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This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics. An extensive bibliography and open problems at the end of each chapter enhance the text.
Takes readers on a path of discovery of rarely examined wave phenomena and their possible usage. Chapters begin by formulating a question, followed by explanations of what is exciting about it, where the mystery might lie, and what could be the potential value of answering the question.
CD-ROM contains: articles in PDF format and "charge cloud movies" in Quick Time format.
The measurement of spin-polarization observables in reactions of nuclei and particles is of great utility and advantage when the effects of single-spin sub-states are to be investigated. Indeed, the unpolarized differential cross-section encompasses the averaging over the spin states of the particles, and thus loses details of the interaction process. This introductory text combines, in a single volume, course-based lecture notes on spin physics and on polarized-ion sources with the aim of providing a concise yet self-contained starting point for newcomers to the field, as well as for lecturers in search of suitable material for their courses and seminars. A significant part of the book is devoted to introducing the formal theory—a description of polarization and of nuclear reactions with polarized particles. The remainder of the text describes the physical basis of methods and devices necessary to perform experiments with polarized particles and to measure polarization and polarization effects in nuclear reactions. The book concludes with a brief review of modern applications in medicine and fusion energy research. For reasons of conciseness and of the pedagogical aims of this volume, examples are mainly taken from low-energy installations such as tandem Van de Graaff laboratories, although the emphasis of present research is shifting to medium- and high-energy nuclear physics. Consequently, this volume is restricted to describing non-relativistic processes and focuses on the energy range from astrophysical energies (a few keV) to tens of MeV. It is further restricted to polarimetry of hadronic particles.
This book provides an introduction to the theory and numerical developments of the homogenization method. It's main features are: a comprehensive presentation of homogenization theory; an introduction to the theory of two-phase composite materials; a detailed treatment of structural optimization by using homogenization; a complete discussion of the resulting numerical algorithms with many documented test problems. It will be of interest to researchers, engineers, and advanced graduate students in applied mathematics, mechanical engineering, and structural optimization.
This rigorous yet accessible guide presents a molecular-based description of nonlinear optical polarization analysis of chemical and biological assemblies. It includes discussion of the most common nonlinear optical microscopy and interfacial measurements used for quantitative analysis, specifically second harmonic generation (SHG), two-photon excited fluorescence (2PEF), vibrational sum frequency generation (SFG), and coherent anti-Stokes Raman spectroscopy/stimulated Raman spectroscopy (CARS/SRS). A linear algebra mathematical framework is developed, allowing step-wise systematic connections to be made between the observable measurements and the molecular response. Effects considered include local field corrections, the molecular orientation distribution, rotations between the molecular frame, the local frame and the laboratory frame, and simplifications from molecular and macromolecular symmetry. Specific examples are provided throughout the book, working from the common and relatively simple case studies through to the most general scenarios.
This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data. In this book the trade-off between resolution and stability when the data are noisy is addressed. Efficient imaging algorithms are provided and their resolution and stability with respect to noise in the measurements analyzed. It also shows that high-order polarization tensors provide an accurate representation of the target. Moreover, a dictionary-matching technique based on new invariants for the generalized polarization tensors is introduced. Matlab codes for the main algorithms described in this book are provided. Numerical illustrations using these codes in order to highlight the performance and show the limitations of numerical approaches for multistatic imaging are presented.
Acoustic and electromagnetic waves underlie a range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. This book, written by an international researcher, presents some of the research in a complete way. It is useful for graduate students in mathematics, physics, and engineering.
Polarization and Correlation Phenomena in Atomic Collisions: A Practical Theory Course bridges the gap between traditional courses in quantum mechanics and practical investigations. The authors' goal is to guide students in training their ability to perform theoretical calculations of polarization and correlation characteristics of various processes in atomic collisions. The book provides a concise description of the density matrix and statistical tensor formalism and presents a general approach to the description of angular correlation and polarization phenomena. It illustrates an application of the angular momentum technique to a broad variety of atomic processes. The book contains derivations of the most important expressions for observable quantities in electron-atom and ion-atom scattering, including that for polarized beams and/or polarized targets, in photo-induced processes, autoionization and cascades of atomic transitions. Spin-polarization and angular distributions of the reaction products are described, including the angular correlations in different types of coincidence measurements. The considered processes exemplify the general approach and the number of examples can be easily extended by a reader. The book supplies researchers, both theoreticians and experimentalists with a collection of helpful formulae and tables, and can serve as a reference book. Based on a highly regarded course at Moscow State University and elsewhere, the book provides real guidance on theoretical calculations of practical use.
The Encyclopedia of Physical Chemistry and Chemical Physics introduces possibly unfamiliar areas, explains important experimental and computational techniques, and describes modern endeavors. The encyclopedia quickly provides the basics, defines the scope of each subdiscipline, and indicates where to go for a more complete and detailed explanation. Particular attention has been paid to symbols and abbreviations to make this a user-friendly encyclopedia. Care has been taken to ensure that the reading level is suitable for the trained chemist or physicist. The encyclopedia is divided in three major sections: FUNDAMENTALS: the mechanics of atoms and molecules and their interactions, the macroscopic and statistical description of systems at equilibrium, and the basic ways of treating reacting systems. The contributions in this section assume a somewhat less sophisticated audience than the two subsequent sections. At least a portion of each article inevitably covers material that might also be found in a modern, undergraduate physical chemistry text. METHODS: the instrumentation and fundamental theory employed in the major spectroscopic techniques, the experimental means for characterizing materials, the instrumentation and basic theory employed in the study of chemical kinetics, and the computational techniques used to predict the static and dynamic properties of materials. APPLICATIONS: specific topics of current interest and intensive research. For the practicing physicist or chemist, this encyclopedia is the place to start when confronted with a new problem or when the techniques of an unfamiliar area might be exploited. For a graduate student in chemistry or physics, the encyclopedia gives a synopsis of the basics and an overview of the range of activities in which physical principles are applied to chemical problems. It will lead any of these groups to the salient points of a new field as rapidly as possible and gives pointers as to where to read about the topic in more detail.