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.

Why does a piano sound like a piano? A similar question can be asked of virtually all musical instruments. A particular note - such as middle C - can be produced by a piano, a violin, a clarinet, and many other instruments, yet it is easy for even a musically untrained listener to distinguish between these different instruments. A central quest in the study of musical instruments is to understand why the sound of the "same" note depends greatly on the instrument, and to elucidate which aspects of an instrument are most critical in producing the musical tones characteristic of the instrument. The primary goal of Physics of the Piano is to investigate these questions for the piano. The explanations in this book use a minimum of mathematics, and are intended for anyone who is interested in music and musical instruments. At the same time, there are many insights relating physics and the piano that will likely be interesting and perhaps surprising for many physicists.

This is a unique book on the mathematics of signals written for hearing-science researchers. Designed to follow an introductory text on psychoacoustic, Signals, Sound, and Sensation takes the reader through the mathematics of signal processing from its beginnings in the Fourier transform to advanced topics in modulation, dispersion relations, minimum phase systems, sampled data, and nonlinear distortion. While the book is organized like an introductory engineering text on signals, the examples and exercises come from research on the perception of sound. A unique feature of the book is the consistent application of the Fourier transform, which unifies topics as diverse as cochlear filtering and digital recording. More than 250 exercises are included. Many of them are devoted to practical research in perception, while others explore surprising auditory illusions generated by special signals. A working knowledge of elementary calculus is the only prerequisite. Signals, Sound, and Sensation will help readers acquire the quantitative skills they need to solve signal problems that arise in their everyday work. Periodic signals, aperiodic signals, and noise - along with their linear and nonlinear transformations - are covered in detail. More advanced mathematical topics are treated in the appendices. In no other book are signal mathematics and psychoacoustics so neatly intertwined. Researchers and advanced students in the psychology of auditory perception will find this book indispensable.

Norton's Complex Variables for Scientists and Engineers is a new textbook, originally written for the Complex Analysis term of an undergraduate Mathematical Methods of Physics sequence at UCLA. It does not assume any prior knowledge of complex numbers or functions and is therefore suitable for a first course in the subject for undergraduate students who have had an introductory course in the standard calculus of real variables.
The book provides a thorough grounding in the theory of complex functions. The mathematics is careful, yet accessible to any student who knows basic calculus. It covers the subjects essential in any scientific or engineering discipline that uses mathematics beyond the elementary level. The reader will find a clear presentation of complex differentiation and integration, Cauchy's theorem and integral formula, and infinite series and products. There is a long and thorough section on applying the residue theorem to the evaluation of real integrals, and a section on special functions and their integral representations. The book includes the conformal property of analytic functions and its applications to boundary value problems in electrostatics; a topological analysis that leads to the extension of the residue theorem to multiply-connected regions and contours; a section on the method of steepest descent; a section on the Riemann zeta function; and a discussion of the convergence of integral representations, which is rarely presented in detail in introductory texts. Those who want to see the mathematics done carefully, and who are looking for more than a 'cook-book' treatment that presents the basic techniques without exploring all the nooks and crannies of the subject, will find these sections especially satisfying. The preface suggests how to extract a bare-bones course for those in a hurry, without losing sight of the beauty and depth of the subjects.

Energy is at the heart of physics (and of huge importance to society) and yet no book exists specifically to explain it, and in simple terms. In tracking the history of energy, this book is filled with the thrill of the chase, the mystery of smoke and mirrors, and presents a fascinating human-interest story. Following the history provides a crucial aid to understanding: this book explains the intellectual revolutions required to comprehend energy, revolutions as profound as those stemming from Relativity and Quantum Theory. Texts by Descartes, Leibniz, Bernoulli, d'Alembert, Lagrange, Hamilton, Boltzmann, Clausius, Carnot and others are made accessible, and the engines of Watt and Joule are explained.
Many fascinating questions are covered, including:
- Why just kinetic and potential energies - is one more fundamental than the other?
- What are heat, temperature and action?
- What is the Hamiltonian?
- What have engines to do with physics?
- Why did the steam-engine evolve only in England?
- Why S=klogW works and why temperature is IT.
Using only a minimum of mathematics, this book explains the emergence of the modern concept of energy, in all its forms: Hamilton's mechanics and how it shaped twentieth-century physics, and the meaning of kinetic energy, potential energy, temperature, action, and entropy. It is as much an explanation of fundamental physics as a history of the fascinating discoveries that lie behind our knowledge today.

The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.

This book provides a comprehensive overview of statistical descriptions of turbulent flows. Its main objectives are to point out why ordinary perturbative treatments of the Navier-Stokes equation have been rather futile, and to present recent advances in non-perturbative treatments, e.g., the instanton method and a stochastic interpretation of turbulent energy transfer. After a brief introduction to the basic equations of turbulent fluid motion, the book outlines a probabilistic treatment of the Navier-Stokes equation and chiefly focuses on the emergence of a multi-point hierarchy and the notion of the closure problem of turbulence. Furthermore, empirically observed multiscaling features and their impact on possible closure methods are discussed, and each is put into the context of its original field of use, e.g., the renormalization group method is addressed in relation to the theory of critical phenomena. The intended readership consists of physicists and engineers who want to get acquainted with the prevalent concepts and methods in this research area.

We experience elasticity everywhere in daily life: in the straightening or curling of hairs, the irreversible deformations of car bodies after a crash, or the bouncing of elastic balls in ping-pong or soccer. The theory of elasticity is essential to the recent developments of applied and fundamental science, such as the bio-mechanics of DNA filaments and other macro-molecules, and the animation of virtual characters in computer graphics and materials science. In this book, the emphasis is on the elasticity of thin bodies (plates, shells, rods) in connection with geometry. It covers such topics as the mechanics of hairs (curled and straight), the buckling instabilities of stressed plates, including folds and conical points appearing at larger stresses, the geometric rigidity of elastic shells, and the delamination of thin compressed films. It applies general methods of classical analysis, including advanced nonlinear aspects (bifurcation theory, boundary layer analysis), to derive detailed, fully explicit solutions to specific problems. These theoretical concepts are discussed in connection with experiments. The book is self-contained. Mathematical prerequisites are vector analysis and differential equations. The book can serve as a concrete introduction to nonlinear methods in analysis.

This book presents the proceedings of the 46th National Symposium on Acoustics (NSA 2017). The main goal of this symposium is to discuss key opportunities and challenges in acoustics, especially as applied to engineering problems. The book covers topics ranging from hydro-acoustics, environmental acoustics, bio-acoustics to musical acoustics, electro-acoustics and sound perception. The contents of this volume will prove useful to researchers and practicing engineers working on acoustics problems.

Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation and rotation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used obtain and analyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and to study the effects of changing parameters.
The book will be useful to students and lecturers in undergraduate and graduate courses on classical mechanics, and students and lecturers in courses in computational physics.

The field of Digital Signal Processing has developed so fast in the last two decades that it can be found in the graduate and undergraduate programs of most universities. This development is related to the growing available techno logies for implementing digital signal processing algorithms. The tremendous growth of development in the digital signal processing area has turned some of its specialized areas into fields themselves. If accurate information of the signals to be processed is available, the designer can easily choose the most appropriate algorithm to process the signal. When dealing with signals whose statistical properties are unknown, fixed algorithms do not process these signals efficiently. The solution is to use an adaptive filter that automatically changes its characteristics by optimizing the internal parameters. The adaptive filtering algorithms are essential in many statistical signal processing applications. Although the field of adaptive signal processing has been subject of research for over three decades, it was in the eighties that a major growth occurred in research and applications. Two main reasons can be credited to this growth, the availability of implementation tools and the appearance of early textbooks exposing the subject in an organized form. Presently, there is still a lot of activities going on in the area of adaptive filtering. In spite of that, the theor etical development in the linear-adaptive-filtering area reached a maturity that justifies a text treating the various methods in a unified way, emphasizing the algorithms that work well in practical implementation."

This book uses a novel concept to teach the finite element method, applying it to solid mechanics. This major conceptual shift takes away lengthy theoretical derivations in the face-to-face interactions with students and focuses on the summary of key equations and concepts; and to practice these on well-chosen example problems. For this new, 2nd edition, many examples and design modifications have been added, so that the learning-by-doing features of this book make it easier to understand the concepts and put them into practice. The theoretical derivations are provided as additional reading and students must study and review the derivations in a self-study approach. The book provides the theoretical foundations to solve a comprehensive design project in tensile testing. A classical clip-on extensometer serves as the demonstrator on which to apply the provided concepts. The major goal is to derive the calibration curve based on different approaches, i.e., analytical mechanics and based on the finite element method, and to consider further design questions such as technical drawings, manufacturing, and cost assessment. Working with two concepts, i.e., analytical and computational mechanics strengthens the vertical integration of knowledge and allows the student to compare and understand the different concepts, as well as highlighting the essential need for benchmarking any numerical result.

This book covers the author's research achievements and the latest advances in high-speed pneumatic control theory and applied technologies. It presents the basic theory and highlights pioneering technologies resulting from research and development efforts in aerospace, aviation and other major equipment, including: pneumatic servo control theory, pneumatic nonlinear mechanisms, aerothermodynamics, pneumatic servo mechanisms, and high-speed pneumatic control theory.

Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, in the formalism of Minkowski's four-dimensional space-time, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein field equation, as well as many modern cosmological subjects, from primordial inflation and cosmic microwave anisotropy to the dark energy that propels an accelerating universe.
The author presents the subject with an emphasis on physical examples and simple applications without the full tensor apparatus. The reader first learns how to describe curved spacetime. At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, precession of Mercury's perihelion, black holes, and cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Many modern topics in cosmology are discussed in this book: from inflation, cosmic microwave anisotropy to the "dark energy" that propels an accelerating universe.
Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity and cosmology on their own.

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.

This book presents collaborative research presented by experts in the field of nonlinear science provides the reader with contemporary, cutting-edge, research works that bridge the gap between theory and device realizations of nonlinear phenomena. The conference provides a unique forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: chaos gates, social networks, communication, sensors, lasers, molecular motors, biomedical anomalies, and stochastic resonance. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2018) held in Maui, Hawaii, 2018. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.

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 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

Generalized dynamic thermoelasticity is a vital area of research in continuum mechanics, free of the classical paradox of infinite propagation speeds of thermal signals in Fourier-type heat conduction. Besides that paradox, the classical dynamic thermoelasticity theory offers either unsatisfactory or poor descriptions of a solid's response at low temperatures or to a fast transient loading (say, due to short laser pulses). Several models have been developed and intensively studied over the past four decades, yet this book, which aims to provide a point of reference in the field, is the first monograph on the subject since the 1970s.
Thermoelasticity with Finite Wave Speeds focuses on dynamic thermoelasticity governed by hyperbolic equations, and, in particular, on the two leading theories: that of Lord-Shulman (with one relaxation time), and that of Green-Lindsay (with two relaxation times). While the resulting field equations are linear partial differential ones, the complexity of the theories is due to the coupling of mechanical with thermal fields. The mathematical aspects of both theories - existence and uniqueness theorems, domain of influence theorems, convolutional variational principles - as well as with the methods for various initial/boundary value problems are explained and illustrated in detail and several applications of generalized thermoelasticity are reviewed.

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 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.

Acoustic microscopy enables the elastic properties of materials to be imaged and measured with the resolution of a good microscope. By using frequencies in the microwave regime, it is possible to make the acoustic wavelength comparable with the wavelength of light, and hence to achieve a resolution comparable with an optical microscope. Solids can support both longitudinal and transverse acoustic waves. At surfaces a unique combination of the two known as Raleigh waves can propagate, and in many circumstances these dominate the contrast in acoustic microscopy. Following the invention of scanning probe microscopes, it is now possible to use an atomic force microscope to detect the acoustic vibration of a surface with resolution in the nanometre range, thus beating the diffraction limit by operating in the extreme near-field. This second edition of Acoustic Microscopy has a major new chapter on the technique and applications of acoustically excited probe microscopy.

Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general. They provide a unifying framework for many seemingly disparate physical systems, such as n-particle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems.
Geometric Mechanics and Symmetry is a friendly and fast-paced introduction to the geometric approach to classical mechanics, suitable for a one- or two- semester course for beginning graduate students or advanced undergraduates. It fills a gap between traditional classical mechanics texts and advanced modern mathematical treatments of the subject. After a summary of the necessary elements of calculus on smooth manifolds and basic Lie group theory, the main body of the text considers how symmetry reduction of Hamilton's principle allows one to derive and analyze the Euler-Poincare equations for dynamics on Lie groups.
Additional topics deal with rigid and pseudo-rigid bodies, the heavy top, shallow water waves, geophysical fluid dynamics and computational anatomy. The text ends with a discussion of the semidirect-product Euler-Poincare reduction theorem for ideal fluid dynamics.
A variety of examples and figures illustrate the material, while the many exercises, both solved and unsolved, make the book a valuable class text."

This new edition has been thoroughly revised, expanded and contain some updates function of the novel results and shift of scientific interest in the topics. The book has a Foreword by Jerry L. Bona and Hongqiu Chen. The book is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. This book is intended for graduate students and researchers in mathematics, physics and engineering.