Bücher der Reihe De Gruyter Studies in Mathematical Physics

Diffraction theory describes scattering mechanisms for waves of various physical nature, scattered by objects of different shapes and materials. This book proposes new methods to account for the contour shape, edge profile and boundary conditions of three-dimensional scatterers (in particularly, flat polygons and polyhedrals). A standard method to refine the physical optics approximation (PO) is the heuristic method of edge waves (MEW). In comparison with MEW, the presented approaches simplify the solving and refining the PO approximation without solving a corresponding two-dimensional problem. Furthermore these methods allow to take into account the field perturbation in the vicinity of vertices. While the analytical formulas obtained by using these new approaches are as simple as in the PO case, the accuracy can be even higher than for MEW. On the basis of the developed methods construction of solutions for wave propagation in urban area and elastic wave diffraction (including seismic waves) are proposed. The book is useful for specialists who solve scientific and engineering problems in wave propagation and for students and postgraduate students.

With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. ContentsQuantum Groups and Quantum AlgebrasHighest-Weight Modules over Quantum AlgebrasPositive-Energy Representations of Noncompact Quantum AlgebrasDuality for Quantum GroupsInvariant q-Difference OperatorsInvariant q-Difference Operators Related to GLq(n)q-Maxwell Equations Hierarchies

This book introduces notation, terminology, and basic ideas of relativistic quantum theories. The discussion proceeds systematically from the principle of relativity and postulates of quantum logics to the construction of Poincare invariant few-particle models of interaction and scattering. It is the first of three volumes formulating a consistent relativistic quantum theory of interacting charged particles. a Contents Quantum logic Poincare group Quantum mechanics and relativity Observables Elementary particles Interaction Scattering Delta function Groups and vector spaces Group of rotations Lie groups and Lie algebras Hilbert space Operators Subspaces and projections Representations of groups and algebras Pseudo-orthogonal representation of Lorentz group

The book provides a concise and rigor introduction to the fundamentals of methods for solving the principal problems of modern non-linear dynamics. This monograph covers the basic issues of the theory of integrable systems and the theory of dynamical chaos both in nonintegrable conservative and in dissipative systems. A distinguishing feature of the material exposition is to add some comments, historical information, brief biographies and portraits of the researchers who made the most significant contribution to science. This allows one to present the material as accessible and attractive to students to acquire indepth scientific knowledge of nonlinear mechanics, feel the atmosphere where those or other important discoveries were made. The book can be used as a textbook for advanced undergraduate and graduate students majoring in high-tech industries and high technology (the science based on high technology) to help them to develop lateral thinking in early stages of training. Contents:Nonlinear OscillationsIntegrable SystemsStability of Motion and Structural StabilityChaos in Conservative SystemsChaos and Fractal Attractors in Dissipative SystemsConclusionReferencesIndex

The purpose of this book is to give a systematic pedagogical exposition of the quantitative analysis of Wilson lines and gauge-invariant correlation functions in quantum chromodynamics. Using techniques from the previous volume (Wilson Lines in Quantum Field Theory, 2014), an ab initio methodology is developed and practical tools for its implementation are presented. Emphasis is put on the implications of gauge invariance and path-dependence properties of transverse-momentum dependent parton density functions. The latter are associated with the QCD factorization approach to semi-inclusive hadronic processes, studied at currently operating and planned experimental facilities. Contents:IntroductionParticle Number Operators in Quantum Mechanics and in Quantum Field TheoryGeometry of Quantum Field TheoriesBasics of Wilson Lines in QCDGauge-Invariant Parton DensitiesSimplifying Wilson Line CalculationsBrief Literature GuideConventions and Reference FormulaeIntegrationsBibliographyIndex

Relativistic celestial mechanics - investigating the motion celestial bodies under the influence of general relativity - is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics - starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area. This first volume of a two-volume series is concerned with theoretical foundations such as post-Newtonian solutions to the two-body problem, light propagation through time-dependent gravitational fields, as well as cosmological effects on the movement of bodies in the solar systems. On the occasion of his 80-th birthday, these two volumes honor V. A. Brumberg - one of the pioneers in modern relativistic celestial mechanics. Contributions include: M. Soffel: On the DSX-framework T. Damour: The general relativistic two body problem G. Schaefer: Hamiltonian dynamics of spinning compact binaries through high post-Newtonian approximations A. Petrov and S. Kopeikin: Post-Newtonian approximations in cosmology T. Futamase: On the backreaction problem in cosmology Y. Xie and S. Kopeikin: Covariant theory of the post-Newtonian equations of motion of extended bodies S. Kopeikin and P. Korobkov: General relativistic theory of light propagation in multipolar gravitational fields

This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid. The methods are normally based on the Bateman-Luke variational formalism combined with perturbation theory. The derived approximate equations of spatial motions of the body-liquid mechanical system (these equations are called mathematical models in the title) take the form of a finite-dimensional system of nonlinear ordinary differential equations coupling quasi-velocities of the rigid body motions and generalized coordinates responsible for displacements of the natural sloshing modes. Algorithms for computing the hydrodynamic coefficients in the approximate mathematical models are proposed. Numerical values of these coefficients are listed for some tank shapes and liquid fillings. The mathematical models are also derived for the contained liquid characterized by the Newton-type dissipation. Formulas for hydrodynamic force and moment are derived in terms of the solid body quasi-velocities and the sloshing-related generalized coordinates. For prescribed harmonic excitations of upright circular (annular) cylindrical and/or conical tanks, the steady-state sloshing regimes are theoretically classified; the results are compared with known experimental data. The book can be useful for both experienced and early-stage mechanicians, applied mathematicians and engineers interested in (semi-)analytical approaches to the "e;fluid-structure"e; interaction problems, their fundamental mathematical background as well as in modeling the dynamics of complex mechanical systems containing a rigid tank partly filled by a liquid.

Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.

Phononic crystals are artificial periodic structures that can alter efficiently the flow of sound, acoustic waves, or elastic waves. They were introduced about twenty years ago and have gained increasing interest since then, both because of their amazing physical properties and because of their potential applications. The topic of phononic crystals stands as the cross-road of physics (condensed matter physics, wave propagation in inhomogeneous and periodic media) and engineering (acoustics, ultrasonics, mechanical engineering, electrical engineering). Phononic crystals cover a wide range of scales, from meter-size periodic structures for sound in air to nanometer-size structures for information processing or thermal phonon control in integrated circuits. Phononic crystals have a definite relation with the topic of photonic crystals in optics. The marriage of phononic and photonic crystals also provides a promising structural basis for enhanced sound and light interaction. As the topic is getting popular, it is nowadays presented and discussed at various international conferences. After the first ten years during which the topic has remained mainly theoretical with a few proof-of-concept demonstrations in the literature, the evolution has been towards applications, instrumentation, and novel designs. The physical explanations for various effects are now well understood and efficient numerical methods and analysis tools have been developed. The book contains a comprehensive set of finite element model (FEM) scripts for solving basic phononic crystal problems. The scripts are short, easy to read, and efficient, allowing the reader to generate for him(her)self band structures for 2D and 3D phononic crystals, to compute Bloch waves, waveguide and cavity modes, and more.

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

This monograph provides a systematic treatment of differential geometry in modeling of incompatible fiite deformations in solids. Included are discussions of generalized deformations and stress measures on smooth manifolds, geometrical formalizations for structurally inhomogeneous bodies, representations for configurational forces, and evolution equations.

The revised edition gives a comprehensive mathematical and physical presentation of fluid flows in non-classical models of convection - relevant in nature as well as in industry. After the concise coverage of fluid dynamics and heat transfer theory it discusses recent research. The authors provide the theoretical foundation on a topic relevant from metallurgy, ecology to chemistry, crystal physics and many other fields.

With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This fourth volume covers AdS/CFT, Virasoro and affine (super-)algebras.

Magnetohydrodynamics describes dynamics in electrically conductive fluids. These occur in our environment as well as in our atmosphere and magnetosphere, and play a role in the sun's interaction with our planet. This work gives the basic information on turbulence in nature, comprising the needed equations, notions and numerical simulations. The current state of our knowledge and future implications of MHD turbulence are outlined systematically. It is indispensable for all scientists engaged in research of our atmosphere and in space science.

This work deals with the matrix methods of continuous signal and image processing according to which strip-transformation is used. The authors suggest ways to solve a problem of evaluating potential noise immunity and synthesis of an optimal filter for the case of pulse noises, of applying the two-dimensional strip-transformation for storage and noise immune transmission of images. The strip-transformation of images is illustrated by examples and classes of images invariant relative to symmetrical orthogonal transformations. The monograph is intended for scientists and specialists whose activities are connected with computer signals and images processing, instrumentation and metrology. It can also be used by undergraduates, as well as by post-graduates for studying computer methods of signal and image processing.

Consists of reviews on a multitude of advanced topics in the area, covering both classical as well as modern developments, while focusing on applications and experiments.

The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly.In this monograph, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

Strong pulsed magnetic fields are important for several fields in physics and engineering, such as power generation and accelerator facilities. Basic aspects of the generation of strong and superstrong pulsed magnetic fields technique are given, including the physics and hydrodynamics of the conductors interacting with the field as well as an account of the significant progress in generation of strong magnetic fields using the magnetic accumulation technique. Results of computer simulations as well as a survey of available field technology are completing the volume.

Back-action of aerodynamics onto structures such as wings cause vibrations and may resonantly couple to them, thus causing instabilities (flutter) and endangering the whole structure. By careful choices of geometry, materials and damping mechanisms, hazardous effects on wind engines, planes, turbines and cars can be avoided. Besides an introduction into the problem of flutter, new formulations of flutter problems are given as well as a treatise of supersonic flutter and of a whole range of mechanical effects. Numerical and analytical methods to study them are developed and applied to the analysis of new classes of flutter problems for plates and shallow shells of arbitrary plane form. Specific problems discussed in the book in the context of numerical simulations are supplemented by Fortran code examples (available on the website).

Generalising Newton's law of gravitation, general relativity is one of the pillars of modern physics. On the occasion of general relativity's centennial, this book features leading scientists in the different branches of gravitational research who review the history and the advances in the main fields of applications of the theory.

This work provides the current theory and observations behind the cosmological phenomenon of dark energy. The approach is comprehensive with rigorous mathematical theory and relevant astronomical observations discussed in context. The book treats the background and history starting with the new-found importance of Einstein's cosmological constant (proposed long ago) in dark energy formulation, as well as the frontiers of dark energy. The authorsdo not presuppose advanced knowledge of astronomy, and basic mathematical concepts used in modern cosmology are presented in a simple, but rigorous way. All this makes the book useful for both astronomers and physicists, and also for university students of physical sciences.

This monograph is devoted to the creation of a comprehensive formalism for quantitative description of polarized modes' linear interaction in modern single-mode optic fibers. The theory of random connections between polarized modes, developed in the monograph, allows calculations of the zero shift deviations for a fiber ring interferometer. The monograph addresses also the Sagnac effect and the Thomas precession. Devices such as gyroscopes, used in navigation and flight control, work based on this technology. Given the ever increasing market for navigation and air traffic, researchers and practitioners in research and industry need a fundamental and sound understanding of the principles. This work presents the underlying physical foundations.

Various nanoclusters and microparticles are considered in excited and ionized gases, as well as various processes with their participation. The concepts of these processes were developed 50 - 100 years ago mostly for dense media, and basing on these concepts, we analyze these processes in gases in two opposite regimes, so that in the kinetic regime surrounding atoms of a buffer gas do not partake in processesinvolving small particles, and the diffusion regime corresponds to a dense gas where interaction of small particles with a buffer gas subjects to laws of hydrodynamics. For calculation or estimation of the rates of these processes, we are based on the liquid drop model for small particles which was introduced in physics by N. Bohr about 80 years ago for the analysis of properties of atomic nuclei including the nuclear fusion and the hard sphere model (or the model of billiard balls) which was used by J. C. Maxwell 150 years ago and helped to create the kinetic theory of gases. These models along with the analysis of their accuracy allow one to study various processes, such as transport processes in gases involving small particles, charging of small particles in gases, chemical processes, atom attachment and quenching of excited atomic particles on the surface of a small particle, nucleation processes for small particles including coagulation, coalescence and growth of fractal aggregates, chain aggregates, fractal fibres and aerogels. Each analysis is finished by analytic formulas or simple models which allow us to calculate the rate of a certain real process with a known accuracy or to estimate this, and criteria of validity are given for these expressions obtained. Examples of real objects and processes involving small particles are analyzed.

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

Most of the problems arising in science and engineering are nonlinear. They are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems, and often break down for problems with strong nonlinearity. This book presents the current theoretical developments and applications of Keller-Box method to nonlinear problems. The first half of the book addresses basic concepts to understand the theoretical framework for the method. In the second half of the book, the authors give a number of examples of coupled nonlinear problems that have been solved by means of the Keller-Box method. The particular area of focus is on fluid flow problems governed by nonlinear equations.

Physical models of gas discharge processes in gas flows and numerical simulation methods, which are used for numerical simulation of these phenomena are considered in the book. Significant attention is given to a solution of two-dimensional problems of physical mechanics of electric arc, radio-frequency, micro-wave, and optical discharges, as well as to investigation of electrodynamic structure of direct current glow discharges. Problems of modern computational magnetohydrodynamics (MHD) are considered also. Prospects of the different kinds of discharges use in aerospace applications are discussed. This book is intended for scientists and engineers concerned with physical gas dynamics, physics of the low-temperature plasma and gas discharges, and also for students and post-graduate students of physical and technical specialties of universities.

This book is essentially based on the lecture course on "e;Statistical Physics"e;, which was taught by the author at the physical faculty of the Ural State University in Ekaterinburg since 1992. This course was intended for all physics students, not especially for those specializing in theoretical physics. In this sense the material presented here contains the necessary minimum of knowledge of statistical physics (also often called statistical mechanics), which is in author's opinion necessary for every person wishing to obtain a general education in the field of physics. This posed the rather difficultproblem of the choice of material and compact enough presentation. At the same time it necessarily should contain all the basic principles of statistical physics, as well as its main applications to different physical problems, mainly from the field of the theory of condensed matter. Extended version of these lectures were published in Russian in 2003. For the present English edition, some of the material was rewritten and several new sections and paragraphs were added, bringing contents more up to date and adding more discussion on some more difficult cases.

Deformations of elastic bodies are encountered in many areas in science, engineering and technology. In the last decades, various numerical approaches using the finite element technique have been developed, but many are not adequate to address the full complexity.This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements. Other than comparable books, this work also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.