Methods

During past years many countries constructed large accelerators for investigating heavy ion collisions, and new theoretical techniques for analysing results and making predictions were developed. Semi-classical methods were studied in the early days of quantum mechanics. Their application to heavy ion collisions has led to new advances and a number of different schools have grown up, each one emphasising different aspects of the theory. The aim of this book is to present a unified treatment of various lines of development. This book will be of great interest to graduate students wishing to learn about semi-classical methods in nuclear physics and to theoretical and experimental nuclear physicists, especially those working in heavy ion physics. It will also be of interest to research workers in other areas, such as atomic physics and quantum chemistry, where similar techniques are used.

Mathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students' physical intuition as he guides them through the mathematical methods required to study upper-level physics. Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material. It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions ('By the Ways') as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, many t

Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.

Now in its third edition, Mathematical Concepts in the Physical Sciences, 3rd Edition provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.This book is intended for students who have had a two-semester or three-semester introductory calculus course. Its purpose is to help students develop, in a short time, a basic competence in each of the many areas of mathematics needed in advanced courses in physics, chemistry, and engineering. Students are given sufficient depth to gain a solid foundation (this is not a recipe book). At the same time, they are not overwhelmed with detailed proofs that are more appropriate for students of mathematics. The emphasis is on mathematical methods rather than applications, but students are given some idea of how the methods will be used along with some simple applications.

This is a concise graduate level introduction to analytical functional methods in quantum field theory. Functional integral methods provide relatively simple solutions to a wide range of problems in quantum field theory. After introducing the basic mathematical background, this book goes on to study applications and consequences of the formalism to the study of series expansions, measure, phase transitions, physics on spaces with nontrivial topologies, stochastic quantisation, fermions, QED, non-abelian gauge theories, symmetry breaking, the effective potential, finite temperature field theory, instantons and compositeness. Serious attention is paid to the shortcomings of the conventional formalism (e.g. problems of measure) as well as detailed appraisal of the ambiguities of series summation. This book will be of great use to graduate students in theoretical physics wishing to learn the use of functional integrals in quantum field theory. It will also be a useful reference for researc

The purpose of this book is to present the basic elements of numerical methods for compressible flows. It is appropriate for advanced undergraduate and graduate students and specialists working in high speed flows. The focus is on the unsteady one-dimensional Euler equations which form the basis for numerical algorithms in compressible fluid mechanics. The book is restricted to the basic concepts of finite volume methods, and even in this regard is not intended to be exhaustive in its treatment. Although the practical applications of the one-dimensional Euler equations are limited, virtually all numerical algorithms for inviscid compressible flow in two and three dimensions owe their origin to techniques developed in the context of the one-dimensional Euler equations. The author believes it is therefore essential to understand the development and implementation of these algorithms in their original one-dimensional context. The text is supplemented by numerous end-of-chapter exercises.

The purpose of this book is to present the basic elements of numerical methods for compressible flows. It is appropriate for advanced undergraduate and graduate students and specialists working in high speed flows. The focus is on the unsteady one-dimensional Euler equations which form the basis for numerical algorithms in compressible fluid mechanics. The book is restricted to the basic concepts of finite volume methods, and even in this regard is not intended to be exhaustive in its treatment. Although the practical applications of the one-dimensional Euler equations are limited, virtually all numerical algorithms for inviscid compressible flow in two and three dimensions owe their origin to techniques developed in the context of the one-dimensional Euler equations. The author believes it is therefore essential to understand the development and implementation of these algorithms in their original one-dimensional context. The text is supplemented by numerous end-of-chapter exercises.

Applied Methods for Trade Policy Analysis provides a comprehensive introduction to the applied economic modeling of trade policies. The book introduces the reader to trade policy concepts, welfare measurement, accounting frameworks, and both partial and general equilibrium modeling approaches. It first covers these topics at a basic level and then introduces the reader to a number of more advanced topics: imperfect competition, dynamic modeling, labour market structure, and environmental modeling. Economic graduate students, professors, and policy makers will find the collection to be an important reference tool.

Significant advancements in methodologies and statistical techniques in cross-cultural psychological research abound, but general practice, education, and most researchers in psychology rarely use them. This leads to misinterpretations, misrepresentations, and prejudice. The authors expertly demonstrate the importance of methodological rigor to safeguard appropriate inferences about similarities and differences, particularly when methods have not been developed in the cultural contexts where they are used. The book features acculturation and identity, including contributions on remote acculturation, religiosity, and organizational contexts. It also covers individual differences and evaluates methodological progress in educational assessment, emotions, motivation, and personality. Methodological and psychometric perspectives on equivalence and bias, as well as measurement invariance in cross-cultural research, are a central theme. From study design to data interpretation, it is essentia

Significant advancements in methodologies and statistical techniques in cross-cultural psychological research abound, but general practice, education, and most researchers in psychology rarely use them. This leads to misinterpretations, misrepresentations, and prejudice. The authors expertly demonstrate the importance of methodological rigor to safeguard appropriate inferences about similarities and differences, particularly when methods have not been developed in the cultural contexts where they are used. The book features acculturation and identity, including contributions on remote acculturation, religiosity, and organizational contexts. It also covers individual differences and evaluates methodological progress in educational assessment, emotions, motivation, and personality. Methodological and psychometric perspectives on equivalence and bias, as well as measurement invariance in cross-cultural research, are a central theme. From study design to data interpretation, it is essentia

Soft computing techniques are emerging as an important tool in solving design, performance and optimisation problems in electromagnetics. Soft Computing in Electromagnetics offers detailed discussion on the application of soft computing concepts in the field of metamaterial antennas, radar absorbers, transmission line characterisation and optimised radar absorbing material (RAM) and introduces implementation of soft computing tools in a relatively new area of metamaterials. The soft computing methods are used to optimise fault detection, electromagnetic propagation and path loss detection. The development of two CAD packages for design of metamaterial split ring resonators (SRR) and path-loss prediction is discussed. The concepts are explained with the help of algorithms and the corresponding software codes. Numerical examples and MATLAB codes are provided throughout the text to facilitate understanding.

Providing a pedagogical introduction to the essential principles of path integrals and Hamiltonians, this book describes cutting-edge quantum mathematical techniques applicable to a vast range of fields, from quantum mechanics, solid state physics, statistical mechanics, quantum field theory, and superstring theory to financial modeling, polymers, biology, chemistry, and quantum finance. Eschewing use of the Schrödinger equation, the powerful and flexible combination of Hamiltonian operators and path integrals is used to study a range of different quantum and classical random systems, succinctly demonstrating the interplay between a system's path integral, state space, and Hamiltonian. With a practical emphasis on the methodological and mathematical aspects of each derivation, this is a perfect introduction to these versatile mathematical methods, suitable for researchers and graduate students in physics and engineering.

Geometric group theory is a vibrant subject at the heart of modern mathematics. It is currently enjoying a period of rapid growth and great influence marked by a deepening of its fertile interactions with logic, analysis and large-scale geometry, and striking progress has been made on classical problems at the heart of cohomological group theory. This volume provides the reader with a tour through a selection of the most important trends in the field, including limit groups, quasi-isometric rigidity, non-positive curvature in group theory, and L2-methods in geometry, topology and group theory. Major survey articles exploring recent developments in the field are supported by shorter research papers, which are written in a style that readers approaching the field for the first time will find inviting.

Corpus linguistics continues to be a vibrant methodology applied across highly diverse fields of research in the language sciences. With the current steep rise in corpus sizes, computational power, statistical literacy and multi-purpose software tools, and inspired by neighbouring disciplines, approaches have diversified to an extent that calls for an intensification of the accompanying critical debate. Bringing together a team of leading experts, this book follows a unique design, comparing advanced methods and approaches current in corpus linguistics, to stimulate reflective evaluation and discussion. Each chapter explores the strengths and weaknesses of different datasets and techniques, presenting a case study and allowing readers to gauge methodological options in practice. Contributions also provide suggestions for further reading, and data and analysis scripts are included in an online appendix. This is an important and timely volume, and will be essential reading for any lingui

Contests are prevalent in many areas, including sports, rent seeking, patent races, innovation inducement, labor markets, scientific projects, crowdsourcing and other online services, and allocation of computer system resources. This book provides unified, comprehensive coverage of contest theory as developed in economics, computer science, and statistics, with a focus on online services applications, allowing professionals, researchers and students to learn about the underlying theoretical principles and to test them in practice. The book sets contest design in a game-theoretic framework that can be used to model a wide-range of problems and efficiency measures such as total and individual output and social welfare, and offers insight into how the structure of prizes relates to desired contest design objectives. Methods for rating the skills and ranking of players are presented, as are proportional allocation and similar allocation mechanisms, simultaneous contests, sharing utility of

This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate studen

2D infrared (IR) spectroscopy is a cutting-edge technique, with applications in subjects as diverse as the energy sciences, biophysics and physical chemistry. This book introduces the essential concepts of 2D IR spectroscopy step-by-step to build an intuitive and in-depth understanding of the method. This unique book introduces the mathematical formalism in a simple manner, examines the design considerations for implementing the methods in the laboratory, and contains working computer code to simulate 2D IR spectra and exercises to illustrate involved concepts. Readers will learn how to accurately interpret 2D IR spectra, design their own spectrometer and invent their own pulse sequences. It is an excellent starting point for graduate students and researchers new to this exciting field. Computer codes and answers to the exercises can be downloaded from the authors' website, available at www.cambridge.org/9781107000056.

This comprehensive guide offers a new approach for developing and implementing robust computational methodologies that uncover the key geometric and topological information from signals and images. With the help of detailed real-world examples and applications, readers will learn how to solve complex signal and image processing problems in fields ranging from remote sensing to medical imaging, bioinformatics, robotics, security, and defence. With an emphasis on intuitive and application-driven arguments, this text covers not only a range of methods in use today, but also introduces promising new developments for the future, bringing the reader up-to-date with the state of the art in signal and image analysis. Covering basic principles as well as advanced concepts and applications, and with examples and homework exercises, this is an invaluable resource for graduate students, researchers, and industry practitioners in a range of fields including signal and image processing, biomedical e

Best-worst scaling (BWS) is an extension of the method of paired comparison to multiple choices that asks participants to choose both the most and the least attractive options or features from a set of choices. It is an increasingly popular way for academics and practitioners in social science, business, and other disciplines to study and model choice. This book provides an authoritative and systematic treatment of best-worst scaling, introducing readers to the theory and methods for three broad classes of applications. It uses a variety of case studies to illustrate simple but reliable ways to design, implement, apply, and analyze choice data in specific contexts, and showcases the wide range of potential applications across many different disciplines. Best-worst scaling avoids many rating scale problems and will appeal to those wanting to measure subjective quantities with known measurement properties that can be easily interpreted and applied.