The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering. Science evolves, and this means that the problems of current interest continually change. What does not change as quickly is the approach used to derive the relevant mathematical models, and the methods used to analyze the models. Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of a specific application. This does not mean applications are not considered, they are, and connections with experiment are a staple of this book. The book, as well as the individual chapters, is written in such a way that the material becomes more sophisticated as you progress. This provides some flexibility in how the book is used, allowing consideration for the breadth and depth of the material covered. Moreover, there are a wide spectrum of exercises and detailed illustrations that significantly enrich the material. Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful. The material, and topics, have been updated to include recent developments in mathematical modeling. The exercises have also been expanded to include these changes, as well as enhance those from the first edition. Review of first edition: "The goal of this book is to introduce the mathematical tools needed for analyzing and deriving mathematical models. ... Holmes is able to integrate the theory with application in a very nice way providing an excellent book on applied mathematics. ... One of the best features of the book is the abundant number of exercises found at the end of each chapter. ... I think this is a great book, and I recommend it for scholarly purposes by students, teachers, and researchers." Joe Latulippe, The Mathematical Association of America, December, 2009

Energy storage devices are a crucial area of research and development across many engineering disciplines and industries. While batteries provide the significant advantage of high energy density, their limited life cycles, disposal challenges and charge and discharge management constraints undercut their effectiveness in certain applications. Compared to electrochemical cells, supercapacitors are charge-storage devices with much longer life cycles, yet they have traditionally been hobbled by limited DC voltage capabilities and energy density. However, recent advances are improving these issues.

This book provides the opportunity to expand your knowledge of innovative supercapacitor applications, comparing them to other commonly used energy storage devices. It will strengthen your understanding of energy storage from a practical, applications-based point-of-view, without requiring detailed examination of underlying electrochemical equations. No matter what your field, you will find inspiration and guidance in the cutting-edge advances in energy storage devices in this book.
Provides explanations of the latest energy storage devices in a practical applications-based context Includes examples of circuit designs that optimize the use of supercapacitors, and pathways to improve existing designs by effectively managing energy storage devices crucial to both low and high power applications.Covers batteries, BMS (battery management systems) and cutting-edge advances in supercapacitors, providing a unique compare and contrast examination demonstrating applications where each technology can offer unique benefits

Many open questions in Theoretical Physics pertain to strongly interacting quantum systems such as the quark-gluon plasma (QGP) produced in heavy-ion collisions or the strange-metal phase observed in many high-temperature superconductors. These systems are notoriously difficult to study using traditional methods such as perturbation theory, but the gauge/gravity duality offers a successful alternative approach, which maps strongly interacting quantum gauge theories to computationally tractable, classical gravity theories. This book begins with a pedagogical introduction to how the duality can be used to extract transport properties of quantum systems from their gravity dual. It then presents new results on hydrodynamic transport in strongly interacting quantum fluids, providing strong evidence that the Haack-Yarom identity between second-order transport coefficients holds for all fluids with a classical gravity dual and may be a universal feature of all strongly coupled quantum fluids such as the QGP. Newly derived Kubo formulae, expressing transport coefficients in terms of quantum correlators, hold independently of the duality. Lastly, the book discusses new results on magnetic impurities in strongly correlated metals, including the first dual gravity description of an inter-impurity coupling, crucial for the quantum criticality underlying the strange-metal phase.

In its fifth extended edition the successful monograph package "Multiphase Flow Dynamics" contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present first volume the local volume and time averaging is used to derive a complete set of conservation equations for three fluids each of them having multi components as constituents. Large parts of the book are devoted on the design of successful numerical methods for solving the obtained system of partial differential equations. Finally the analysis is repeated for boundary fitted curvilinear coordinate systems designing methods applicable for interconnected multi-blocks. This fifth edition includes various updates, extensions, improvements and corrections, as well as a completely new chapter containing the basic physics describing the multi-phase flow in turbines, compressors, pumps and other rotating hydraulic machines.

Advances in Energy, Environment and Chemical Engineering collects papers resulting from the conference on Energy, Environment and Chemical Engineering (AEECE 2022), Dali, China, 24-26 June, 2022. The primary goal is to promote research and developmental activities in energy technology, environment engineering and chemical engineering. Moreover, it aims to promote scientific information interchange between scholars from the top universities, business associations, research centers and high-tech enterprises working all around the world. The conference conducts in-depth exchanges and discussions on relevant topics such as energy engineering, environment technology and advanced chemical technology, aiming to provide an academic and technical communication platform for scholars and engineers engaged in scientific research and engineering practice in the field of saving technologies, environmental chemistry, clean production and so on. By sharing the research status of scientific research achievements and cutting-edge technologies, it helps scholars and engineers all over the world comprehend the academic development trend and broaden research ideas. So as to strengthen international academic research, academic topics exchange and discussion, and promote the industrialization cooperation of academic achievements.

Some extremum and unilateral boundary value problems in viscous hydrodynamics.- On axisymmetric motion of the fluid with a free surface.- On the occurrence of singularities in axisymmetrical problems of hele-shaw type.- New asymptotic method for solving of mixed boundary value problems.- Some results on the thermistor problem.- New applications of energy methods to parabolic and elliptic free boundary problems.- A localized finite element method for nonlinear water wave problems.- Approximate method of investigation of normal oscillations of viscous incompressible liquid in container.- The classical Stefan problem as the limit case of the Stefan problem with a kinetic condition at the free boundary.- A mathematical model of oscillations energy dissipation of viscous liquid in a tank.- Existence of the classical solution of a two-phase multidimensional Stefan problem on any finite time interval.- Asymptotic theory of propagation of nonstationary surface and internal waves over uneven bottom.- Multiparametric problems of two-dimensional free boundary seepage.- Nonisothermal two-phase filtration in porous media.- Explicit solution of time-dependent free boundary problems.- Nonequilibrium phase transitions in frozen grounds.- System of variational inequalities arising in nonlinear diffusion with phase change.- Contact viscoelastoplastic problem for a beam.- Application of a finite-element method to two-dimensional contact problems.- Computations of a gas bubble motion in liquid.- Waves on the liquid-gas free surface in the presence of the acoustic field in gas.- Smooth bore in a two-layer fluid.- Numerical calculation of movable free and contact boundaries in problems of dynamic deformation of viscoelastic bodies.- On the canonical variables for two-dimensional vortex hydrodynamics of incompressible fluid.- About the method with regularization for solving the contact problem in elasticity.- Space evolution of tornado-like vortex core.- Optimal shape design for parabolic system and two-phase Stefan problem.- Incompressible fluid flows with free boundary and the methods for their research.- On the Stefan problems for the system of equations arising in the modelling of liquid-phase epitaxy processes.- Stefan problem with surface tension as a limit of the phase field model.- The modelization of transformation phase via the resolution of an inclusion problem with moving boundary.- To the problem of constructing weak solutions in dynamic elastoplasticity.- The justification of the conjugate conditions for the Euler's and Darcy's equations.- On an evolution problem of thermo-capillary convection.- Front tracking methods for one-dimensional moving boundary problems.- On Cauchy problem for long wave equations.- On fixed point (trial) methods for free boundary problems.- Nonlinear theory of dynamics of a viscous fluid with a free boundary in the process of a solid body wetting.

Many diverse materials, from man-made plastics to slurry, behave in ways that cannot be predicted using straightforward 'classical' equations. This book provides a guide, with examples, for those who wish to make predictions about the mechanical and thermal behaviour of non-Newtonian materials in engineering and processing technology. There is an emphasis on the practical solution of problems using computer methods, and on the correlation between theory and experimental work.

This textbook provides a detailed introduction to the use of software in combination with simple and economical hardware (a sound level meter with calibrated AC output and a digital recording system) to obtain sophisticated measurements usually requiring expensive equipment. It emphasizes the use of free, open source, and multiplatform software. Many commercial acoustical measurement systems use software algorithms as an integral component; however the methods are not disclosed. This book enables the reader to develop useful algorithms and provides insight into the use of digital audio editing tools to document features in the signal. Topics covered include acoustical measurement principles, in-depth critical study of uncertainty applied to acoustical measurements, digital signal processing from the basics, and metrologically-oriented spectral and statistical analysis of signals. The student will gain a deep understanding of the use of software for measurement purposes; the ability to implement software-based measurement systems; familiarity with the hardware necessary to acquire and store signals; an appreciation for the key issue of long-term preservation of signals; and a full grasp of the often neglected issue of uncertainty in acoustical measurements. Pedagogical features include in-text worked-out examples, end-of-chapter problems, a glossary of metrology terms, and extensive appendices covering statistics, proofs, additional examples, file formats, and underlying theory.

Wave evolution on a falling film is a classical hydrodynamic instability whose rich wave dynamics have been carefully recorded in the last fifty years. Such waves are known to profoundly affect the mass and heat transfer of multi-phase industrial units.

This book describes the collective effort of both authors and their students in constructing a comprehensive theory to describe the complex wave evolution from nearly harmonic waves at the inlet to complex spatio-temporal patterns involving solitary waves downstream. The mathematical theory represents a significant breakthrough from classical linear stability theories, which can only describe the inlet harmonic waves and also extends classical soliton theory for integrable systems to real solitrary wave dynamics with dissipation. One unique feature of falling-film solitary wave dynamics, which drives much of the spatio-temporal wave evolution, is the irreversible coalescence of such localized wave structures. It represents the first full description of a hydrodynamic instability from inception to developed chaos. This approach should prove useful for other complex hydrodynamic instabilities and would allow industrial engineers to better design their multi-phase apparati by exploiting the deciphered wave dynamics. This publication gives a comprehensive review of all experimental records and existing theories and significantly advances state of the art on the subject and are complimented by complex and attractive graphics from computational fluid mechanics.

The principle aim of the book is to present a self-contained, modern account of similarity and symmetry methods, which are important mathematical tools for both physicists, engineers and applied mathematicians. The idea is to provide a balanced presentation of the mathematical techniques and applications of symmetry methods in mathematics, physics and engineering. That is why it includes recent developments and many examples in finding systematically conservation laws, local and nonlocal symmetries for ordinary and partial differential equations. The role of continuous symmetries in classical and quantum field theories is exposed at a technical level accessible even for non specialists. The importance of symmetries in continuum mechanics and mechanics of materials is highlighted through recent developments, such as the construction of constitutive models for various materials combining Lie symmetries with experimental data. As a whole this book is a unique collection of contributions from experts in the field, including specialists in the mathematical treatment of symmetries, researchers using symmetries from a fundamental, applied or numerical viewpoint. The book is a fascinating overview of symmetry methods aimed for graduate students in physics, mathematics and engineering, as well as researchers either willing to enter in the field or to capture recent developments and applications of symmetry methods in different scientific fields.

This book gives you the tools you need to understand and determine changing propagation characteristics found in different physical situations and locations. The book presents a practical digital propagation model based entirely on the physical principles of wave propagation.

Assessing the Energy Efficiency of Pumps and Pump Units, developed in cooperation with Europump, is the first book available providing the background, methodology, and assessment tools for understanding and calculating energy efficiency for pumps and extended products (pumps+motors+drives). Responding to new EU requirements for pump efficiency, and US DOE exploratory work in setting pump energy efficiency guidelines, this book provides explanation, derivation, and illustration of PA and EPA methods for assessing energy efficiency. It surveys legislation related to pump energy efficiencies, provides background on pump and motor efficiencies, and describes the concept of Energy Efficiency Index (EEI) for circulators and single and multi-pump systems.

This new edition includes brand-new developments in the modeling of processes in the column apparatuses. It analyzes the radial velocity component and axial variation in the axial velocity in the column. These models are described in five new chapters. The book presents models of chemical and interphase mass transfer processes in industrial column apparatuses, using convection-diffusion and average-concentration models. It also introduces average concentration models for quantitative analysis, which use the average values of the velocity and concentration over the cross-sectional area of the column. The new models are used to analyze a broad range of processes (simple and complex chemical reactions, physical and chemical absorption, physical and chemical adsorption, catalytic reactions in the cases of physical and chemical adsorption mechanism), and make it possible to model sulfur dioxide gas purification processes.

This book highlights the symmetry properties of acoustic fields and describes the gauge invariance approach, which can be used to reveal those properties. Symmetry is the key theoretical framework of metamaterials, as has been demonstrated by the successful fabrication of acoustical metamaterials. The book first provides the necessary theoretical background, which includes the covariant derivative, the vector potential, and invariance in coordinate transformation. This is followed by descriptions of global gauge invariance (isotropy), and of local gauge invariance (anisotropy). Sections on time reversal symmetry, reflection invariance, and invariance of finite amplitude waves round out the coverage.

This thesis studies the effects of superplasticizers, polyacrylate latexes and asphalt emulsions, which differ in molecular/particle size from nanometers to microns, on the rheological properties of fresh cement pastes (FCPs), as well as the action mechanisms involved. It systematically investigates the rheological properties and microstructure of cement-based materials, and elucidates the adsorption behaviors of polycarboxylate polymers with different functional groups and their effects on cement hydration. Moreover, it reveals how the working mechanism of naphthalene sulfonate formaldehyde (NSF) differs from that of polycarboxylate ether-based (PCE) superplasticizers. Lastly, it develops a conceptual microstructure model and two rheological equations. These findings lend theoretical support to the development of new chemical admixtures and new, higher-performance, cement-based composites.

This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Loewner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive bibliography covering over twelve decades of results and an introduction rich in historical and biographical details complement the eight main chapters of this monograph. Given its systematic and consistent notation and background results, this book provides a self-contained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics.

This book presents an introduction to the classical theories of continuum mechanics; in particular, to the theories of ideal, compressible, and viscous fluids, and to the linear and nonlinear theories of elasticity. These theories are important, not only because they are applicable to a majority of the problems in continuum mechanics arising in practice, but because they form a solid base upon which one can readily construct more complex theories of material behavior. Further, although attention is limited to the classical theories, the treatment is modern with a major emphasis on foundations and structure

This book discusses the thermal-elastic mechanics problems of concrete rectangular thin plate. Using theoretical derivation combined with numerical examples, it explains in detail the analytical solution of the deflection, bending moment, thermal vibration and thermal buckling of concrete rectangular thin plate. To facilitate application, the book also includes deflection and bending moment calculation tables of concrete rectangular thin plate with four edges supported and with free boundary conditions.

The work in this thesis was a part of the experiment of squeezed light injection into the LIGO interferometer. The work first discusses the detailed design of the squeezed light source which would be used for the experiment. The specific design is the doubly-resonant, traveling-wave bow-tie cavity squeezed light source with a new modified coherent sideband locking technique. The thesis describes the properties affecting the squeezing magnitudes and offers solutions which improve the gain. The first part also includes the detailed modeling of the back-scattering noise of a traveling Optical Parametric Oscillator (OPO). In the second part, the thesis discusses the LIGO Squeezed Light Injection Experiment, undertaken to test squeezed light injection into a 4km interferometric gravitational wave detector. The results show the first ever measurement of squeezing enhancement in a full-scale suspended gravitational wave interferometer with Fabry-Perot arms. Further, it showed that the presence of a squeezed-light source added no additional noise in the low frequency band. The result was the best sensitivity achieved by any gravitational wave detector. The thesis is very well organized with the adequate theoretical background including basics of Quantum Optics, Quantum noise pertaining to gravitational wave detectors in various configurations, along with extensive referencing necessary for the experimental set-up. For any non-experimental scientist, this introduction is a very useful and enjoyable reading. The author is the winner of the 2013 GWIC Theses Prize.

The book provides a state-of-art overview of computational methods for nonlinear aeroelasticity and load analysis, focusing on key techniques and fundamental principles for CFD/CSD coupling in temporal domain. CFD/CSD coupling software design and applications of CFD/CSD coupling techniques are discussed in detail as well. It is an essential reference for researchers and students in mechanics and applied mathematics.

This is a guide to the design and application of elliptical dielectric waveguides and fibers. Written by one of the pioneers of optical fiber technology, it shows the theoretical basis of the technology, demonstrates the practical uses for elliptical fibers, guides the reader through design criteria and trade-offs, and gives immediate access to collected data and references on the topic. "Elliptical Fiber Waveguides" begins with an historical overview, and then provides detailed coverage of specific waveguide and fiber modes, including all relevant specifications and data currently available. The book examines the use of elliptical fibers for a wide variety of recent applications, including sensors, rare-earth-doped fiber sources, and amplifiers. With its 278 equations, 161 figures, and nearly 200 references to the literature, "Elliptical Fiber Waveguides" brings together in one source the complete body of information currently available on this promising technology.