, namely the identification of the mechanical stresses which must be sustained by the respective body parts, when they move the body or its parts against resistance. In the first part of the book the focus is on 'primitive' animals and later on the emphasis shifts to highly specialized mammals. Readers will learn more about living and fossil animals. A section of the book is dedicated to human evolution but not to produce another evolutionary tree, nor to refine a former one, but to contribute to answering the question: "WHY early humans have developed their particular body shape".

This book provides a comprehensive yet concise presentation of the analysis methods of lightweight engineering in the context of the statics of beam structures and is divided into four sections. Starting from very general remarks on the fundamentals of elasticity theory, the first section also addresses plane problems as well as strength criteria of isotropic materials. The second section is devoted to the analytical treatment of the statics of beam structures, addressing beams under bending, shear and torsion. The third section deals with the work and energy methods in lightweight construction, spanning classical methods and modern computational methods such as the finite element method. Finally, the fourth section addresses more advanced beam models, discussing hybrid structures as well as laminated and sandwich beams, in addition to shear field beams and shear deformable beams. This book is intended for students at technical colleges and universities, as well as for engineers in practice and researchers in engineering.

The Tenth International Symposium on Continuum Models and Discrete Systems (CMDSIO) took place at the Shoresh Holiday Complex in Shoresh, Israel, near the Capital City Jerusalem, from 30 June until 4 July 2003. The previous symposia in this series were: CMDS 1 (Kielce, Poland, 1975) CMDS2 (Mont Gabriel, Canada, 1977) CMDS3 (Freudenstadt, German Federal Republic, 1979) CMDS4 (Stockholm, Sweden, 1981) CMDS5 (Nottingham, England, 1985) CMDS6 (Dijon, France, 1989) CMDS7 (Paderborn, Germany, 1992) CMDS8 (Varna, Bulgaria, 1995) CMDS9 (Istanbul, Turkey, 1998) As in the previous symposia, participation was by invitation from the Inter- national Scientific Committee. Participants were chosen from a list of recom- mendations of the committee members, as well as from applications following advertisement of the symposium on the internet and in email messages to po- tential participants. The members of the International Scientific Committee were: Karl-Heinz Anthony CMDS7 Chairman (University ofPaderborn, Germany) David J. Bergman, Conference Chairman (Tel Aviv University, Israel) Bikas K. Chakrabatii (Saha Institute of Nuclear Physics Calcutta, West Bengal, India) Hans Jurgen Herrmann (University of Stuttgart, Germany; and ESPCI, Paris, France) Esin Inan, CMDS9 Chairwoman (Istanbul Technical University, Istanbul, Turkey) Dominique Jeulin (ENSMP, Fontainebleau, France) Mark Kachanov (Tufts University, Boston, MA, USA) David Kinderlehrer (Carnegie-Mellon University, Pittsburgh, PA, USA) Arnold M. Kosevich (B. Verkin Institute for Low Temperature Physics, Khat"kov, Ukraine) Valery M. Levin (Petrozavodsk State University, Petrozavodsk, Russia) Konstantin Z.

GNSS Seismogeodesy: Theory and Applications combines GNSS and seismology theory and applications to offer both disciplines the background information needed to combine forces. It explores the opportunities for integrating GNSS and seismometers, as well as applications for earthquake and tsunami early warning applications. The book allows seismologists to better understand how GNSS positions are computed and how they can be combined with seismic data and allows geodesists to better understand how to apply GNSS to monitoring of crustal motion. This book is a valuable reference for researchers and students studying the interdisciplinary connection between GNSS geodesy and strong-motion seismology. It will also be ideal for anyone working on new approaches for monitoring and predicting geologic hazards.