This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.

This volume contains the papers presented at the IUTAM Symposium on Geometry and Statistics of Turbulence, held in November 1999, at the Shonan International Village Center, Hayama (Kanagawa-ken), Japan. The Symposium was proposed in 1996, aiming at organizing concen trated discussions on current understanding of fluid turbulence with empha sis on the statistics and the underlying geometric structures. The decision of the General Assembly of International Union of Theoretical and Applied Mechanics (IUTAM) to accept the proposal was greeted with enthusiasm. Turbulence is often characterized as having the properties of mixing, inter mittency, non-Gaussian statistics, and so on. Interest is growing recently in how these properties are related to formation and evolution of struc tures. Note that the intermittency is meant for passive scalars as well as for turbulence velocity or rate of dissipation. There were eighty-eight participants in the Symposium. They came from thirteen countries, and fifty-seven papers were presented. The presenta tions comprised a wide variety of fundamental subjects of mathematics, statistical analyses, physical models as well as engineering applications. Among the subjects discussed are (a) Degree of self-similarity in cascade, (b) Fine-scale structures and degree of Markovian property in turbulence, (c) Dynamics of vorticity and rates of strain, (d) Statistics associated with vortex structures, (e) Topology, structures and statistics of passive scalar advection, (f) Partial differential equations governing PDFs of velocity in crements, (g) Thermal turbulences, (h) Channel and pipe flow turbulences, and others.

This book presents theoretical fundamentals and applications of a new numerical model that has the ability to simulate wave propagation. Coverage examines linear waves in ideal fluids and elastic domains. In addition, the book includes a numerical simulation of wave propagation based on scalar and vector wave equations, as well as fluid-structure interaction and soil-structure interaction.

The revised edition gives a comprehensive mathematical and physical presentation of fluid flows in non-classical models of convection - relevant in nature as well as in industry. After the concise coverage of fluid dynamics and heat transfer theory it discusses recent research. This monograph provides the theoretical foundation on a topic relevant to metallurgy, ecology, meteorology, geo-and astrophysics, aerospace industry, chemistry, crystal physics, and many other fields.

Thisisthe?rstbookinworldliteraturedevotedtoapplicationsoftheisotopic e?ect in solids. It is accessible to physicists, chemists, electronic engineers, and material scientists alike. This book is intended both as tutorial and as reference. Readers seeking to learn the basics of application of the isotopic e?ect in solids should start by reading the ?rst few overview chapters, and then dig into descriptions of speci?c applications to see how they really work. It is hoped that it will be useful to undergraduate and graduate students of physics and optics as well as engineers, physicists, material scientists, and medical doctors who are interested in investigation or applications of the isotopic e?ect in solids. This book is a state-of-the-art introduction to very recent activity in solid-state physics which has developed in the main during the last half century and promises a new technology of isotopic engineering. Important applications are to be expected for information storage and dev- oping materials for computer memory, quantum computers, isotopic ?bers, isotopic optoelectronics, and quantum electronics as well as UV lasers. The references I cite are those with which I am most familiar and which have helped us understand the subject as presented here. There has been no attempttogivecredittoeachcontributor, butIhavetriedtocitetheoriginal papers, which brought new and important results (methods) to applications of the isotopic e?ect in solids, covered in this text

This book is based on the author's lecture notes for his Introductory Newtonian Mechanics course at the Hellenic Naval Academy. In order to familiarize students with the use of several basic mathematical tools, such as vectors, differential operators and differential equations, it first presents the elements of vector analysis that are needed in the subsequent chapters. Further, the Mathematical Supplement at the end of the book offers a brief introduction to the concepts of differential calculus mentioned. The main text is divided into three parts, the first of which presents the mechanics of a single particle from both the kinetic and the dynamical perspectives. The second part then focuses on the mechanics of more complex structures, such as systems of particles, rigid bodies and ideal fluids, while the third part consists of 60 fully solved problems. Though chiefly intended as a primary text for freshman-level physics courses, the book can also be used as a supplemental (tutorial) resource for introductory courses on classical mechanics for physicists and engineers

While systems at equilibrium are treated in a unified manner through the partition function formalism, the statistical physics of out-of-equilibrium systems covers a large variety of situations that are often without apparent connection. This book proposes a unified perspective on the whole set of systems near equilibrium: it brings out the profound unity of the laws which govern them and gathers a large number of results usually fragmented in the literature. The reader will find in this book a pedagogical account of the fundamental results: physical origins of irreversibility, fluctuation-dissipation theorem, Boltzmann equation, linear response, Onsager relations, transport phenomena, Langevin and Fokker-Planck equations. The book's comprehensive organisation makes it valuable both as a textbook about irreversible phenomena and as a reference book for researchers.

This book discusses the parametric modeling, performance evaluation, design optimization and comparative study of the high-speed, parallel pick-and-place robots. It collects the modeling methodology, evaluation criteria and design guidelines for parallel PnP robots to provide a systematic analysis method for robotic developers. Furthermore, it gathers the research results previously scattered in many prestigious international journals and conference proceedings and methodically edits them and presents them in a unified form. The book is of interest to researchers, R&D engineers and graduate students in industrial parallel robotics who wish to learn the core principles, methods, algorithms, and applications.

This book presents the basics and methods of nanoscale analytical techniques for tribology field. It gives guidance to the application of mechanical, microstructural, chemical characterization methods and topography analysis of materials. It provides an overview of the of state-of-the-art for researchers and practitioners in the field of tribology. It shows different examples to the application of mechanical, microstructural, chemical characterization methods and topography analysis of materials. Friction and Wear phenomena are governed by complexe processes at the interface of sliding surfaces. For a detailed understanding of these phenomena many surface sensitive techniques have become available in recent years. The applied methods are atom probe tomography, in situ TEM, SERS, NEXAFS, in situ XPS, nanoindentation and in situ Raman spectroscopy. A survey of new related numerical calculations completes this book. This concerns ab-initio coupling, numerical calculations for mechanical aspects and density functional theory (DFT) to study chemical reactivity.

The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the single-mode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape centsn, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the nonlinear effects modify the linear mode shape centsn. Therefore, in the case of large-amplitude oscillations, the single-mode discretization may yield inaccurate mode shapes. References 1. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A., Nonnal Modes and Localization in Nonlinear Systems, Wiley, New York, 1

This book covers the simulation of evaporating saltwater falling films with and without turbulence wires. The methods presented within can be applied to a variety of applications including the food and pharmaceutical industry, as well as in nuclear technology. This topic is ideal for researchers in chemical engineering.

The book covers basic approaches to the nuclear fuel state of energy reactors in the last stages of the nuclear fuel cycle, these have been developed by the authors based on Ukrainian Nuclear Power Plant (NPP) operational experience. The book starts by looking at the physical safety basis of water-water energetic reactor (WWER) nuclear fuel. It goes on to discuss modern approaches to the heat exchange modelling in nuclear power plant equipment. Next, the safety criteria when making a decision about dry storage for WWER-1000 fuel assembly are discussed. Then the effect of reactor capacity cyclic changes on energy accumulation of creep formations in fuel cladding is covered in full, along with a chapter on the analysis of WWER-1000 fuel cladding failure. Finally, the book finishes with a description of thermal safety criteria for dry storage of spent nuclear fuel. The book is essential reading for anyone concerned with NPP maintenance and safety.

Satellite Gravimetry and the Solid Earth: Mathematical Foundations presents the theories behind satellite gravimetry data and their connections to solid Earth. It covers the theory of satellite gravimetry and data analysis, presenting it in a way that is accessible across geophysical disciplines. Through a discussion of satellite measurements and the mathematical concepts behind them, the book shows how various satellite measurements, such as satellite orbit, acceleration, vector gravimetry, gravity gradiometry, and integral energy methods can contribute to an understanding of the gravity field and solid Earth geophysics. Bridging the gap between geodesy and geophysics, this book is a valuable resource for researchers and students studying gravity, gravimetry and a variety of geophysical and Earth Science fields.

This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. Contents Discrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves

This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems - i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of "quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".

This volume contains results gained from the EU-funded 6th Framework project ADIGMA (Adaptive Higher-order Variational Methods for Aerodynamic Applications in Industry). The goal of ADIGMA was the development and utilization of innovative adaptive higher-order methods for the compressible flow equations enabling reliable, mesh independent numerical solutions for large-scale aerodynamic applications in aircraft industry. The ADIGMA consortium was comprised of 22 organizations which included the main European aircraft manufacturers, the major European research establishments and several universities, all with well proven expertise in Computational Fluid Dynamics (CFD). The book presents an introduction to the project, exhibits partners methods and approaches and provides a critical assessment of the newly developed methods for industrial aerodynamic applications. The best numerical strategies for integration as major building blocks for the next generation of industrial flow solvers are identified. "

The book is based on the author's PhD thesis, which deals with the concept of time in quantum gravity and its relevance for the physics of the early Universe. It presents a consistent and complete new relational formulation of quantum gravity (more specifically, of quantum mechanics models with diffeomorphism invariance), which is applied to potentially observable cosmological effects. The work provides answers to the following questions: How can the dynamics of quantum states of matter and geometry be defined in a diffeomorphism-invariant way? What is the relevant space of physical states and which operators act on it? How are the quantum states related to probabilities in the absence of a preferred time? The answers can provide a further part of the route to constructing a fundamental theory of quantum gravity. The book is well-suited to graduate students as well as professional researchers in the fields of general relativity and gravitation, cosmology, and quantum foundations.

This thesis studies various aspects of non-critical strings both as an example of a non-trivial and solvable model of quantum gravity and as a consistent approximation to the confining flux tube in quantum chromodynamics (QCD). It proposes and develops a new technique for calculating the finite volume spectrum of confining flux tubes. This technique is based on approximate integrability and it played a game-changing role in the study of confining strings. Previously, a theoretical interpretation of available high quality lattice data was impossible, because the conventional perturbative expansion for calculating the string spectra was badly asymptotically diverging in the regime accessible on the lattice. With the new approach, energy levels can be calculated for much shorter flux tubes than was previously possible, allowing for a quantitative comparison with existing lattice data. The improved theoretical control makes it manifest that existing lattice data provides strong evidence for a new pseudoscalar particle localized on the QCD fluxtube - the worldsheet axion. The new technique paves a novel and promising path towards understanding the dynamics of quark confinement.

Advances in processing methods are not only improving the quality and yield of lubricant base stocks, they are also reducing the dependence on more expensive crude oil starting materials. Process Chemistry of Lubricant Base Stocks provides a comprehensive understanding of the chemistry behind the processes involved in petroleum base stock production from crude oil fractions. This book examines hydroprocessing technologies that, driven by the demand for higher performance in finished lubricants, have transformed processing treatments throughout the industry. The author relates the properties of base stocks to their chemical composition and describes the process steps used in their manufacture. The book highlights catalytic processes, including hydrocracking, hydrofinishing, and catalytic dewaxing. It also covers traditional solvent-based separation methods used to remove impurities, enhance performance, and improve oxidation resistance. The final chapters discuss the production of Food Grade white oils and paraffins and the gas-to-liquids processes used to produce highly paraffinic base stocks via Fischer-Tropsch chemistry. Process Chemistry of Lubricant Base Stocks provides historical and conceptual background to the technologies used to make base stocks, thorough references, and a unique emphasis on chemical, not just engineering, aspects of lubricant processing-making this book an ideal and practical reference for scientists across a wide range of disciplines.

Compendium of Hydrogen Energy: Hydrogen Production and Purification, the first text in a four-volume series, focuses on the production of hydrogen. As many experts believe that the hydrogen economy will eventually replace the fossil fuel economy as our primary source of energy, the text provides a timely discussion on this interesting topic. The text details the methods of hydrogen production using fossil fuels, also exploring sustainable extraction methods of hydrogen production from water and hydrogen purification processes.

Thermodynamics sets fundamental laws for all physical processes and is central to driving and maintaining planetary dynamics. But how do Earth system processes perform work, where do they derive energy from, and what are the limits? This accessible book describes how the laws of thermodynamics apply to Earth system processes, from solar radiation to motion, geochemical cycling and biotic activity. It presents a novel view of the thermodynamic Earth system explaining how it functions and evolves, how different forms of disequilibrium are being maintained, and how evolutionary trends can be interpreted as thermodynamic trends. It also offers an original perspective on human activity, formulating this in terms of a thermodynamic, Earth system process. This book uses simple conceptual models and basic mathematical treatments to illustrate the application of thermodynamics to Earth system processes, making it ideal for researchers and graduate students across a range of Earth and environmental science disciplines.

This book is intended as a study aid for the finite element method. Based on the free computer algebra system Maxima, we offer routines to symbolically or numerically solve problems from the context of two-dimensional problems. For this rather advanced topic, classical 'hand calculations' are difficult to perform and the incorporation of a computer algebra system is a convenient approach to handle, for example, larger matrix operations. The mechanical theories focus on the classical two-dimensional structural elements, i.e., plane elements, thin or classical plates, and thick or shear deformable plate elements. The use of a computer algebra system and the incorporated functions, e.g., for matrix operations, allows to focus more on the methodology of the finite element method and not on standard procedures. Furthermore, we offer a graphical user interface (GUI) to facilitate the model definition. Thus, the user may enter the required definitions in a source code manner directly in wxMaxima or use the GUI which is able to execute wxMaxime to perform the calculations.

This book provides a general introduction to fluid mechanics in the form of biographies and popular science. Based on the author's extensive teaching experience, it combines natural science and human history, knowledge inheritance and cognition law to replace abstract concepts of fluid mechanics with intuitive and understandable physical concepts. In seven chapters, it describes the development of fluid mechanics, aerodynamics, hydrodynamics, computational fluid dynamics, experimental fluid dynamics, wind tunnel and water tunnel equipment, the mystery of flight and aerodynamic principles, and leading figures in fluid mechanics in order to spark beginners' interest and allow them to gain a comprehensive understanding of the field's development. It also provides a list of references for further study.

This volume contains the proceedings of the XIX International Colloquium on Mechanical Fatigue of Metals, held at the Faculty of Engineering of the University of Porto, Portugal, 5-7 September 2018. This International Colloquium facilitated and encouraged the exchange of knowledge and experiences among the different communities involved in both basic and applied research in the field of the fatigue of metals, looking at the problem of fatigue exploring analytical and numerical simulative approaches. Fatigue damage represents one of the most important types of damage to which structural materials are subjected in normal industrial services that can finally result in a sudden and unexpected abrupt fracture. Since metal alloys are still today the most used materials in designing the majority of components and structures able to carry the highest service loads, the study of the different aspects of metals fatigue attracts permanent attention of scientists, engineers and designers.

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fourth volume collects authoritative chapters covering several applications of fractional calculus in physics, including classical and continuum mechanics.