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."

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.

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.

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.

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.

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 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.

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 ................................................................ ."

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.

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.

This text provides an overview of important theory, principles, and concepts in the field of thermodynamics, making this abstract and complex subject easy to comprehend while building practical skills in the process. It enhances understanding of heat transfer, steam tables, energy concepts, power generation, psychrometry, refrigeration cycles, and more. Practical, easily accessible case studies illustrate various thermodynamics principles. Each chapter concludes with a list of questions or problems, with answers at the back of the book.

This book provides a brief introduction to rational continuum mechanics in a form suitable for students of engineering, mathematics and science. The presentation is tightly focused on the simplest case of the classical mechanics of nonpolar materials, leaving aside the effects of internal structure, temperature and electromagnetism, and excluding other mathematical models, such as statistical mechanics, relativistic mechanics and quantum mechanics. Within the limitations of the simplest mechanical theory, the author had provided a text that is largely self-contained. Though the book is primarily an introduction to continuum mechanics, the lure and attraction inherent in the subject may also recommend the book as a vehicle by which the student can obtain a broader appreciation of certain important methods and results from classical and modern analysis.

Der bekannte Astronom Karl Schwarzschild (1873-1916) gilt als der Begrunder der Astrophysik und als hervorragender Forscher mit einer erstaunlichen Bandbreite seiner Interessen. Arbeiten zur Himmelsmechanik, Elektrodynamik und Relativitatstheorie weisen ihn als vorzuglichen Mathematiker und Physiker auf der Hohe seiner Zeit aus. Untersuchungen zur Photographischen Photometrie, Optik und Spektroskopie zeigen den versierten Beobachter, der sein Messinstrumentarium beherrscht, und schliesslich arbeitete Schwarzschild als Astrophysiker an Sternatmospharen, Kometen, Struktur und Dynamik von Sternsystemen. Die in seinem kurzen Leben entstandene Fulle an wissenschaftlichen Arbeiten ist in drei Banden der Gesamtausgabe gesammelt, erganzt durch biographisches Material, Annotationen von Fachleuten und einen Essay des Nobelpreistragers S. Chandrasekhar."

This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory's role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.

This book discusses the application of independent continuous mapping method in predicting and the optimization of the mechanical performance of buckling with displacement, stress and static constrains. Each model is explained by mathematical theories and followed by simulation with frequently-used softwares. With abundant project data, the book is an essential reference for mechanical engineers, structural engineers and industrial designers.

The Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Gottingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. The Theory of the Top: Volume III. Perturbations: Astronomical and Geophysical Applications is the third installment in a series of four self-contained English translations that provide insights into kinetic theory and kinematics."

This volume constitutes the Proceedings of the IUTAM Symposium on 'Scaling in Solid Mechanics', held in Cardiff from 25th to 29th June 2007. The Symposium was convened to address and place on record topical issues in theoretical, experimental and computational aspects of scaling approaches to solid mechanics and related fields. Scaling is a rapidly expanding area of research having multidisciplinaryapplications. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated.

Scaling methods apply wherever there is similarity across many scales or a need to bridge different scales, e.g. the nanoscale and macroscale. The emphasis in the Symposium was upon fundamental issues such as: mathematical foundations of scaling methods based on transformations and connections between multi-scale approaches and transformations. The Symposium remained focussed on fundamental research issues of practical significance. The topics considered included damage accumulation, growth of fatigue cracks, development of patterns of flaws in the earth's core and in ice, abrasiveness of rough surfaces, and so on. The Symposium showed that scaling methods cannot be reduced solely to dimensional analysis and fractal approaches. Modern scaling approaches consist of a great diversity of techniques.

These proceedings contain lectures on state-of-the-art developments in self-similar solutions, fractal models, models involving interplay between different scales, size effects in fracture of solids and bundles of fibres, scaling in problems of fracture mechanics, nanomechanics, contact mechanics and testing of materials byindentation, scaling issues in mechanics of agglomeration of adhesive particles, and in biomimetic of adhesive contact.

This title provides an introduction to molecular-microsimulation methods for colloidal dispersions and is suitable for both self-study and reference. It provides the reader with a systematic understanding of the theoretical background to simulation methods, together with a wide range of practical skills for developing computational programs. Exercises are included at the end of each chapter to further assist the understanding of the subjects addressed.
- Provides the reader with the theoretical background to molecular-microsimulation methods
- Suitable for both self-study and reference
- Aids the reader in developing programs to meet their own requirements

Ready access to computers has de?ned a new era in teaching and learning. The opportunity to extend the subject matter of traditional science and engineering curricula into the realm of scienti?c computing has become not only desirable, but also necessary. Thanks to portability and low overhead and operating cost, experimentation by numerical simulation has become a viable substitute, and occasionally the only alternative, to physical experimentation. The new framework has necessitated the writing of texts and monographs from a modern perspective that incorporates numerical and computer progr- ming aspects as an integral part of the discourse. Under this modern directive, methods, concepts, and ideas are presented in a uni?ed fashion that motivates and underlines the urgency of the new elements, but neither compromises nor oversimpli?es the rigor of the classical approach. Interfacing fundamental concepts and practical methods of scienti?c c- puting can be implemented on di?erent levels. In one approach, theory and implementation are kept complementary and presented in a sequential fashion. In another approach, the coupling involves deriving computational methods and simulation algorithms, and translating equations into computer code - structions immediately following problem formulations. Seamlessly interjecting methods of scienti?c computing in the traditional discourse o?ers a powerful venue for developing analytical skills and obtaining physical insight.

Because of its versatility in analyzing a broad range of applications, multibody dynamics has grown in the past two decades to be an important tool for designing, prototyping, and simulating complex articulated mechanical systems. This textbooka "a result of the authora (TM)s many years of research and teachinga "brings together diverse concepts of dynamics, combining the efforts of many researchers in the field of mechanics. Bridging the gap between dynamics and engineering applications such as microrobotics, virtual reality simulation of interactive mechanical systems, nanomechanics, flexible biosystems, crash simulation, and biomechanics, the book puts into perspective the importance of modeling in the dynamic simulation and solution of problems in these fields.

To help engineering students and practicing engineers understand the rigid-body dynamics concepts needed for the book, the author presents a compiled overview of particle dynamics and Newtona (TM)s second law of motion in the first chapter. A particular strength of the work is its use of matrices to generate kinematic coefficients associated with the formulation of the governing equations of motion. Additional features of the book include:

* numerous worked examples at the end of each section

* introduction of boundary-element methods (BEM) in the description of flexible systems

* up-to-date solution techniques for rigid and flexible multibody dynamics using finite- element methods (FEM)

* inclusion of MATLAB-based simulations and graphical solutions

* in-depth presentation of constrained systems

* presentation of the general form of equations of motion ready for computerimplementation

* two unique chapters on stability and linearization of the equations of motion

Junior/senior undergraduates and first-year graduate engineering students taking a course in dynamics, physics, control, robotics, or biomechanics will find this a useful book with a strong computer orientation towards the subject. The work may also be used as a self-study resource or research reference for practitioners in the above-mentioned fields.

Understanding finance and accounting principles is important in interfacing and conducting business with accountants, financial analysts, and members of upper management. In a relatively simple and easy-to-understand manner, this book familiarizes professionals with decision making skills founded on financial calculations and quantitative analysis. It covers finance and accounting ratios and other metrics; income statements, balance sheets, cash flow, and working capital concepts; inventory concepts; life cycle, period, direct, and indirect costs; and energy performance contracting. Each chapter concludes with a list of questions or problems for self-assessment and knowledge affirmation purposes. Answers to the questions are at the back of the book.