Lecture Notes

Hall (U. of Aberdeen) compiles the theoretical aspects of the literature on symmetries in general relativity that have been produced over the past few decades. He is not offering a textbook, he warns,

Haug (astronomy and astrophysics) and Nakel (physics, both U. of Tubingen, Germany) represent the theoretical and experimental developments in the process, which strives to describe the coupling of th

This monograph contains the results of my research in the area of asymmet­ ric theory of elasticity, conducted from 1969 to 1986 under the direction of PROFESSOR WITOLD NOWACKI. I am indebted to PROFE

A gentle introduction to advanced topics such as parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to ‘compute’ solutions to problems, hence a

Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for prec

Geomechanics is the mechanics of geomaterials, i.e. soils and rocks, and deals with fascinating problems such as settlements, stability of excavations, tunnels and offshore platforms, landslides, eart

This book is devoted to the deformation and failure in metallic materials, summarizing the results of a research programme financed by the "Deutsche Forschungsgemeinschaft". It presents the recent eng

This book summarizes a set of lectures given at U.C. Berkeley in the Fall of 2001, highlighting the connection between traffic flow, queuing systems and supply chains. The book unveils the root causes

This book provides a concrete introduction to quantum fields on a lattice: a precise and non-perturbative definition of quantum field theory obtained by replacing continuous space-time by a discrete set of points on a lattice. The path integral on the lattice is explained in concrete examples using weak and strong coupling expansions. Fundamental concepts such as 'triviality' of Higgs fields and confinement of quarks and gluons into hadrons are described and illustrated with the results of numerical simulations. The book also provides an introduction to chiral symmetry and chiral gauge theory, as well as quantized non-abelian gauge fields, scaling and universality. Based on the lecture notes of a course given by the author, this book contains many explanatory examples and exercises, and is suitable as a textbook for advanced undergraduate and graduate courses.

The book investigates bargaining between two agents. It presents the history of bargaining analysis from Francis Y. Edgeworth's first formal study, followed by cooperative and noncooperative game-theo

Many computionally challenging problems omnipresent in science and engineering exhibit multiscale phenomena so that the task of computing or even representing all scales of action is computationally v

This book covers quantum mechanics in macroscopic systems, focusing on quantum fluctuations and localization by quantum interference. Based on elementary quantum and statistical physics, the book poin

Looking at quantum phase transitions, Continentino (U. Federal Fluminense, Brazil) concentrates on those that occur in strongly correlated electronic systems. He presents the scaling theory of quantum

Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science a

Economic, marketing, and legislative considerations are increasingly leading companies to take back and recover their products after use. From a logistics perspective, these initiatives give rise to n

Go to, let us go down, and there confound their language, that they may not understand one another's speech. So the LORD scattered them abroad from thence upon the face of all the earth: and they left

Lattice gauge theory is a fairly young research area in Theoretical Particle Physics. It is of great promise as it offers the framework for an ab-initio treatment of the nonperturbative features of st

This book provides an accessible and up-to-date introduction to how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. Beginning with a summary of key ideas from perturbative quantum field theory and an introduction to the Hopf algebra structure of renormalization, early chapters discuss the rationality of ladder diagrams and simple link diagrams. The necessary basics of knot theory are then presented and the number-theoretic relationship between the topology of Feynman diagrams and knot theory is explored. Later chapters discuss four-term relations motivated by the discovery of Vassiliev invariants in knot theory and draw a link to algebraic structures recently observed in noncommutative geometry. Detailed references are included. Dealing with material at perhaps the most productive interface between mathematics and physics, the book will be of interest to theoretical and particle physicists, and mathematicians.

This book concerns programming techniques like object-oriented programming and generic (template) programming. These modern techniques have proven to increase flexibility, modularization, code reuse a

This book is an introduction to the applications in nonequilibrium statistical mechanics of chaotic dynamics, and also to the use of techniques in statistical mechanics important for an understanding of the chaotic behaviour of fluid systems. The fundamental concepts of dynamical systems theory are reviewed and simple examples are given. Advanced topics including SRB and Gibbs measures, unstable periodic orbit expansions, and applications to billiard-ball systems, are then explained. The text emphasises the connections between transport coefficients, needed to describe macroscopic properties of fluid flows, and quantities, such as Lyapunov exponents and Kolmogorov-Sinai entropies, which describe the microscopic, chaotic behaviour of the fluid. Later chapters consider the roles of the expanding and contracting manifolds of hyperbolic dynamical systems and the large number of particles in macroscopic systems. Exercises, detailed references and suggestions for further reading are included

The chapters of this book have been presented at the 1st Workshop of the Nonlinear Control Network*, which was held in Ghent, March 15,16, 1999. These contributions give an overview of some of the cur

This proceedings volume consists of papers presented at the Seventh International Workshop on Computer-Aided Scheduling of Pllblic Transport, which was held at th th the Massachusetts Institute of Tec

The Dirac operator has many useful applications in theoretical physics and mathematics. This book provides a clear, concise and self-contained introduction to the global theory of the Dirac operator and to the analysis of spectral asymptotics with local or non-local boundary conditions. The theory is introduced at a level suitable for graduate students. Numerous examples are then given to illustrate the peculiar properties of the Dirac operator, and the role of boundary conditions in heat-kernel asymptotics and quantum field theory. Topics covered include the introduction of spin-structures in Riemannian and Lorentzian manifolds; applications of index theory; heat-kernel asymptotics for operators of Laplace type; quark boundary conditions; one-loop quantum cosmology; conformally covariant operators; and the role of the Dirac operator in some recent investigations of four-manifolds. This volume provides graduate students with a rigorous introduction and researchers with a valuable refer

Optimization problems arising in practice usually contain several random parameters. Hence, in order to obtain optimal solutions being robust with respect to random parameter variations, the mostly av

This book provides an introduction to lattice models of polymers. This is an important topic both in the theory of critical phenomena and the modelling of polymers. The first two chapters introduce the basic theory of random, directed and self-avoiding walks. The next two chapters develop and expand this theory to explore the self-avoiding walk in both two and three dimensions. Following chapters describe polymers near a surface, dense polymers, self-interacting polymers and branched polymers. The book closes with discussions of some geometrical and topological properties of polymers, and of self-avoiding surfaces on a lattice. The volume combines results from rigorous analytical and numerical work to give a coherent picture of the properties of lattice models of polymers. This book will be valuable for graduate students and researchers working in statistical mechanics, theoretical physics and polymer physics. It will also be of interest to those working in applied mathematics and theo

This volume describes the Pomeron, an object of crucial importance in very high energy particle physics. The book starts with a general description of the Pomeron within the framework of Regge theory. The emergence of the Pomeron within scalar field theory is discussed next, providing a natural foundation on which to develop the more realistic case of QCD. The reggeization of the gluon is demonstrated and used to build the Pomeron of perturbative QCD. The dynamical nature of the Pomeron is then investigated. The role of the Pomeron in small-x deep inelastic scattering and in diffractive scattering is also examined in detail. The volume concludes with a study of the colour dipole approach to high energy scattering and the explicit role of unitarity corrections. This book will be of interest to theoretical and experimental particle physicists, and applied mathematicians.

This book introduces the use of Lie algebra and differential geometry methods to study nonlinear integrable systems of Toda type. Many challenging problems in theoretical physics are related to the solution of nonlinear systems of partial differential equations. One of the most fruitful approaches in recent years has resulted from a merging of group algebraic and geometric techniques. The book gives a comprehensive introduction to this exciting branch of science. Chapters 1 and 2 review basic notions of Lie algebras and differential geometry with an emphasis on further applications to integrable nonlinear systems. Chapter 3 contains a derivation of Toda type systems and their general solutions based on Lie algebra and differential geometry methods. The last chapter examines explicit solutions of the corresponding equations. The book is written in an accessible 'lecture note' style with many examples and exercises to illustrate key points and to reinforce understanding.

This controversial book examines one of the most fundamental questions of modern cosmology: how much matter is there in the Universe? This issue affects theories of the origin and evolution of the Universe as well as its geometrical structure and ultimate fate. The authors discuss all the relevant cosmological and astrophysical evidence and come to the conclusion that the balance of arguments presently lies with a density of around twenty per cent of the critical density required for the Universe to ultimately recollapse. Because the arguments presented constitute a 'state-of-the-art' analysis of the observational and theoretical arguments surrounding the existence of dark matter, primordial nucleosynthesis, large-scale structure formation and the cosmic microwave background radiation, this study provides the reader with an indispensable introduction to the most exciting recent developments in modern cosmology. Written by two eminent cosmologists, this topical and provocative book will

This volume presents the proceedings of the International Workshop on Database Issues for Data Visualization, held in conjunction with the IEEE Visualization '93 conference in San Jose, California in

This timely review provides a self-contained introduction to the mathematical theory of stationary black holes and a self-consistent exposition of the corresponding uniqueness theorems. The opening chapters examine the general properties of space-times admitting Killing fields and derive the Kerr-Newman metric. Strong emphasis is given to the geometrical concepts. The general features of stationary black holes and the laws of black hole mechanics are then reviewed. Critical steps towards the proof of the 'no-hair' theorem are then discussed, including the methods used by Israel, the divergence formulae derived by Carter, Robinson and others, and finally the sigma model identities and the positive mass theorem. The book is rounded off with an extension of the electro-vacuum uniqueness theorem to self-gravitating scalar fields and harmonic mappings. This volume provides a rigorous textbook for graduate students in physics and mathematics. It also offers an invaluable, up-to-date referenc

Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduate-level introduction to differential geometry of complex Finsler metrics. Af

This author provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. His aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules. The book begins with a brief review of some aspects of Einstein's theory of relativity that are of particular importance for field theory, before going on to consider the relativistic quantum mechanics of free particles, interacting fields, and particles with spin. The techniques learnt in the chapters are then demonstrated in examples that might be encountered in real accelerator physics. Further chapters contain discussions of renormalization, massive and massless vector fields and unitarity. A final chapter presents concluding arguments concerning quantum electrodynamics. The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and di

The theorems of Hawking and Penrose show that space-times are likely to contain incomplete geodesics. Such geodesics are said to end at a singularity if it is impossible to continue the space-time and geodesic without violating the usual topological and smoothness conditions on the space-time. In this book the different possible singularities are defined, and the mathematical methods needed to extend the space-time are described in detail. The results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor. While the Friedmann singularity is analysed as an example, the emphasis is on general theorems and techniques rather than on the classification of particular exact solutions.

This book shows how modern cosmology and astronomy have led to the need to introduce dark matter in the universe. Some of this dark matter is in the familiar form of protons, electrons and neutrons, but most of it must have a more exotic form. The favoured, but not the only, possibility is neutrinos of non-zero rest mass, pair-created in the hot big bang and surviving to the present day. After a review of modern cosmology, this book gives a detailed account of the author's recent theory in which these neutrinos decay into photons which are the main ionising agents in hydrogen and nitrogen in the interstellar and intergalactic medium. This theory, though speculative, explains a number of rather different puzzling phenomena in astronomy and cosmology in a unified way and predicts values of various important quantities such as the mass of the decaying neutrino and the Hubble constant. Written by a cosmologist of the first rank, this topical book will be essential reading to all cosmologis

Experts in operations research and developers of softwareapplication systems have been treading separate paths formany years. It is urgently necessary to reset this course sothat the demanding require