P. A. Martin
Colorado School of Mines

Multiple Scattering
Interaction of Time-Harmonic Waves with N Obstacles

Series: Encyclopedia of Mathematics and its Applications (No. 107)
Hardback (ISBN-13: 9780521865548 | ISBN-10: 0521865549)

The interaction of waves with obstacles is an everyday phenomenon in science and engineering, arising for example in acoustics, electromagnetism, seismology and hydrodynamics. The mathematical theory and technology needed to understand the phenomenon is known as multiple scattering, and this book is the first devoted to the subject. The author covers a variety of techniques, describing first the single-obstacle methods and then extending them to the multiple-obstacle case. A key ingredient in many of these extensions is an appropriate addition theorem: a coherent, thorough exposition of these theorems is given, and computational and numerical issues around them are explored. The application of these methods to different types of problems is also explained; in particular, sound waves, electromagnetic radiation, waves in solids and water waves. A comprehensive bibliography of some 1400 items rounds off the book, which will be an essential reference on the topic for applied mathematicians, physicists and engineers.

* Describes all the main methods for solving multiple scattering problems exactly, as well as the main approximate solution methods; gives thorough exposition of addition theorems
* Contains many historical remarks and an extensive 1400-item bibliography
* Covers the four main application areas of acoustics, elastodynamics, electromagnetics and hydrodynamics

Contents

Preface; 1. Introduction; 2. Addition theorems in two dimensions; 3. Addition theorems in three dimensions; 4. Methods based on separation of variables; 5. Integral equation methods I: basic theory; 6. Integral equation methods II: further details; 7. Null-field and T-matrix methods; 8. Approximations; Appendices; Comments on the bibliography; Bibliography; Citation index; Index.

Angelo Favini University of Bologna, Italy
Alfredo Lorenzi Univ degli Studi di Milano, Italy

Differential Equations: Inverse and Direct Problems

Series: Lecture Notes in Pure and Applied Mathematics Volume: 251

ISBN: 1584886048
Publication Date: 6/9/2006
Number of Pages: 304
Availability: In Stock

Covers topics in various disciplinary fields of differential equations
Features contributions from leading international experts
Examines standard as well as new research results, such as identification problems for degenerate integrodifferential equations and complete abstract second-order equations of elliptic type in a UMD Banach space
Illustrates the concepts and applications of the concepts with over 500 equations

With contributions from some of the leading authorities in the field, the work in Differential Equations: Inverse and Direct Problems stimulates the preparation of new research results and offers exciting possibilities not only in the future of mathematics but also in physics, engineering, superconductivity in special materials, and other scientific fields.

Exploring the hypotheses and numerical approaches that relate to pure and applied mathematics, this collection of research papers and surveys extends the theories and methods of differential equations. The book begins with discussions on Banach spaces, linear and nonlinear theory of semigroups, integrodifferential equations, the physical interpretation of general Wentzell boundary conditions, and unconditional martingale difference (UMD) spaces. It then proceeds to deal with models in superconductivity, hyperbolic partial differential equations (PDEs), blowup of solutions, reaction-diffusion equation with memory, and Navier-Stokes equations. The volume ends with analyses on Fourier-Laplace multipliers, gradient estimates for Dirichlet parabolic problems, a nonlinear system of PDEs, and the complex Ginzburg-Landau equation.

By combining direct and inverse problems into one book, this compilation is a useful reference for those working in the world of pure or applied mathematics.

Contents

Alfred Gray / University of Maryland, College Park, MD
Elsa Abbena / University di Torino, Italy
Simon Salamon / Politecnico of Torino, Torino, Italy

Modern Differential Geometry of Curves and Surfaces with Mathematica,
Third Edition

Series: Studies in Advanced Mathematics Volume: 47

ISBN: 1584884487
Publication Date: 6/21/2006
Number of Pages: 1016

Provides up-to-date Mathematica notebook files in each chapter containing input code and important programs used in the book
Presents material about curves and surfaces, together with accurate interesting pictures, Mathematica instructions for making the pictures, and Mathematica programs for computing functions such as curvature and torsion
Contains more than 400 illustrations and a range of new applications that will appeal particularly to physicists and engineers

Introduces techniques from numerical analysis to differential geometry and gives Mathematica programs for numerical computation and drawing of geodesics on an arbitrary surface
Includes capsule biographies with portraits of over 75 mathematicians and scientists that places the material in perspective through history

Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray's famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray's death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions.

The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi's formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted.

Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.

Contents

John Cannon / University of Central Florida, Orlando, USA
Bhimsen Shivamoggi / University of Central Florida, Orlando, USA

Mathematical and Physical Theory of Turbulence

Series: Lecture Notes in Pure and Applied Mathematics Volume: 250

ISBN: 0824723236
Publication Date: 6/15/2006
Number of Pages: 208
Availability: In Stock

Surveys recent developments and original expert research in 2D, 3D, and scalar turbulence
Studies the use of wavelets to describe several aspects of Navier-Stokes turbulence
Examines the connection among governing equations, constitutive theory, and the closure problem
Discusses the significance of the law of conservation of angular momentum for freely evolving homogeneous turbulence
Presents a new concept of turbulence modeling to simulate the effect of turbulence on the flows as realistically as possible

Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence.

Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier-Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities and inviscid dissipation energy; validity of the idealized model incorporating local isotropy, homogeneity, and universality of small scales of high Reynolds numbers, Lagrangian statistics, and measurements; and subrigid-scale modeling and hybrid methods involving a mix of Reynolds-averaged Navier-Stokes (RANS), large-eddy simulations (LES), and direct numerical simulations (DNS).

By sharing their expertise and recent research results, the authoritative contributors in Mathematical and Physical Theory of Turbulence promote further advances in the field, benefiting applied mathematicians, physicists, and engineers involved in understanding the complex issues of the turbulence problem.

Contents

Leandro Nunes de Castro / Catholic University of Santos, Brazil

Fundamentals of Natural Computing:
Basic Concepts, Algorithms, and Applications

Series: Chapman & Hall/CRC Computer & Information Science Series Volume: 11
ISBN: 1584886439
Publication Date: 6/2/2006
Number of Pages: 696

Integrates the basic concepts, algorithms, and applications from a wide range of disciplines in a single, coherent text
Presents worked examples that illustrate innovative concepts and tools used for solving real-world problems
Includes 36 pseudocodes of algorithms for quick and efficient implementation of natural computing algorithms
Contains a glossary with biological, chemical, and physical terminology and a summary of theoretical, computing, and mathematical background used in the text
Provides references to additional information in recent literature and practical support materials available on relevant Web sites, for students as well as instructors

Natural computing brings together nature and computing to develop new computational tools for problem solving; to synthesize natural patterns and behaviors in computers; and to potentially design novel types of computers. Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications presents a wide-ranging survey of novel techniques and important applications of nature-based computing.

This book presents theoretical and philosophical discussions, pseudocodes for algorithms, and computing paradigms that illustrate how computational techniques can be used to solve complex problems, simulate nature, explain natural phenomena, and possibly allow the development of new computing technologies. The author features a consistent and approachable, textbook-style format that includes lucid figures, tables, real-world examples, and different types of exercises that complement the concepts while encouraging readers to apply the computational tools in each chapter. Building progressively upon core concepts of nature-inspired techniques, the topics include evolutionary computing, neurocomputing, swarm intelligence, immunocomputing, fractal geometry, artificial life, quantum computing, and DNA computing.

Fundamentals of Natural Computing is a self-contained introduction and a practical guide to nature-based computational approaches that will find numerous applications in a variety of growing fields including engineering, computer science, biological modeling, and bioinformatics.

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