Space exploration and advanced astronomy have dramatically expanded our knowledge of outer space and made it possible to study the indepth mechanisms underlying various natural phenomena caused by complex interaction of physical-chemical and dynamical processes in the universe. Huge breakthroughs in astrophysics and the planetary s- ences have led to increasingly complicated models of such media as giant molecular clouds giving birth to stars, protoplanetary accretion disks associated with the solar system’s formation, planetary atmospheres and circumplanetary space. The creation of these models was promoted by the development of basic approaches in modern - chanics and physics paralleled by the great advancement in the computer sciences. As a result, numerous multidimensional non-stationary problems involving the analysis of evolutionary processes can be investigated using wide-range numerical experiments. Turbulence belongs to the most widespread and, at the same time, the most complicated natural phenomena, related to the origin and development of organized structures (- dies of different scale) at a definite flow regime of fluids in essentially non-linear - drodynamic systems. This is also one of the most complex and intriguing sections of the mechanics of fluids. The direct numerical modeling of turbulent flows encounters large mathematical difficulties, while the development of a general turbulence theory is hardly possible because of the complexity of interacting coherent structures. Three-dimensional non-steady motions arise in such a system under loss of la- nar flow stability defined by the critical value of the Reynolds number.

In a rapidly evolving field such as computational physics, six years is an eternity. Even though many of the elementary techniques described here are of venerable age, their assembly into sophisticated combined methods and their intensive application to ever new problems is an ongoing and exciting process. After six years, a new the new vistas edition of this textbook must therefore take into account some of that have opened up recently. Apart from these additions and some didactic improvements, the general struc­ ture of the book holds good. The first three chapters are devoted to a thorough, if concise, treatment of the main ingredients from numerical mathematics: finite differences, linear algebra, and stochastics. This exercise will prove valuable when we proceed, in chapters 4 and 5, to combine these elementary tools into powerful instruments for the integration of differential equations. The final chapters are devoted to a number of applications in selected fields: statistical physics, quantum mechanics, and hydrodynamics. I will gradually augment this text by web-resident sample programs. These will be written in JAVA and will be accompanied by short explanations and references to this text. Thus it may prove worthwhile to pay an occasional visit to my web-site www.ap.univie.ac.at/users/Franz.Vesely/ to see if any new applets have sprung up.

This book is intended to be an easy, concise, but rather complete, introduc­ the ISO/ANSI C++ programming language with special empha­ tion to sis on object-oriented numeric computation for students and professionals in science and engineering. The description of the language is platform­ independent. Thus it applies to different operating systems such as UNIX, Linux, MacOS, Windows, and DOS, as long as a standard C++ compiler is equipped. The prerequisite of this book is elementary knowledge of cal­ culus and linear algebra. However, this prerequisite is hardly necessary if this book is going to be used as a textbook for teaching C++ and all the sections on numeric methods are skipped. Programming experience in an­ other language such as FORTRAN, C, Ada, Pascal, Maple, or Matlab will certainly help, but is not presumed. All C++ features are introduced in an easy way through concepts such as functions, complex numbers, vectors, matrices, and integrals, which are familiar to every student and professional in science and engineering.

There are very few concepts that fascinate equally a theoretical physicist studying black holes and a patient undergoing seriolls mental psychosis. Time, undoubtedly, can well be ranked among them. For the measure of time inside a black hole is no less bizarre than the perception of time by a schizophrenic, who may perceive it as completely "suspended," "standing still," or even "reversing its direction. " The nature of time is certainly shrouded in profound mystery. This, perhaps, since the concept entails multifarious, and occasionally incongruous, facets. No wonder the subject attracts the serious attention of scholars on the one hand, and of the lay public on the other. Our Advanced Research Workshop is an excellent il­ lustration of this point, as the reader will soon discover. It turned out to be a unique professional forum for an unusually lively, effective and fruitful exchange of ideas and beliefs among 48 participants from 20 countries worldwide, selected out of more than a hundred applicants. The present book is based on the select talks presented at the meeting, and aims to provide the interested layperson and specialist alike with a multidisciplinary sampling of the most up-to-date scholarly research on the nature of time. It represents a coherent, state-of-the-art volume showing that research relevant to this topic is necessarily interdisciplinary and does not ignore such delicate issues as "altered" states of consciousness, religion and metaphysics.

This book builds bridges between two yet separated branches of theoretical and mathematical chemistry: Chemical Graph Theory and Electronic Structure Calculations. Although either of the fields have developed their own techniques, problems, methods, and favorite benchmark cases independent from each other, the authors have managed to bring them together by using the localization-delocalization matrix (LDM). The LDM is a novel molecular descriptor that fingerprints a molecule by condensing the complicated electronic information in one, mathematically manageable, object. In this book, the authors introduce the readers to modeling techniques based on LDMs. Their technique offers a high accuracy as well as robust predictive power, often dramatically surpassing the potential of either of the constituting methods on their own.

The book presents the winners of the Abel Prize in mathematics for the period 2018–2022:

This is volume 2 of Planets, Stars and Stellar Systems, a six-volume compendium of modern astronomical research, covering subjects of key interest to the main fields of contemporary astronomy. This volume on “Astronomical Techniques, Software, and Data” edited by Howard E. Bond presents accessible review chapters on Astronomical Photometry, Astronomical Spectroscopy, Infrared Astronomy Fundamentals, Astronomical Polarimetry: Polarized Views of Stars and Planets, Sky Surveys,Techniques of Radio Astronomy,Radio and Optical Interferometry: Basic Observing Techniques and Data Analysis, Absolute Calibration of Spectrophotometric Standard Stars,Virtual Observatories, Data Mining, and Astroinformatics, Statistical Methods for Astronomy, Numerical Techniques in Astrophysics.

The goal of this book is to expose the reader to the indispensable role that mathematics plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fibre bundles and their applications to differential geometry and gauge theories.

It is with great emotion that we present here this volume dedicated to the memory of Bernard Jouvet, Docteur es Sciences, Directeur des Recher­ ches at the Centre National pour la Recherche Scientifique. The life and the career as a physicist of Professor Jouvet are evoked in the following pages by Professor F. Cerulus, a friend of long standing of Professor Jouvet. The contributions have been written by physicists who were friends, collaborators or former students of Professor Jouvet. I express here my gratitude for their contributions.

In my original proposal to Springer for a book on Quantal Density Functional Theory, I had envisaged one that was as complete in its presentation as possible, describing the basic theory as well as the approximation methods and a host of applications. However,after workingon the bookforabout ?ve years, I realizedthat the goal was too ambitious, and that I would be writing for another ?ve years for it to be achieved. Fortunately,there was a natural breakin the material, and I proposed to my editor, Dr. Claus Ascheron, that we split the book into two components: the ?rst on the basic theoretical framework, and the second on approximation methods and applications. Dr. Ascheron consented, and I am thankful to him for agreeing to do so. Hence, we published Quantal Density Functional Theory in 2004, and are now publishing Quantal Density Functional Theory II: Approximation Methods and Applications. One signi?cant advantage of this, as it turns out, is that I have been able to incorporate in each volume the most recent understandings available. This volume, like the earlier one, is aimed at advanced undergraduates in physics and chemistry, graduate students and researchers in the ?eld. It is written in the same pedagogical style with details of all proofs and numerous ?gures provided to explain the physics.

In the last 40 years geophysicists have found that it is possible to construct images and even determine important physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. To make these images and extract this information requires the application of an advanced understanding of the mathematical physics of wave propagation. The oil and gas industry labels a major collection of the necessary seismic data processing methods by the name seismic "migration".

Low-dimensional semiconductors have become a vital part of today's semiconductor physics, and excitons in these systems are ideal objects that bring textbook quantum mechanics to life. Furthermore, their theoretical understanding is important for experiments and optoelectronic devices. The author develops the effective-mass theory of excitons in low-dimensional semiconductors and describes numerical methods for calculating the optical absorption including Coulomb interaction, geometry, and external fields. The theory is applied to Fano resonances in low-dimensional semiconductors and the Zener breakdown in superlattices. Comparing theoretical results with experiments, the book is essentially self-contained; it is a hands-on approach with detailed derivations, worked examples, illustrative figures, and computer programs. The book is clearly structured and will be valuable as an advanced-level self-study or course book for graduate students, lecturers, and researchers.

This book provides a succinct overview of recent progress in characterization of heat carriers describing atomic motion in liquids. Unlike solids and gases where heat carriers are typically described by phonons and real atomic particles, the nature of effective heat carriers in liquids is still elusive.

Der beliebte Grundkurs Theoretische Physik deckt in sieben Bänden alle für Bachelor/Master- oder Diplom-Studiengänge maßgeblichen Gebiete ab. Jeder Band vermittelt gut durchdacht das im jeweiligen Semester nötige theoretische-physikalische Rüstzeug. Zahlreiche Übungsaufgaben mit ausführlichen Lösungen dienen der Vertiefung des Stoffes.

Simulation of materials at the atomistic level is an important tool in studying microscopic structures and processes. The atomic interactions necessary for the simulations are correctly described by Quantum Mechanics, but the size of systems and the length of processes that can be modelled are still limited. The framework of Gaussian Approximation Potentials that is developed in this thesis allows us to generate interatomic potentials automatically, based on quantum mechanical data. The resulting potentials offer several orders of magnitude faster computations, while maintaining quantum mechanical accuracy. The method has already been successfully applied for semiconductors and metals.