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.
Thứ Hai, 2 tháng 3, 2015
Non-fickian Solute Transport in Porous Media
Physics of Societal Issues - Second Edition
This book provides the reader with essential tools needed to analyze complex societal issues and demonstrates the transition from physics to modern-day laws and treaties. This second edition features new equation-oriented material and extensive data sets drawing upon current information from experts in their fields. Problems to challenge the reader and extend discussion are presented on three timely
Thứ Hai, 2 tháng 2, 2015
Mathematical Modeling in Continuum Mechanics
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrdinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
A First Course in Fourier Analysis
This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.
Thứ Hai, 19 tháng 1, 2015
Partial Differential Equation Analysis in Biomedical Engineering
Aimed at graduates and researchers, and requiring only a basic knowledge of multi-variable calculus, this introduction to computer-based partial differential equation (PDE) modeling provides readers with the practical methods necessary to develop and use PDE mathematical models in biomedical engineering. Taking an applied approach, rather than using abstract mathematics, the reader is instructed through six biomedical example applications, each example characterized by step-by-step discussions of established numerical methods and implemented in reliable computer routines. Adopting this technique, the reader will understand how PDE models are formulated, implemented and tested. Supported by a set of rigorously tested general purpose PDE routines online, and with enhanced understanding through animations, this book will be ideal for anyone faced with interpreting large experimental data sets that need to be analyzed with PDE models in biomedical engineering.
Thứ Bảy, 17 tháng 1, 2015
Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes
The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematical investigation of the model, which covers a complete study of the well-posedness of a number of initial-boundary value problems, their reduction to time-dependent boundary integral equations by means of suitable potential representations, and the solution of the latter in Sobolev spaces.
From Quantum Cohomology to Integrable Systems
Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry. Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework. Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.
Structural Equation Modeling
This volume is intended to serve as a didactically-oriented resource covering a broad range of advanced topics often not discussedin introductory courses on structural equation modeling (SEM). Such topics are important in furthering the understandingof foundations and assumptions underlying SEM as well as in exploring SEM as a potential tool to address new types ofresearch questions that might not have arisen during a first course. Chapters focus on the clear explanation and application oftopics, rather than on analytical derivations, and contain syntax and partial output files from popular SEM software.
Thứ Hai, 12 tháng 1, 2015
Complex Variables
This text gives an overview of the basic properties of holomorphic functions of one complex variable. Topics studied in this overview include a detailed description of differential forms, homotopy theory, and homology theory, as the analytic properties of holomorphic functions, the solvability of the inhomogeneous Cauchy-Riemann equation with emphasis on the notation of compact families, the theory of growth of subharmonic functions, and an introduction to the theory of sheaves, covering spaces and Riemann surfaces. To further illuminate the material, a large number of exercises of differing levels of difficulty have been added.
Thứ Ba, 6 tháng 1, 2015
Diagrammatica
This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. The book begins with a brief review of some aspects of Einstein’s theory of relativity that are of particular importance for field theory, before going on to consider the relativistic quantum mechanics of free particles, interacting fields, and particles with spin. The techniques learned in the chapters are then demonstrated in examples that might be encountered in real accelerator physics. Further chapters contain discussions on renormalization, massive and massless vector fields and unitarity. A final chapter presents concluding arguments concerning quantum electrodynamics. The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. An appendix containing a comprehensive summary of the rules and conventions used is followed by an appendix specifying the full Lagrangian of the Standard Model and the corresponding Feynman rules. To make the book useful for a wide audience a final appendix provides a discussion on the metric used, and an easy to use dictionary connecting equations written with different metric. Written as a textbook, many diagrams and examples are included.
Thứ Ba, 30 tháng 12, 2014
Transport in Multilayered Nanostructures
This novel book is the first comprehensive text on dynamical mean-field theory (DMFT), which has emerged over the past two decades as one of the most powerful new developments in many-body physics. Written by one of the key researchers in the field, the volume develops the formalism of many-body Green’s functions using the equation of motion approach, which requires an undergraduate solid state physics course and a graduate quantum mechanics course as prerequisites. The DMFT is applied to study transport in multilayered nanostructures, which is likely to be one of the most prominent applications of nanotechnology in the coming years. The text is modern in scope focusing on exact numerical methods rather than the perturbation theory. Formalism is developed first for the bulk and then for the inhomogeneous multilayered systems. The science behind the metal-insulator transition, electronic charge reconstruction, and superconductivity are thoroughly described. The book covers complete derivations and emphasizes how to carry out numerical calculations, including discussions of parallel programming algorithms. Detailed descriptions of the crossover from tunneling to thermally activated transport, of the properties of Josephson junctions with barriers tuned near the metal-insulator transition, and of thermoelectric coolers and power generators are provided as applications of the theory.
Thứ Bảy, 27 tháng 12, 2014
Electronic States in Crystals of Finite Size
The theory of electronic states in the traditionally solid state physics is essentially a theory of electronic states in crystals of infinite size. However, any real crystal always has a finite size. This book presents an analytical theory on the electronic states in ideal low-dimensional systems and finite crystals recently developed by the author based on a differential equation theory approach. It gives some exact and general fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals and provides new insights on some fundamental problems in low-dimensional systems such as the surface states, quantum confinement effects etc, some of them are quite different from what are traditionally believed in the solid state physics community.