Electromagnetic Properties of Multiphase Dielectrics

Electromagnetic Properties of Multiphase Dielectrics

Recently, several applications, primarily driven by microtechnology, have emerged where the use of materials with tailored electromagnetic (dielectric) properties are necessary for a successful overall design. The “tailored” aggregate properties are achieved by combining an easily moldable base matrix with particles having dielectric properties that are chosen to deliver (desired) effective properties. In many cases, the analysis of such materials requires the simulation of the macroscopic and microscopic electromagnetic response, as well as its resulting coupled thermal response, which can be important to determine possible failures in “hot spots.” This necessitates a stress analysis. Furthermore, because, oftentimes, such processes initiate degratory chemical processes, it can be necessary to also include models for these processes as well. A central objective of this work is to provide basic models and numerical solution strategies to analyze the coupled response of such materials by direct simulation using standard laptop/desktop equipment. Accordingly, this monograph covers: (1) The foundations of Maxwell’s equations, (2) Basic homogenization theory,(3) Coupled systems (electromagnetic, thermal, mechanical and chemical),(4) Numerical methods and(5) An introduction to select biological problems.The text can be viewed as a research monograph suitable for use in an upper-division undergraduate or first year graduate course geared towards students in the applied sciences, mechanics and mathematics that have an interest in the analysis of particulate materials.

Electromagnetic Properties of Multiphase Dielectrics

Mathematics and Art

Mathematics and Art

Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work. This book emphasizes and renews the deep relation between Mathematics and Art. The Forum Discussion suggests to develop a deeper interpenetration between these two cultural fields, notably in the teaching of both Mathematics and Art.

Mathematics and Art

Linear Algebra

Linear Algebra

Every student of mathematics needs a sound grounding in the techniques of linear algebra. It forms the basis of the study of linear equations, matrices, linear mappings, and differential equations, and comprises a central part of any course in mathematics. This textbook provides a rigorous introduction to the main concepts of linear algebra which will be suitable for all students coming to the subject for the first time. The book is in two parts: Part One develops the basic theory of vector spaces and linear maps, including dimension, determinants, and eigenvalues and eigenvectors. Part Two goes on to develop more advanced topics and in particular the study of canonical forms for matrices. Professor Berberian is at pains to explain all the ideas underlying the proofs of results as well as to give numerous examples and applications. There is an abundant supply of exercises to reinforce the reader’s grasp of the material and to elaborate on ideas from the text. As a result, this book presents a well-rounded and mathematically sound first course in linear algebra.

Linear Algebra

Maple By Example

Maple By Example

Maple by Example, Third Edition, is a reference/text with CD for beginning and experienced students, professional engineers, and other Maple users. This new edition has been updated to be compatible with the most recent release of the Maple software. Coverage includes built-in Maple commands used in courses and practices that involve calculus, linear algebra, business mathematics, ordinary and partial differential equations, numerical methods, graphics and more. The CD-ROM provides updated Maple input and all text from the book.

Maple By Example

An Introduction to Stochastic Differential Equations

An Introduction to Stochastic Differential Equations

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An Introduction to Stochastic Differential Equations

Constitutive Relations under Impact Loadings

Constitutive Relations under Impact Loadings

The book describes behavior of materials (ductile, brittle and composites) under impact loadings and high strain rates. The three aspects: experimental, theoretical and numerical are in the focus of interest. Hopkinson bars are mainly used as experimental devices to describe dynamic behavior of materials. The precise description of experimental techniques and interpretation of wave interaction are carefully discussed. Theoretical background refers to rate dependent thermo viscoplastic formulation. This includes the discussion of well posedness of initial boundary value problems and the solution of the system of governing equations using numerical methods. Explicit time integration is used in computations to solve dynamic problems. In addition, many applications in aeronautic and automotive industries are exposed.

Constitutive Relations under Impact Loadings

Non-fickian Solute Transport in Porous Media

Non-fickian Solute Transport in Porous Media

The advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick s law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.

Non-fickian Solute Transport in Porous Media

Cosmic Update

Cosmic Update

‘…The Multiversal book series is equally unique, providing book-length extensions of the lectures with enough additional depth for those who truly want to explore these fields, while also providing the kind of clarity that is appropriate for interested lay people to grasp the general principles involved.’ – Lawrence M. KraussCosmic Update Covers:A novel approach to uncover the dark faces of the Standard Model of cosmology.The possibility that Dark Energy and Dark Matter are manifestations of the inhomogeneous geometry of our Universe.On the history of cosmological model building and the general architecture of cosmological modes.Illustrations on the Large Scale Structure of the Universe.A new perspective on the classical static Einstein Cosmos.Global properties of World Models including their Topology.The Arrow of Time in a Universe with a Positive Cosmological Constant.Exploring the consequences of a fundamental Cosmological Constant for our Universe. Exploring why the current observed acceleration of the Universe may not be its final destiny.Demonstrating that nature forbids the existence of a pure Cosmological Constant.Our current understanding of the long term (in time scales that greatly exceed the current age of the Universe) future of the Universe.The long term fate and eventual destruction of the astrophysical objects that populate the universe — including clusters, galaxies, stars, planets, and black holes. The material is presented in a layperson-friendly language followed by addition technical sections that explain the basic equations and principles. This feature is very attractive to readers who want to learn more about the theories involved beyond the basic description. ‘Multiversal Journeys is a trademark of Farzad Nekoogar and Multiversal Journeys, a 501 (c) (3) nonprofit organization.’

Cosmic Update

Chaos

Chaos

This eleventh volume in the Poincar Seminar Series presents an interdisciplinary perspective on the concept of Time, which poses some of the most challenging questions in science. Five articles, written by the Fields medalist C. Villani, the two outstanding theoretical physicists T. Damour and C. Jarzynski, the leading experimentalist C. Salomon, and the famous philosopher of science H. Price, describe recent developments related to the mathematical, physical, experimental, and philosophical facets of this fascinating concept. These articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a description of the manifold fundamental physical issues in play with time, in particular with the changes of perspective implied by Special and General Relativity; a mathematically precise discussion of irreversibility and entropy in the context of Boltzmann’s and Vlasov’s equations; a thorough survey of the recently developed thermodynamics at the nanoscale, the scale most relevant to biological physics; a description of the new cold atom space clock PHARAO to be installed in 2015 onboard the International Space Station, which will allow a test of Einstein’s gravitational shift with a record precision of 2 10-6, and enable a test of the stability over time of the fundamental constants of physics, an issue first raised by Dirac in 1937; and last, but not least, a logical and clarifying philosophical discussion of Time’s arrow, a phrase first coined by Eddington in 1928 in a challenge to physics to resolve the puzzle of the time-asymmetry of our universe, and echoed here in a short pome en prose by C. de Mitry. This book should be of broad general interest to physicists, mathematicians, and philosophers.

Chaos

FEFLOW

FEFLOW

FEFLOW is an acronym of Finite Element subsurface FLOW simulation system and solves the governing flow, mass and heat transport equations in porous and fractured media by a multidimensional finite element method for complex geometric and parametric situations including variable fluid density, variable saturation, free surface(s), multispecies reaction kinetics, non-isothermal flow and multidiffusive effects. FEFLOW comprises theoretical work, modeling experiences and simulation practice from a period of about 40 years. In this light, the main objective of the present book is to share this achieved level of modeling with all required details of the physical and numerical background with the reader. The book is intended to put advanced theoretical and numerical methods into the hands of modeling practitioners and scientists. It starts with a more general theory for all relevant flow and transport phenomena on the basis of the continuum approach, systematically develops the basic framework for important classes of problems (e.g., multiphase/multispecies non-isothermal flow and transport phenomena, discrete features, aquifer-averaged equations, geothermal processes), introduces finite-element techniques for solving the basic balance equations, in detail discusses advanced numerical algorithms for the resulting nonlinear and linear problems and completes with a number of benchmarks, applications and exercises to illustrate the different types of problems and ways to tackle them successfully (e.g., flow and seepage problems, unsaturated-saturated flow, advective-diffusion transport, saltwater intrusion, geothermal and thermohaline flow).

FEFLOW

Vortex, Molecular Spin and Nanovorticity

Vortex, Molecular Spin and Nanovorticity

The subject of this book is the physics of vortices. A detailed analysis of the dynamics of vortices will be presented. The important topics of vorticity and molecular spin will be dealt with, including the electromagnetic analogy and quantization in superfluids. The effect of molecular spin on the dynamics of molecular nano-confined fluids using the extended Navier-Stokes equations will also be covered especially important to the theory and applicability of nanofluidics and associated devices. The nanoscale boundary layer and nanoscale vortex core are regions of intense vorticity (molecular spin). It will be shown, based on molecular kinetic theory and thermodynamics, that the macroscopic (solid body) rotation must be accompanied by internal rotation of the molecules. Electric polarization of the internal molecular rotations about the local rotation axis the Barnett effect occurs. In such a spin aligned system, major changes in the physical properties of the fluid result.

Vortex, Molecular Spin and Nanovorticity

Boundary Value Problems

Boundary Value Problems

Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables.

Boundary Value Problems

Langes Handbook of Chemistry - 15th Edition

Langes Handbook of Chemistry - 15th Edition

A standard reference for chemists for 70 years, this new Sixteenth Edition features an enormous compilation of facts, data, tabular material, and experimental findings in every area of chemistry.Included in this massive compendium are listings of the properties of approximately 4,400 organic and 1,400 inorganic compounds. This Sixteenth Edition offers 40% new or extensively revised content and starting with this edition, the author includes equations that allow users to calculate important values such as temperature and pressure.

Langes Handbook of Chemistry - 15th Edition

A First Course in Differential Equations with Modeling Applications

A First Course in Differential Equations with Modeling Applications

A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 10th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, Remarks boxes, definitions, and group projects. Written in a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

A First Course in Differential Equations with Modeling Applications

A Systems Description of Flow Through Porous Media

A Systems Description of Flow Through Porous Media

This text forms part of material taught during a course in advanced reservoir simulation at Delft University of Technology over the past 10 years. The contents have also been presented at various short courses for industrial and academic researchers interested in background knowledge needed to perform research in the area of closed-loop reservoir management, also known as smart fields, related to e.g. model-based production optimization, data assimilation (or history matching), model reduction, or upscaling techniques. Each of these topics has connections to system-theoretical concepts. The introductory part of the course, i.e. the systems description of flow through porous media, forms the topic of this brief monograph. The main objective is to present the classic reservoir simulation equations in a notation that facilitates the use of concepts from the systems-and-control literature. Although the theory is limited to the relatively simple situation of horizontal two-phase (oil-water) flow, it covers several typical aspects of porous-media flow. The first chapter gives a brief review of the basic equations to represent single-phase and two-phase flow. It discusses the governing partial-differential equations, their physical interpretation, spatial discretization with finite differences, and the treatment of wells. It contains well-known theory and is primarily meant to form a basis for the next chapter where the equations will be reformulated in terms of systems-and-control notation.

A Systems Description of Flow Through Porous Media

Numerical Methods for Controlled Stochastic Delay Systems

Numerical Methods for Controlled Stochastic Delay Systems

The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. Because such problems are infinite-dimensional, many new issues arise in getting good numerical approximations and in the convergence proofs. Useful forms of numerical algorithms and system approximations are developed in this work, and the convergence proofs are given. All of the usual cost functions are treated as well as singular and impulsive controls. A major concern is on representations and approximations that use minimal memory. Featuring numerical algorithms and examples with applications to control and modern communications systems, this book is the first on the subject and will be of great interest to all those who work with stochastic delay equations and whose main interest is in either the use of the algorithms or in the underlying mathematics. An excellent resource for graduate students, researchers, and practitioners, the work may be used as a graduate-level textbook for a special topics course or seminar on numerical methods in stochastic control.

Numerical Methods for Controlled Stochastic Delay Systems

Mathematica in Action - Third edition

Mathematica in Action - Third edition

With the third edition of his popular Mathematica in Action, award-winning author Stan Wagon guides readers through the important changes that have been made to Mathematica 6.0. To utilize the more sophisticated graphics capabilities of 6.0, Wagon has significantly expanded the chapters on surfaces and the parametric plotting of surfaces. The chapter on differential equations now includes material from VisualDSolve , built into Mathematica 6.0. Like previous editions, this is not only an introduction to Mathematica 6.0, but also a tour of modern mathematics by one of the fields most gifted expositors. Wagon explores some of the most important areas of modern mathematics with new chapters on optimization, including algebraic and numerical optimization, and linear and integer programming. Connections are also made to computer science with new material on graphs and networks. Wagon is the author of nine books on mathematics, including A Course in Computational Number Theory , named one of the ten best math books of 2000 by the American Library Association. He has written extensively on the educational applications of Mathematica, inlcuding the books VisualDSolve: Visualizing Differential Equations with Mathematica, and Animating Calculus: Mathematica Notebooks for the Laboratory. From Reviews of the Second Edition: ‘The bottom line is that is an outstanding book containing many examples of real uses of Mathematica for the novice, intermediate, and expert user.’ Mark McClure, Mathematica in Education and Research Journal ‘In a dazzling range of examples Stan Wagon shows how such features as animation, 3-dimensional graphics and high-precision integer arithmetic can contribute to our understanding and enjoyment of mathematics.’ Richard Walker, The Mathematical Gazette

Mathematica in Action - Third edition

Semigroups of Linear Operators and Applications to Partial Differential Equations

Semigroups of Linear Operators and Applications to Partial Differential Equations

Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Semigroups of Linear Operators and Applications to Partial Differential Equations

Free Convection Film Flows and Heat Transfer - Second Edition

Free Convection Film Flows and Heat Transfer - Second Edition

This book presents recent developments in our systematic studies of hydrodynamics and heat and mass transfer in laminar free convection, accelerating film boiling and condensation of Newtonian fluids, as well as accelerating film flow of non-Newtonian power-law fluids (FFNF). These new developments provided in this book are (i) novel system of analysis models based on the developed New Similarity Analysis Method; (ii) a system of advanced methods for treatment of gas temperature- dependent physical properties, and liquid temperature- dependent physical properties; (iii) the organically combined models of the governing mathematical models with those on treatment model of variable physical properties; (iv) rigorous approach of overcoming a challenge on accurate solution of three-point boundary value problem related to two-phase film boiling and condensation; and (v) A pseudo-similarity method of dealing with thermal boundary layer of FFNF for greatly simplifies the heat-transfer analysis and numerical calculation. A system of practical application equations on heat and mass transfer are provided in each chapter, which are formulated based on the rigorous numerical solutions with consideration of variable physical properties. In addition, in the second edition, other new research developments are further included on resolving an even big challenge associated with investigations of laminar free film condensation of vapour-gas mixture. They involve the novel methods for treatment of concentration- and temperature- dependent physical properties of vapour-gas mixture, and for rigorous solution of interfacial vapour saturation temperature, which have lead to rigorous analysis and calculation results on two-phase film flow velocity, temperature, and concentration fields, as well as condensate heat and mass transfer.

Free Convection Film Flows and Heat Transfer - Second Edition

Truly Nonlinear Oscillations

Truly Nonlinear Oscillations

This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of truly nonlinear (TNL) oscillator equations. The volume gives a general overview of the author’s work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a dire.

Truly Nonlinear Oscillations