This book provides the mathematical foundations of the theory of hyperhamiltonian dynamics, together with a discussion of physical applications. In addition, some open problems are discussed. Hyperhamiltonian mechanics represents a generalization of Hamiltonian mechanics, in which the role of the symplectic structure is taken by a hyperkahler one (thus there are three Kahler/symplectic forms satisfying quaternionic relations). This has proved to be of use in the description of physical systems with spin, including those which do not admit a Hamiltonian formulation. The book is the first monograph on the subject, which has previously been treated only in research papers.

First published in 2016. This practical study guide serves as a valuable companion text, providing workedout solutions to all of the problems presented in Guide to Energy Management, Eighth Edition. Covering each chapter in sequence, the author has provided detailed instructions to guide you through every step in the problemsolving process. You'll find all the help you need to fully master and apply the stateoftheart concepts and strategies presented in Guide to Energy Management.

The book provides readers with an understanding of the mutual conditioning of spacetime and interactions and matter. The spacetime manifold will be looked at to be a reservoir for the parametrization of operation Lie groups or subgroup classes of Lie groups. With basic operation groups or Lie algebras, all physical structures can be interpreted in terms of corresponding realizations or representations. Physical properties are related eigenvalues or invariants. As an explicit example of operational spacetime is proposed, called electroweak spacetime, parametrizing the classes of the internal hypercharge - isospin group in the general linear group in two complex dimensions, i.e., the Lorentz cover group, extended by the casual (dilation) and phase group. Its representations and invariants will be investigated with the aim to connect them, qualitatively and numerically, with the properties of interactions and particles as arising in the representations of its tangent Minkowski spaces.

This 2nd edition volume of Modern Gas-Based Temperature and Pressure Measurements follows the first publication in 1992. It collects a much larger set of information, reference data, and bibliography in temperature and pressure metrology of gaseous substances, including the physical-chemical issues related to gaseous substances. The book provides solutions to practical applications where gases are used in different thermodynamic conditions. Modern Gas-Based Temperature and Pressure Measurements, 2nd edition is the only comprehensive survey of methods for pressure measurement in gaseous media used in the medium-to-low pressure range closely connected with thermometry. It assembles current information on thermometry and manometry that involve the use of gaseous substances which are likely to be valid methods for the future. As such, it is an important resource for the researcher. This edition is updated through the very latest scientific and technical developments of gas-based temperature and pressure measurements using thermometry and manometry, and brings all of the techniques together under one cover. This book fills the gap in international literature, as no other recently published book provides a comprehensive survey for gaseous media closely connected with thermometry. Updates in this new edition include revised appendices and new chapters on Mutual Recognition Agreement of the Comite International des Poids et Mesures and its main applications, and developments in the European Metrology Society.

"Stochastic Tools in Mathematics and Science" covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, renormalization, basic statistical mechanics, and generalized Langevin equations and the Mori-Zwanzig formalism. The applications include sampling algorithms, data assimilation, prediction from partial data, spectral analysis, and turbulence. The book is based on lecture notes from a class that has attracted graduate and advanced undergraduate students from mathematics and from many other science departments at the University of California, Berkeley. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications. For this new edition the material has been thoroughly reorganized and updated, and new sections on scaling, sampling, filtering and data assimilation, based on recent research, have been added. There are additional figures and exercises. Review of earlier edition: "This is an excellent concise textbook which can be used for self-study by graduate and advanced undergraduate students and as a recommended textbook for an introductory course on probabilistic tools in science." Mathematical Reviews, 2006

Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems.
There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between theory and practice, fundamentals and advanced subjects, and generality and specialization. None of the books in this area have completely studied and analyzed nonlinear equation in dynamical and vibratory systems using the latest analytical and numerical methods, so that the user can solve the problems without the need of studying too many different references. Thereby in this book, by the use of the latest analytic, numeric laboratorial methods and using more than 300 references like books, papers and the researches done by the authors and by considering almost all possible processes and situation, new theories has been proposed to encounter applied problems in engineering and applied sciences. In this way, the user (bachelor's, master's and PhD students, university teachers and even in research centers in different fields of mechanical, civil, aerospace, electrical, chemical, applied mathematics, physics, and etc.) can encounter such systems confidently. In the different chapters of the book, not only are the linear and especially nonlinear problems with oscillatory form broadly discussed, but also applied examples are practically solved by the proposed methodology.

This book is based upon lectures presented in the summer of 2009 at the INFN-Laboratori Nazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci. The symposium included such prestigious lecturers as S. Ferrara, G. Dall'Agata, J.F. Morales, J. Simon and M. Trigiante. All lectures were given at a pedagogical, introductory level, which is reflected in the specific "flavor" of this volume. The book also benefits from extensive discussions about, and the related reworking of, the various contributions. It is the fifth volume in a series of books on the general topics of supersymmetry, supergravity, black holes and the attractor mechanism.

F. dell'Isola, L. Placidi: Variational principles are a powerful tool also for formulating field theories. - F. dell'Isola, P. Seppecher, A. Madeo: Beyond Euler-Cauchy Continua. The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument. - B. Bourdin, G.A. Francfort: Fracture. - S. Gavrilyuk: Multiphase flow modeling via Hamilton's principle. - V. L. Berdichevsky: Introduction to stochastic variational problems. - A. Carcaterra: New concepts in damping generation and control: theoretical formulation and industrial applications. - F. dell'Isola, P. Seppecher, A. Madeo: Fluid shock wave generation at solid-material discontinuity surfaces in porous media.

Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones.
The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.

Fatigue of the pressurized fuselages of transport aircraft is a significant problem all builders and users of aircraft have to cope with for reasons associated with assuring a sufficient lifetime and safety, and formulating adequate inspection procedures. These aspects are all addressed in various formal protocols for creating and maintaining airworthiness, including damage tolerance considerations. In most transport aircraft, fatigue occurs in lap joints, sometimes leading to circumstances that threaten safety in critical ways. The problem of fatigue of lap joints has been considerably enlarged by the goal of extending aircraft lifetimes.

Fatigue of riveted lap joints between aluminium alloy sheets, typical of the pressurized aircraft fuselage, is the major topic of the present book. The richly illustrated and well-structured chapters treat subjects such as: structural design solutions and loading conditions for fuselage skin joints; relevance of laboratory test results for simple lap joint specimens to riveted joints in a real structure; effect of various production and design related variables on the riveted joint fatigue behaviour; analytical and experimental results on load transmission in mechanically fastened lap joints; theoretical and experimental analysis of secondary bending and its implications for riveted joint fatigue performance; nucleation and shape development of fatigue cracks in riveted longitudinal lap joints; overview of experimental investigations into the multi-site damage for full scale fuselage panels and riveted lap joint specimens; fatigue crack growth and fatigue life prediction methodology for riveted lap joints; residual strength predictions for riveted lap joints in a fuselage structure. The major issues of each chapter are recapitulated in the last section.

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This title provides an overview of the innovative use of electro-kinetic phenomena in experimentally exploring non-equilibrium regions of chemically non-reacting systems. Transport phenomena mediated by charged liquid-liquid interfaces and solid-liquid interfaces are also covered. Transport phenomena mediated by electrified interfaces are discussed in the context of a number of important areas, including, soil/water systems, phase transfer catalysis, animal/plant physiology and mimicking taste/smell sensing mechanisms.
- Provides an overview of the innovative use of electro-kinetic phenomena
- Discusses conventional electro-kinetics and other transport phenomena mediated by charged interfaces
- Of special interest to those working in the area of interface science

This book explores the role of singularities in general relativity (GR): The theory predicts that when a sufficient large mass collapses, no known force is able to stop it until all mass is concentrated at a point. The question arises, whether an acceptable physical theory should have a singularity, not even a coordinate singularity. The appearance of a singularity shows the limitations of the theory. In GR this limitation is the strong gravitational force acting near and at a super-massive concentration of a central mass. First, a historical overview is given, on former attempts to extend GR (which includes Einstein himself), all with distinct motivations. It will be shown that the only possible algebraic extension is to introduce pseudo-complex (pc) coordinates, otherwise for weak gravitational fields non-physical ghost solutions appear. Thus, the need to use pc-variables. We will see, that the theory contains a minimal length, with important consequences. After that, the pc-GR is formulated and compared to the former attempts. A new variational principle is introduced, which requires in the Einstein equations an additional contribution. Alternatively, the standard variational principle can be applied, but one has to introduce a constraint with the same former results. The additional contribution will be associated to vacuum fluctuation, whose dependence on the radial distance can be approximately obtained, using semi-classical Quantum Mechanics. The main point is that pc-GR predicts that mass not only curves the space but also changes the vacuum structure of the space itself. In the following chapters, the minimal length will be set to zero, due to its smallness. Nevertheless, the pc-GR will keep a remnant of the pc-description, namely that the appearance of a term, which we may call "dark energy", is inevitable. The first application will be discussed in chapter 3, namely solutions of central mass distributions. For a non-rotating massive object it is the pc-Schwarzschild solution, for a rotating massive object the pc-Kerr solution and for a charged massive object it will be the Reissner-Nordstroem solution. This chapter serves to become familiar on how to resolve problems in pc-GR and on how to interpret the results. One of the main consequences is, that we can eliminate the event horizon and thus there will be no black holes. The huge massive objects in the center of nearly any galaxy and the so-called galactic black holes are within pc-GR still there, but with the absence of an event horizon! Chapter 4 gives another application of the theory, namely the Robertson-Walker solution, which we use to model different outcomes of the evolution of the universe. Finally the capability of this theory to predict new phenomena is illustrated.

This book develops a uniform accurate method which is capable of dealing with vibrations of laminated beams, plates and shells with arbitrary boundary conditions including classical boundaries, elastic supports and their combinations. It also provides numerous solutions for various configurations including various boundary conditions, laminated schemes, geometry and material parameters, which fill certain gaps in this area of reach and may serve as benchmark solutions for the readers. For each case, corresponding fundamental equations in the framework of classical and shear deformation theory are developed. Following the fundamental equations, numerous free vibration results are presented for various configurations including different boundary conditions, laminated sequences and geometry and material properties. The proposed method and corresponding formulations can be readily extended to static analysis.

Over the last decade, Computational Fluid Dynamics (CFD) has become a - ture technology for the development of new products in aeronautical industry. Aerodynamic design engineers have progressively taken advantage of the pos- bilities o?ered by the numericalsolutionof the Reynolds averagedNavier-Stokes (RANS) equations. Signi?cant improvements in physical modeling and solution algorithms as well as the enormous increase of computer power enable hi- ?delity numerical simulations in all stages of aircraft development. In Germany, the national CFD project MEGAFLOW furthered the dev- opment and availability of RANS solvers for the prediction of complex ?ow problemssigni?cantly. MEGAFLOWwasinitiated by the?rstaviationresearch programoftheFederalGovernmentin1995undertheleadershipoftheDLR(see Kroll, N. , Fassbender, J. K. (Eds). : MEGAFLOW - Numerical Flow Simulation for Aircraft Design; Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Volume 89, Springer, 2005). A network from aircraft industry, DLR and several universities was created with the goal to focus and direct development activities for numerical ?ow simulation towards a common aerodynamic si- lation system providing both a block-structured (FLOWer-Code) and a hybrid (TAU-Code) parallel ? ow prediction capability. Today, both codes have reached a high level of maturity and reliability. They are routinely used at DLR and German aeronautic industry for a wide range of aerodynamic applications. For many universities the MEGAFLOW software represents a platform for the - provementofphysicalmodelsandfortheinvestigationofcomplex?owproblems. The network was established as an e?cient group of very closely co-operating partners with supplementing expertises and experience.

With his Ph.D. thesis, presented here in the format of a "Springer Theses", Paul Fulda won the 2012 GWIC thesis prize awarded by the Gravitational Wave International Committee. The impact of thermal noise on future gravitational wave detectors depends on the size and shape of the interrogating laser beam. It had been known since 2006 that, in theory, higher-order Laguerre-Gauss modes could reduce thermal noise. Paul Fulda's research brings Laguerre-Gauss modes an enormous step forward. His work includes analytical, numerical and experimental work on table-top setups as well as experiments at the Glasgow 10m prototype interferometer. Using numerical simulations the LG33 mode was selected as the optical mode to be tested. Further research by Paul and his colleagues since then concentrated on this mode. Paul has developed and demonstrated simple and effective methods to create this mode with diffractive optics and successfully demonstrated its compatibility with the essential building blocks of gravitational wave detectors, namely, optical cavities, Michelson interferometers and opto-electronic sensing and control systems. Through this work, Laguerre-Gauss modes for interferometers have been transformed from an essentially unknown entity to a well understood option with an experimental basis.

This book discusses the state of the art of the basic theoretical and observational topics related to black hole astrophysics. It covers all the main topics in this wide field, from the theory of accretion disks and formation mechanisms of jet and outflows, to their observed electromagnetic spectrum, and attempts to measure the spin of these objects. Black holes are one of the most fascinating predictions of general relativity and are currently a very hot topic in both physics and astrophysics. In the last five years there have been significant advances in our understanding of these systems, and in the next five years it should become possible to use them to test fundamental physics, in particular to predict the general relativity in the strong field regime. The book is both a reference work for researchers and a textbook for graduate students.

Complex, microstructured materials are widely used in industry and technology and include alloys, ceramics and composites. Focusing on non-destructive evaluation (NDE), this book explores in detail the mathematical modeling and inverse problems encountered when using ultrasound to investigate heterogeneous microstructured materials. The outstanding features of the text are firstly, a clear description of both linear and nonlinear mathematical models derived for modelling the propagation of ultrasonic deformation waves, and secondly, the provision of solutions to the corresponding inverse problems that determine the physical parameters of the models. The data are related to nonlinearities at both a macro- and micro- level, as well as to dispersion. The authors' goal has been to construct algorithms that allow us to determine the parameters within which we are required to characterize microstructure. To achieve this, the authors not only use conventional harmonic waves, but also propose a novel methodology based on using solitary waves in NDE. The book analyzes the uniqueness and stability of the solutions, in addition to providing numerical examples.

The effective theory of quantum gravity coupled to models of particle physics is being probed by cutting edge experiments in both high energy physics (searches for extra dimensions) and cosmology (testing models of inflation). This thesis derives new bounds that may be placed on these models both theoretically and experimentally. In models of extra dimensions, the internal consistency of the theories at high energies are investigated via perturbative unitarity bounds. Similarly it is shown that recent models of Higgs inflation suffer from a breakdown of perturbative unitarity during the inflationary period. In addition, the thesis uses the latest LHC data to derive the first ever experimental bound on the size of the Higgs boson's non-minimal coupling to gravity.

This book investigates the stability and vibrations of conductive, perfectly conductive and superconductive thin bodies in electromagnetic fields. It introduces the main principles and derives basic equations and relations describing interconnected mechanical and electromagnetic processes in deformable electro conductive bodies placed in an external inhomogeneous magnetic field and under the influence of various types of force interactions. Basic equations and relations are addressed in the nonlinear formulation and special emphasis is placed on the mechanical interactions of superconducting thin-body plates with magnetic fields.

"The mathematical investigations referred to bring the whole apparatus of a great science to the examination of the properties of a given mechanism, and have accumulated in this direction rich material, of enduring and increasing value. What is left unexamined is however the other, immensely deeper part of the problem, the question: How did the mechanism, or the elements of which it is composed, originate? What laws govern its building up? Is it indeed formed according to any laws whatever? Or have we simply to accept as data what invention gives us, the analysis of what is thus obtained being the only scientific problem left - as in the case of natural history?" Reuleaux, F., Theoretische Kinematik, Braunschweig: Vieweg, 1875 Reuleaux, F., The Kinematics of Machinery, London: Macmillan, 1876 and New York: Dover, 1963 (translated by A.B.W. Kennedy) This book represents the second part of a larger work dedicated to the structural synthesis of parallel robots. Part 1 already published in 2008 (Gogu 2008a) has presented the methodology proposed for structural synthesis. This book focuses on various topologies of translational parallel robots systematically generated by using the structural synthesis approach proposed in Part 1. The originality of this work resides in the fact that it combines the new formulae for mobility connectivity, redundancy and overconstraints, and the evolutionary morphology in a unified approach of structural synthesis giving interesting innovative solutions for parallel mechanisms.

Developed for the new International A Level specification, these new resources are specifically designed for international students, with a strong focus on progression, recognition and transferable skills, allowing learning in a local context to a global standard. Recognised by universities worldwide and fully comparable to UK reformed GCE A levels. Supports a modular approach, in line with the specification. Appropriate international content puts learning in a real-world context, to a global standard, making it engaging and relevant for all learners. Reviewed by a language specialist to ensure materials are written in a clear and accessible style. The embedded transferable skills, needed for progression to higher education and employment, are signposted so students understand what skills they are developing and therefore go on to use these skills more effectively in the future. Exam practice provides opportunities to assess understanding and progress, so students can make the best progress they can.