This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviting. Central concepts are revisited and explored from multiple viewpoints. Exercises at the end of the chapter help reinforce the material. Representing Finite Groups: A Semisimple Introduction would serve as a textbook for graduate and some advanced undergraduate courses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A final chapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematics and mathematical physics will also find this book useful. A separate solutions manual is available for instructors.

A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition The long-anticipated revision of this well-liked textbook offers many new additions. In the twenty-five years since the original version of this book was published, much has happened in dynamical systems. Mandelbrot and Julia sets were barely ten years old when the first edition appeared, and most of the research involving these objects then centered around iterations of quadratic functions. This research has expanded to include all sorts of different types of functions, including higher-degree polynomials, rational maps, exponential and trigonometric functions, and many others. Several new sections in this edition are devoted to these topics. The area of dynamical systems covered in A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition is quite accessible to students and also offers a wide variety of interesting open questions for students at the undergraduate level to pursue. The only prerequisite for students is a one-year calculus course (no differential equations required); students will easily be exposed to many interesting areas of current research. This course can also serve as a bridge between the low-level, often non-rigorous calculus courses, and the more demanding higher-level mathematics courses. Features More extensive coverage of fractals, including objects like the Sierpinski carpet and others that appear as Julia sets in the later sections on complex dynamics, as well as an actual chaos "game." More detailed coverage of complex dynamical systems like the quadratic family and the exponential maps. New sections on other complex dynamical systems like rational maps. A number of new and expanded computer experiments for students to perform. About the Author Robert L. Devaney is currently professor of mathematics at Boston University. He received his PhD from the University of California at Berkeley under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets.

This book delivers a thorough derivation of nonrelativistic interaction models of electromagnetic field theories with thermoelastic solids and viscous fluids, the intention being to derive unique representations for the observable field quantities. This volume is intended for and will be useful to students and researchers working on all aspects of electromagneto-mechanical interactions in the materials sciences of complex solids and fluids.

In this amazing tour d'horizon, D. Allan Bromley uses the occasion of the centenary of the American Physical Society to reflect upon the growth of physics over the past 100 years, its fragmentation into numerous subdisciplines, the impact physics has had upon modern technology, and the re-emergence of the fundamental unity of the discipline in recent years. Hundreds of historical illustrations accompany the text. Bromley conveys much of the excitement and wonder that research in physics generated in the 20th century and asks what new things are in store in the next century. He covers such topics as relativity and quantum mechanics, the Manhattan project, superconductivity, transistors and the revolution brought about by solid-state electronics, protein folding, the uses of nuclear and atomic physics in biology and medicine, plate tectonics, the expansion of the universe and the Big Bang, and gravitational radiation. Bromley is the Sterling Professor of the Sciences and Dean of Yale University.||From the reviews:||"...A panoramic view of the physics landscape of the past century, in which are embedded an impressive number of major physics accomplishments. And [the book] describes these accomplishments in a language that is comprehensible to an educated reader with or without training in physics...In choice of topics, Bromley is about as complete as can be imagined...An immensely entertaining and illuminating read."|- Physics Today

Magnetic Resonance Imaging is a very important clinical imaging tool. It combines different fields of physics and engineering in a uniquely complex way. MRI is also surprisingly versatile, 'pulse sequences' can be designed to yield many different types of contrast. This versatility is unique to MRI. This short book gives both an in depth account of the methods used for the operation and construction of modern MRI systems and also the principles of sequence design and many examples of applications. An important additional feature of this book is the detailed discussion of the mathematical principles used in building optimal MRI systems and for sequence design. The mathematical discussion is very suitable for undergraduates attending medical physics courses. It is also more complete than usually found in alternative books for physical scientists or more clinically orientated works.

The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago. The foundation of our topic is presented in the contemporary mathematical literature by a lot of publications devoted to certain parts of the above-mentioned themes and connected with the scope of material of this book. There exist some monographs on Stochastic Differential Equations on Manifolds (e. g. [9,36,38,87]) based on the Stratonovich approach. In [7] there is a detailed description of It6 equations on manifolds in Belopolskaya-Dalecky form. Nelson's book [94] deals with Stochastic Mechanics and mean derivatives on Riemannian Manifolds. The books and survey papers on the Lagrange approach to Hydrodynamics [2,31,73,88], etc. , give good presentations of the use of infinite-dimensional ordinary differential geometry in ideal hydrodynamics. We should also refer here to [89,102], to the previous books by the author [53,64], and to many others.

The book collects contributions from experts worldwide addressing recent scholarship in social network analysis such as influence spread, link prediction, dynamic network biclustering, and delurking. It covers both new topics and new solutions to known problems. The contributions rely on established methods and techniques in graph theory, machine learning, stochastic modelling, user behavior analysis and natural language processing, just to name a few. This text provides an understanding of using such methods and techniques in order to manage practical problems and situations. Trends in Social Network Analysis: Information Propagation, User Behavior Modelling, Forecasting, and Vulnerability Assessment appeals to students, researchers, and professionals working in the field.

The volume presents, for the very first time, an exhaustive collection of those modern theoretical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and materials science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciates consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possible way, with the working details of a specific technique.

This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme 'Optimization with PDEs' (OPTPDE).

This book is an up-to-date introduction to univariate spectral analysis at the graduate level, which reflects a new scientific awareness of spectral complexity, as well as the widespread use of spectral analysis on digital computers with considerable computational power. The text provides theoretical and computational guidance on the available techniques, emphasizing those that work in practice. Spectral analysis finds extensive application in the analysis of data arising in many of the physical sciences, ranging from electrical engineering and physics to geophysics and oceanography. A valuable feature of the text is that many examples are given showing the application of spectral analysis to real data sets. Special emphasis is placed on the multitaper technique, because of its practical success in handling spectra with intricate structure, and its power to handle data with or without spectral lines. The text contains a large number of exercises, together with an extensive bibliography.

This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.

In the sixth century AD Simplicius produced detailed commentaries on several of the works of Aristotle, which help in our understanding of the "Physics", and of its interpretation in the ancient world. This is Urmson's translation of Simplicius' commentaries on "Physics 5" in which Aristotle lays down some of the principles of his dynamics and theory of change. What does not count as a change: change of relation?; the flux of time? There is no change of change, yet acceleration is recognized. Aristotle defines "continuous", "contact" and "next", and uses these definitions in discussing when we can claim that the same change or event is still going on.

An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces, representation theory, reflection groups, singularity theory, and in computer science and physics. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa tions of motion (solitons and instantons) allow the physicist to leave the frame work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds."

This is an extensively revised second edition of "Interfacial Transport Phenomena," a unique presentation of transport phenomena or continuum mechanics focused on momentum, energy, and mass transfer at interfaces. It discusses transport phenomena at common lines or three-phase lines of contact. The emphasis is upon achieving an in-depth understanding based upon first principles. It includes exercises and answers, and can serve as a graduate level textbook.

Nominated as an outstanding thesis by the Department of Physics and Astronomy of the University of New Mexico, this thesis seeks to identify the gamma-ray burst (GRB) progenitor. GRBs are extragalactic explosions that briefly outshine entire galaxies, but the mechanism that can release that much energy over a < 100 second burst is still a mystery. The leading candidate for the GRB progenitor is currently a massive star which collapses to form a black hole-accretion disk system that powers the GRB. GRB afterglows, however, do not always show the expected behavior of a relativistic blast wave interacting with the stellar wind that such a progenitor should have produced before its collapse. In this book, the author uses the Zeus-MP astrophysical hydrodynamics code to model the environment around a stellar progenitor prior to the burst. He then develops a new semi-analytic MHD and emission model to produce light curves for GRBs encountering these realistic density profiles. The work ultimately shows that the circumburst medium surrounding a GRB at the time of the explosion is much more complex than a pure wind, and that observed afterglows are entirely consistent with a large subset of proposed stellar progenitors.

This continuing authoritative series deals with the chemistry, materials science, physics and technology of the rare earth elements in an integrated manner. Each chapter is a comprehensive, up-to-date, critical review of a particular segment of the field. The work offers the researcher and graduate student a complete and thorough coverage of this fascinating field.
REVIEW:
"Highly experienced authors have written each review usually at a level suitable for advanced postgraduate students and research workers from a variety of fields. With the great richness of information involving references to other review articles written from different points of view, the books are an important reference source and should be on the shelves of most libraries."-- "Journal of Applied Crystallography"
. Authoritative
. Comprehensive
. Up-to-date
. Critical"

This thesis contains results of Dr. Guilong Gui during his PhD period with the aim to understand incompressible Navier-Stokes equations. It is devoted to the study of the stability to the incompressible Navier-Stokes equations. There is great potential for further theoretical and numerical research in this field. The techniques developed in carrying out this work are expected to be useful for other physical model equations. It is also hopeful that the thesis could serve as a valuable reference on current developments in research topics related to the incompressible Navier-Stokes equations. It was nominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis.

Proceedings of the NATO Advanced Study Institute on Basic Concepts and Applications of Scanning Tunneling Microscopy, Erice, Italy, April 17-29, 1989

The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area. The main focus of the book is on a rigorous derivation of the multi-particle localization in a strong random external potential field. To make the presentation accessible to a wider audience, the authors restrict attention to a relatively simple tight-binding Anderson model on a cubic lattice Zd. This book includes the following cutting-edge features: an introduction to the state-of-the-art single-particle localization theory an extensive discussion of relevant technical aspects of the localization theory a thorough comparison of the multi-particle model with its single-particle counterpart a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model. Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. This is an excellent text for a year-long graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists.

Nine survey articles in this volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. Key topics covered: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, martingale problem and Markov uniqueness of infinite- dimensional Nelson diffusions, analysis in geometric probability theory, measure-preserving shifts on the Wiener space, cohomology on loop spaces, and stochastic Volterra equations Contributors: H. Airault * L. Coutin * L. Decreusefond * C. Leonard * R. Leandre * P. Lescot * P. Malliavin * M. Oberguggenberger * R. Rebolledo * F. Russo * A.S. Ustunel * L. Wu The work, an outgrowth of a workshop on stochastic analysis held in Lisbon, serves as a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, math physics, and physics.

Novel Devices and Atom Manipulation, the second and concluding volume of Progress in Nano-Electro-Optics, focuses on applications to novel devices and atom manipulation. Each chapter is written by a leading scientists in the field. Part II addresses the latest developments in nano-optical techniques, dealing with topics such as: the reasons that the resolution of nano-electro-optical techniques extend beyond the diffraction limit; applications of excitonic polaritons to opto-electronic devices; instrumentation of near-field optical microscopy to study quantum confined systems; and atom manipulation by optical near-field techniques. Together with volume I (Basics and Theory of Near-Field Optics), these overviews are a valuable resource for engineers and scientists working in the field of nano-electro-optics

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A wide range of problems exists in classical and quantum physics, engi neering, and applied mathematics in which special functions arise. The procedure followed in most texts on these topics (e. g., quantum mechanics, electrodynamics, modern physics, classical mechanics, etc. ) is to formu late the problem as a differential equation that is related to one of several special differential equations (Hermite's, Bessel's, Laguerre's, Legendre's, etc. )."