Mathematics plays an important role in mechanics and other human endeavours. Validating examples in this first volume include, for instance: the connection between the golden ratio (the "divine proportion" used by Phidias and many other artists and enshrined in Leonardo's Vitruvian Man, shown on the front cover), and the Fibonacci spiral (observable in botany, e.g., in the placement of sunflower seeds); is the coast of Tuscany infinitely long?; the equal-time free fall of a feather and a lead ball in a vacuum; a simple diagnostic for changing your car's shocks; the Kepler laws of the planets; the dynamics of the Sun-Earth-Moon system; the tides' mechanism; the laws of friction and a wheel rolling down a partially icy slope; and many more. The style is colloquial. The emphasis is on intuition - lengthy but intuitive proofs are preferred to simple non-intuitive ones. The mathematical/mechanical sophistication gradually increases, making the volume widely accessible. Intuition is not at the expense of rigor. Except for grammar-school material, every statement that is later used is rigorously proven. Guidelines that facilitate the reading of the book are presented. The interplay between mathematics and mechanics is presented within a historical context, to show that often mechanics stimulated mathematical developments - Newton comes to mind. Sometimes mathematics was introduced independently of its mechanics applications, such as the absolute calculus for Einstein's general theory of relativity. Bio-sketches of all the scientists encountered are included and show that many of them dealt with both mathematics and mechanics.

Provides an introduction to renewable energy for scientists and engineers, addressing the science and technology of all types of renewable energy in detail, as well as nonrenewables. Includes new chapters covering population dynamics and statistics. Self-study problems have been added for each chapter. Incorporates more worked examples. Completely up-to-date, covering such areas as hydraulic fracturing, integration of renewable energy to power grid, and cost.

The study of sliding friction is one of the oldest problems in physics, and certainly one of the most important from a practical point of view. Low-friction surfaces are in increasingly high demand for high-tech components such as computer storage systems, miniature motors, and aerospace devices. It has been estimated that about 5% of the gross national product in the developed countries is "wasted" on friction and the related wear. In spite of this, remarkable little is understood about the fundamental, microscopic processes responsible for friction and wear. The topic of interfacial sliding has experienced a major burst of in terest and activity since 1987, much of which has developed quite independently and spontaneously. This volume contains contributions from leading scientists on fundamental aspects of sliding friction. Some problems considered are: What is the origin of stick-and-slip motion? What is the origin of the rapid processes taking place within a lub at low sliding velocities? On a metallic surface, is the rication layer electronic or phononic friction the dominating energy dissipation pro cess? What is the role (if any) of self-organized criticality in sliding friction? How thick is the water layer during sliding on ice and snow? These and other questions raised in this book are of course only part ly answered: the topic of sliding friction is still in an early state of development."

This book provides an elementary introduction to one-dimensional fluid flow problems involving shock waves in air. The differential equations of fluid flow are approximated by finite difference equations and these in turn are numerically integrated in a stepwise manner, with artificial viscosity introduced into the numerical calculations in order to deal with shocks. This treatment of the subject is focused on the finite-difference approach to solve the coupled differential equations of fluid flow and presents the results arising from the numerical solution using Mathcad programming. Both plane and spherical shock waves are discussed with particular emphasis on very strong explosive shocks in air. This expanded second edition features substantial new material on sound wave parameters, Riemann's method for numerical integration of the equations of motion, approximate analytical expressions for weak shock waves, short duration piston motion, numerical results for shock wave interactions, and new appendices on the piston withdrawal problem and numerical results for a closed shock tube. This text will appeal to students, researchers, and professionals in shock wave research and related fields. Students in particular will appreciate the benefits of numerical methods in fluid mechanics and the level of presentation.

This is the third volume in a series of books on the general topics of Supers- metric Mechanics, with the ?rst and second volumes being published as Lecture Notes in Physics Vol. 698, Supersymmetric Mechanics - Vol. 1: Supersymmetry, Noncommutativity and Matrix Models (ISBN: 3-540-33313-4), and Lecture Notes in Physics Vol. 701, Supersymmetric Mechanics - Vol. 2: The Attractor Mechanism and Space Time Singularities (ISBN: 3-540-34156-0). The aim of this ongoing collection is to provide a reference corpus of suitable, introductory material to the ?eld, by gathering the signi?cantly expanded and edited versions of all tutorial lectures, given over the years at the well-established annual INFN-Laboratori Nazionali di Frascati Winter School on the Attractor Mechanism, directed by myself. The present set of notes results again from the participation and dedication of prestigious lecturers, such as Iosif Bena, Sergio Ferrara, Renata Kallosh, Per Kraus, Finn Larsen, and Boris Pioline. As usual, the lectures were subsequently carefully edited and reworked, taking into account the extensive follow-up discussions. The present volume emphasizes topics of great recent interest, namely general concepts of attractors in supersymmetric gravity and black holes.

The 1952 Nobel physics laureate Felix Bloch (1905-83) was one of the titans of twentieth-century physics. He laid the fundamentals for the theory of solids and has been called the "father of solid-state physics." His numerous, valuable contributions include the theory of magnetism, measurement of the magnetic moment of the neutron, nuclear magnetic resonance, and the infrared problem in quantum electrodynamics.Statistical mechanics is a crucial subject which explores the understanding of the physical behaviour of many-body systems that create the world around us. Bloch's first-year graduate course at Stanford University was the highlight for several generations of students. Upon his retirement, he worked on a book based on the course. Unfortunately, at the time of his death, the writing was incomplete.This book has been prepared by Professor John Dirk Walecka from Bloch's unfinished masterpiece. It also includes three sets of Bloch's handwritten lecture notes (dating from 1949, 1969 and 1976), and details of lecture notes taken in 1976 by Brian Serot, who gave an invaluable opinion of the course from a student's perspective. All of Bloch's problem sets, some dating back to 1933, have been included.The book is accessible to anyone in the physical sciences at the advanced undergraduate level or the first-year graduate level.

This book offers a detailed, pedagogical introduction to general relativity. It includes a review of what may lie beyond and collects up-to-date essays on the experimental tests of this theory, including the precise timing of the double pulsar J0737-3039. Coverage also details the recent results of the Gravity Probe B mission.

In these volumes, the most significant of the collected papers of the Chinese-American theoretical physicist Tsung-Dao Lee are printed. A complete list of his published papers, in order of publication, appears in the Bibliography of T.D. Lee. The papers have been arranged into ten categories, in most cases according to the subject matter. At the beginning of each of the first eight categories of papers, there is a commentary on the content and significance of all of the papers in the category. The two short final categories do not have any commentaries. The editor would like to thank Dr. Richard Friedberg for his assistance in the early stages of the editorial work on this project, as well as for writing commentaries on the papers of Categories III and IV. I would also like to thank Dr. Norman Christ for writing the commentary on the papers of Category VII. The assistance of Irene Tramm was in valuable in many aspects of preparing this collection, including locating copies of Lee's p pers. GERALD FEINBERG List of Categories of T.D. Lee's Papers Volume 1 I. Weak Interactions II. Early Papers on Astrophysics and Hydrodynamics III. Statistical Mechanics IV. Polarons and Solitons Volume 2 V. Quantum Field Theory VI. Symmetry Principles Volume 3 VII. Discrete Physics VIII. Strong Interaction Models IX. Historical Papers X. Gravity (Continuum Theory) Contents (Volume 3)* Introduction (by G. Feinberg) ............................................................ ix Bibliography of T.D. Lee ................................................................. xiii VII. Discrete Physics Commentary ................................................................ ."

In the past hundred years investigators have learned the significance of complex behavior in deterministic systems. The potential applications of this discovery are as numerous as they are encouraging.This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research. The book begins with a thorough introduction to dynamical systems and their applications. It goes on to develop the theory of regular and stochastic behavior in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM theory, the Melnikov method, and Arnold diffusion. Theoretical discussions are illustrated by a study of the dynamics of small circumasteroidal grains perturbed by solar radiation pressure. With alternative derivations and proofs of established results substituted for those in the standard literature, this work serves as an important source for researchers, students and teachers.Skillfully combining in-depth mathematics and actual physical applications, this book will be of interest to the applied mathematician, the theoretical mechanical engineer and the dynamical astronomer alike.

Aerodynamics is a science engaged in the investigation of the motion of air and other gases and their interaction with bodies, and is one of the most important bases of the aeronautic and astronautic techniques. The continuous improvement of the configurations of the airplanes and the space vehicles aid the constant enhancement of their performances are closely related with the development of the aerodynamics. In the design of new flying vehicles the aerodynamics will play more and more important role. The undertakings of aeronautics and astronautics in our country have gained achievements of world interest, the aerodynamics community has made outstanding contributions for the development of these undertakings and the science of aerodynamics. To promote further the development of the aerodynamics, meet the challenge in the new century, summary the experience, cultivate the professional personnel and to serve better the cause of aeronautics and astronautics and the national economy, the present Series of Modern Aerodynamics is organized and published.

Some of the trades covered in the book are well known but most are only known to a small group or to market specialists. The ability to 'see into' actual trades offers a fascinating and unprecedented insight for those interested in the oil markets and gives the book broad appeal. The book can be used as an educational reference work by market participants and as a more general guide to how the crude oil market operates and the strategies that traders employ. There are very academic books about the theory of trading but nothing that directly covers real-life examples of innovative and winning trades, each of which illuminate a different aspect of trading or a different era in the oil markets. The presentation of each individual trade has been designed so that they can be used as case studies by business schools.

Variational principles have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an idea which came to be a cornerstone of geometrical optics. This book explains variational principles and charts their use throughout modern physics. It examines the analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. The book also offers simple but rich first impressions of Einstein’s General Relativity, Feynman’s Quantum Mechanics, and more that reveal amazing interconnections between various fields of physics.

Stochastic elasticity is a fast developing field that combines nonlinear elasticity and stochastic theories in order to significantly improve model predictions by accounting for uncertainties in the mechanical responses of materials. However, in contrast to the tremendous development of computational methods for large-scale problems, which have been proposed and implemented extensively in recent years, at the fundamental level, there is very little understanding of the uncertainties in the behaviour of elastic materials under large strains. Based on the idea that every large-scale problem starts as a small-scale data problem, this book combines fundamental aspects of finite (large-strain) elasticity and probability theories, which are prerequisites for the quantification of uncertainties in the elastic responses of soft materials. The problems treated in this book are drawn from the analytical continuum mechanics literature and incorporate random variables as basic concepts along with mechanical stresses and strains. Such problems are interesting in their own right but they are also meant to inspire further thinking about how stochastic extensions can be formulated before they can be applied to more complex physical systems.

Dynamical processes in which many timescales coexist are called dispersive. The rate coefficients for dispersive processes depend on time. In the case of a chemical reaction, the time dependence of the rate coefficient, k(t), termed the specific reaction rate, is rationalized in the following way. Reactions by their very nature have to disturb reactivity distributions of the reactants in condensed media, as the more reactive species are the first ones to disappear from the system. The extent of this disturbance depends on the ratio of the rates of reactions to the rate of internal rearrangements (mixing) in the system restoring the initial distribution in reactivity of reactants. If the rates of chemical reactions exceed the rates of internal rearrangements, then the initial distributions in reactant reactivity are not preserved during the course of reactions and the specific reaction rates depend on time. Otherwise the extent of disturbance is negligible and classical kinetics, with a constant specific reaction rate, k, termed the reaction rate constant, may be valid as an approximation. In condensed media dispersive dynamical processes are endemic and this is the first monograph devoted to these processes.

This book offers frameworks for the material modeling of gradient materials both for finite and small deformations within elasticity, plasticity, viscosity, and thermomechanics. The first chapter focuses on balance laws and holds for all gradient materials. The next chapters are dedicated to the material modeling of second and third-order materials under finite deformations. Afterwards the scope is limited to the geometrically linear theory, i.e., to small deformations. The next chapter offers an extension of the concept of internal constraints to gradient materials. The final chapter is dedicated to incompressible viscous gradient fluids with the intention to describe, among other applications, turbulent flows, as already suggested by Saint-Venant in the middle of the 19th century.

Sponsored by the Global Foundation, Inc., these proceedings are derived from the International Conference on Orbis Scientiae II. Topics covered include: gravitational mass, neutrino mass, particle masses, cosmological masses, susy masses, and big bang creation of mass.

In an area as vast and important as rheology, it is essential that the experimentalist understands the underlying theories and shortcomings of the measurement technique used, that they are aware of the likely microstructure of the fluid under study and that from this they can appreciate how the fluid and the measuring system interact with each other. This major handbook, written by an international group of experts in the range of rheological techniques, presents the state of the art in rheological measurement, and concentrates on the techniques and underlying physical principles. The second edition, fully revised and updated to include new techniques is invaluable to polymer and materials scientists, engineers and technologists, and anyone else making rheological measurements on materials whether they be polymeric, biological, slurries, food or other complex fluids.

This book provides the reader with a detailed and captivating account of the story where, for the first time, physicists ventured into proposing a new force of nature beyond the four known ones - the electromagnetic, weak and strong forces, and gravitation - based entirely on the reanalysis of existing experimental data. Back in 1986, Ephraim Fischbach, Sam Aronson, Carrick Talmadge and their collaborators proposed a modification of Newton's Law of universal gravitation. Underlying this proposal were three tantalizing pieces of evidence: 1) an energy dependence of the CP (particle-antiparticle and reflection symmetry) parameters, 2) differences between the measurements of G, the universal gravitational constant, in laboratories and in mineshafts, and 3) a reanalysis of the Eoetvos experiment, which had previously been used to show that the gravitational mass of an object and its inertia mass were equal to approximately one part in a billion. The reanalysis revealed that, contrary to Galileo's position, the force of gravity was in fact very slightly different for different substances. The resulting Fifth Force hypothesis included this composition dependence and also added a small distance dependence to the inverse-square gravitational force. Over the next four years numerous experiments were performed to test the hypothesis. By 1990 there was overwhelming evidence that the Fifth Force, as initially proposed, did not exist. This book discusses how the Fifth Force hypothesis came to be proposed and how it went on to become a showcase of discovery, pursuit and justification in modern physics, prior to its demise. In this new and significantly expanded edition, the material from the first edition is complemented by two essays, one containing Fischbach's personal reminiscences of the proposal, and a second on the ongoing history and impact of the Fifth Force hypothesis from 1990 to the present.

This collection on "Mechanics of Generalized Continua - from Micromechanical Basics to Engineering Applications" brings together leading scientists in this field from France, Russian Federation, and Germany. The attention in this publication is be focussed on the most recent research items, i.e., - new models, - application of well-known models to new problems, - micro-macro aspects, - computational effort, - possibilities to identify the constitutive equations, and - old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

The workshop aims to provide a fundamental understanding of the liquefaction process, necessary to the enhancement of liquefaction prediction. The contributions are divided into eight sections, which include: factors affecting liquefaction susceptibility and field studies of liquefaction.

Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body - especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation.

The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used.

This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid.The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too.

Audience: researchers in applied mathematics, mechanical and civil engineering.

This text features 105 papers dealing with the fundamentals and the applications of poromechanics from the Biot conference of 1998, held in Louvain-la-Neuve. Topics include: wave propogation; numerical modelling; identification of poromechanical parameters; and constitutive modelling.