Bøger i De Gruyter Studies in Mathematical Physics serien

This monograph is devoted to the nonperturbative dynamics in the Standard Model (SM), the basic theory of allfundamental interactions in natureexcept gravity. The Standard Model is divided into two parts: the quantum chromodynamics (QCD) and the electro-weak theory (EWT) are well-defined renormalizable theories in which the perturbation theory is valid. However, for the adequate description of the real physics nonperturbative effects are inevitable. This book describes how these nonperturbative effects may be obtained in the framework of spontaneous generation of effective interactions. The well-known example of such effective interaction is provided by the famous Nambu-Jona-Lasinio effective interaction. Also a spontaneous generation of this interaction in the framework of QCD is described and applied to the method for other effective interactions in QCD and EWT. The method is based on N.N. Bogoliubov's conception of compensation equations. As a result we then describe the principal features of the Standard Model, e.g. Higgs sector, and significant nonperturbative effects including recent results obtained at LHC and TEVATRON.

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

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.

This monograph offers a concise overview of the theoretical description of various collective phenomena in condensed matter physics. These effects include the basic electronic structure in solid state physics, lattice vibrations, superconductivity, light-matter interaction and more advanced topics such as martensitic transistions.

Minkowski Space discusses the space-time, so the mathematical foundations of the theory of special relativity. Further, it delivers all algebraic and geometric tools required by physicists to understand the principles of special relativity and its space-time.

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.

Systems with mechanical degrees of freedom containing unstable objects are analysed in this monograph and algorithms for their control are developed, discussed, and numerically tested. This is achieved by identifying unstable modes of motion and using all available resources to suppress them. By using this approach the region of states from which a stable regime can be reached is maximised. The systems discussed in this book are models for pendula and vehicles and find applications in mechatronics, robotics as well as in mechanical and automotive engineering.

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.

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.