Bücher der Reihe NATO Science Series C

This volume is the documentation of the first Course on 'Neutron Stars, Active Galactic Nuclei and Jets', of an Erice School with a wide astro- physical scope. The choice of the subject was made because of an apparent similari- ty - stressed already at earlier meetings - of four classes of astrophy- sical jet sources: Active Galactic Nuclei, Young Stellar Objects, Binary Neutron Stars and Binary White Dwarfs. They share important properties such as their morphology, high variability and large veloci- ty gradients as well as - with some inference - their broad spectrum, hypersonic outflow and core/lobe power ratio. Despite this apparent similarity of the four source classes, quite different models have been put forward for their description: (i) The central engine of active galactic nuclei has been generally thought to be a black hole, in contrast to the central engine of young stellar objects and cometary nebulae which apparently is a pre-T-Tauri star, some six orders of magnitude less compact, and to the central engine of planetary nebulae which mayor may not be a binary white dwarf. (ii) The elongated lobes, or flow patterns, have been often interpreted as highly directional stellar wind outflows whereas in a few well- mapped cases, the elongated flow appears to be 'pumped up' through a much narrower channel, or jet, both in the extragalactic and stellar sources.

The per iod of an oscillator tells us much about its structure. J. J. Thomson's deduction that a particle with the e/rn of an electron was in the atom is perhaps the most stunning instance. For us, the deduction of the mean density of a star from its oscillation period is another important example. What then can we deduce about an oscillator that is not periodic? If there are several frequencies or if the behavior is chaotic, may we not hope to learn even more delicate vital statistics about its workings? The recent progress in the theory of dynamical systems, particularly in the elucidat ion of the nature of chaos, makes it seem reasonable to ask this now. This is an account of some of the happenings of a workshop at which this question was raised and discussed. ~iTe were inc0rested in seeing ways in which the present understanding of chaos might guide astrophysical modelling and the interpretation of observations. But we did not try to conceal that we were also interested in chaos itself, and that made for a pleasant rapport between the chaoticists and astrophysicists at the meeting. We have several introductory papers on chaos in these proceedings, particularly on the analysis of data from systems that may be suspected of chaotic behavior. The papers of Geisel, Grassberger and Guckenheimer introduce the ways of characterizing chaos and Perdang illustrates how some of these ideas may be put into practice in explicit cases.

Problems in decision making and in other areas such as pattern recogni- tion, control, structural engineering etc. involve numerous aspects of uncertainty. Additional vagueness is introduced as models become more complex but not necessarily more meaningful by the added details. During the last two decades one has become more and more aware of the fact that not all this uncertainty is of stochastic (random) cha- racter and that, therefore, it can not be modelled appropriately by probability theory. This becomes the more obvious the more we want to represent formally human knowledge. As far as uncertain data are concerned, we have neither instru- ments nor reasoning at our disposal as well defined and unquestionable as those used in the probability theory. This almost infallible do- main is the result of a tremendous work by the whole scientific world. But when measures are dubious, bad or no longer possible and when we really have to make use of the richness of human reasoning in its variety, then the theories dealing with the treatment of uncertainty, some quite new and other ones older, provide the required complement, and fill in the gap left in the field of knowledge representation. Nowadays, various theories are widely used: fuzzy sets, belief function, the convenient associations between probability and fuzzines~ etc *** We are more and more in need of a wide range of instruments and theories to build models that are more and more adapted to the most complex systems.

This NATO Advanced Research Workshop was devoted to the pre- sentation, evaluation, and critical discussion of numerical methods in nonrelativistic and relativistic hydrodynamics, radia- tive transfer, and radiation-coupled hydrodynamics. The unifying theme of the lectures was the successful application of these methods to challenging problems in astrophysics. The workshop was subdivided into 3 somewhat independent topics, each with their own subtheme. Under the heading radiation hydrodynamics were brought together context, theory, methodology, and application of radia- tive transfer and radiation hydrodynamics in astrophysics. The intimate coupling between astronomy and radiation physics was underscored by examples from past and present research. Frame-dependence of both the equation of transfer (plus moments) and the underlying radiation quantities was discussed and clarified. Limiting regimes in radiation-coupled flow were identified and described; the dynamic diffusion regime received special emphasis. Numerical methods for continuum and line transfer equations in a given background were presented. Two examples of methods for computing dynamically coupled radia- tion/matter fields were given. In l-d and assuming LTE the complete equations of radiation hydrodynamics can be solved with current computers. Such is not the case in 2- or 3-d, which were identified as target areas for research. The use of flux-limiters was vigorously discussed in this connection, and enlivened the meeting.

Recent developments in supersymmetric field theory, string theory, and brane theory have been revolutionary. The main focus of the present volume is developments of M-theory and its applications to superstring theory, quantum gravity, and the theory of elementary particles. Topics included are D-branes, boundary states, and world volume solitons. Anti-De-Sitter quantum field theory is explained, emphasising the way it can enforce the holography principle, together with the relation to black hole physics and the way Branes provide the microscopic interpretation for the entropy of black holes. Developments in D-branes within type-I superstring and related theories are described. There are also possible phenomenological implications of superstring theory that would lie within the range of quantum gravity effects in the future generation of accelerators, around 1 TeV.

An up-to-date presentation of the progress and current problems in the early universe, cosmic microwave background radiation, large scale structure formation, and the interplay between them. The emphasis is on the mutual impact of fundamental physics and cosmology, both at theoretical and experimental (observational) levels within a deep, well- focused and well-defined programme. The nature of the domain itself leads to different aspects, approaches and points of view on the same topic. Special care has been taken to provide the reader the basis of the different, sometimes competing lines of research. All contributions are uniformly excellent, with a careful selection of the subjects and approaches covered, presenting a unifying and rigorous view of the field. Audience: experimentalists and theoreticians from a variety of backgrounds: physics, astrophysics and astronomy. An excellent reference for post-doctoral scientists. Useful for senior scientists and advanced graduate students.

The theory of stellar atmospheres is one of the most important branches of modern astrophysics. It is first of all a major tool for understanding all aspects of stars. As the physical properties of their outer layers can now be found with high precision, firm conclusions can be drawn about the internal structure and evolution of stars. Moreover, improvements in our knowledge of the chemical composition of stars is shedding new light on the chemical evolution of galaxies and of the Universe as a whole. Because the outer layers of stars are among the best-understood astrophysical objects, the theory of stellar atmospheres plays an important role in the study of many other types of objects. These include planetary nebulae, H II regions, interstellar matter, and objects of interest in high-energy astrophysics, such as accretion disks (close binaries, dwarf novae, cataclysmic variables, quasars, active galactic nuclei), pulsar magnetospheres, and Seyfert galaxies. Finally, as stars provide a laboratory in which plasmas can be studied under more extreme conditions than on earth, the study of stellar atmospheres has strong connections with modern physics. Astronomical observations provided a vital stimulus in the early stages of quantum theory and atomic physics; even today topics such as low-temperature dielectronic recombination develop hand in hand with the interpretation of stellar and nebular spectra. Early work on MHD was similiarly motivated. Many such connections remain to be explored.

Particle production is an important topic in nuclear and particle physics. At high energies, particle production is considered to proceed via parton branching and subsequent fragmentation into hadrons. The study of the dynamics of this process and the study of the structure of hadrons in the context of quantum chromodynamics (QCD) belong to the challenges of the standard model of elementary particle physics, requiring new, nonperturba- tive approaches in field theory. Within a nucleus, many-body dynamics is important and particle production may be used to determine many features of a non-equilibrium quantum system at low or high temperatures. At this Advanced Study Institute the different aspects of particle pro- duction were expanded upon in a series of lectures given by experts in their fields, covering topics ranging from near-threshold meson production in proton-proton collisions to correlations in multi-GeV jet fragmentation in high-energy scattering processes and signals of a quark-gluon plasma formed in ultra-relativistic heavy-ion collisions. Strong emphasis was placed not only on state of the art research, but also on the necessary physics back- ground. The lectures were supplemented by problem sets and discussion sessions. There was also time for students to present short contributions on their research.

For more than 25 years the Standard Model of particle physics has withstood the confrontation with experimental results of increasing precision, but this does not imply that the Standard Model can answer all questions about the ultimate constituents of nature. This book presents a critical examination of the latest experimental results and confronts them with the predictions of the Standard Model. Besides discussions of accelerator results from LEP, HERA and the TEVATRON, attention is paid to the unresolved problems of neutrino oscillations, CP violation, dark matter and cosmology. New theoretical ideas are also analyzed in order to explore possible extensions of the standard model. Realistic plans for future accelerators are presented and their physics potential is discussed, paving the way for the next generation of particle physics experiments.

This book collects the lectures delivered by the Authors during the NATO ASI "e;Fundamentals and Developments of Photocatalytic and Photoelectrochemical Processes"e;, held in Erice (Trapani, Italy) from May 20th to June 2nd 1984. The ASI was devoted to the general field of photochemical conversion and storage of solar energy. It had the aim of defining the "e;state of art"e; and of outlining perspectives, lines of development and practic al utilization of this form of energy. The world energy crisis has stimulated scientists to investigate new routes for finding and testing methods and processes for obtaining renewable and cheap sources of energy. Within this framework, the possibility of solar energy utilization on a large scale must overcome the stage of discovering efficient processes for the photochemical conversion and for the storage. The most promising way for achieving this goal seems the photosplitting of water and related reactions. The methods for obtaining the water photosplitting are essentially based on photoelectrochemical cells and on photocatalytic systems (gas-solid and gas-liquid-solid). Extensive research work is currently done all over the world both in universities and in industrial laboratories in these areas. The ASI has given to the audience a general view of the fundamental aspects and as much as possible a detailed insight of the various methods and processes. A section has been also devoted to the photoreactors, a field in which the interest is ix x FOREWORD steadily increasing and whose development is essential for the practical exploitation of the various methods.

This volume contains the proceedings of the NATO Advanced Research Workshop on `Quantum Chaos -- Theory and Experiment', held at the Niels Bohr Institute, University of Copenhagen, from 28 May to 1 June 1991. The work brings together leading quantum chaos theorists and experimentalists and greatly improves our understanding of the physics of quantum systems whose classical limit is chaotic. Quantum chaos is a subject of considerable current interest in a variety of fields, in particular nuclear physics, chemistry, statistical mechanics, atomic physics, condensed matter physics and nonlinear dynamics. The volume contains lectures about the currently most active fronts of quantum chaos, such as scars, semiclassical methods, quantum diffusion, random matrix spectra, quantum chaos in atomic and nuclear physics, and possible implications of quantum chaos for the problem of quantum measurement. Part of the book -- The Physics of Quantum Measurements -- is dedicated to the memory of John Bell.

The last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "e;Bifurcations and periodic orbits of vector fields"e;. This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy- namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work.

The use of numerical grid methods to solve the Schrodinger equation has rapidly evolved in the past decade.The early attempts to demonstrate the computational viability of grid methods have been largely superseded by applications to specific problems and deeper research into more sophisticated quadrature schemes. Underpinning this research, of course, is the belief that the generic nature of grid methods can enjoy a symbiotic development with advances in computer technology, harnessing this technology in an effective manner. The contributions to this proceedings demonstrate these points in full: several appli- cations displayed creative use and extension of existing grid methodology; other research concentrated on the development of new quadrature schemes or mixed numerical meth- ods. The research represented ranges from highly specific spectral simulations of van der Waals complexs to general schemes for reactive scattering. The novelty of grid methods in Density Functional Theory calculations should also be highlighted since it represents an alternative to standard basis set expansion techniques and might offer distinct advantages to the standard techniques. A deliberate attempt was made to present research material with more motivational and background discussion than is typical of research publications. It is hoped that these contributed proceedings will be useful to students and researchers outside the field to have a rapid and complete introduction to many of the exciting uses of grid methodology in atomic and molecular physics. Special thanks are due to the NATO Science Committee for its generous support of the activities of this workshop.

This volume contains edited versions of 11 contributions given by main speakers at the NATO Advanced Study Institute on lReal and Complex Dynamical Systems in Hiller0d, Denmark, June 20th - July 2nd, 1993. The vision of the institute was to illustrate the interplay between two important fields of Mathematics: Real Dynamical Systems and Complex Dynamical Systems. The interaction between these two fields has been growing over the years. Problems in Real Dynamical Systems have recently been solved using complex tools in the real or by extension to the complex. In return, problems in Complex Dynamical Systems have been settled using results from Real Dynamical Systems. The programme of the institute was to examine the state of the art of central parts of both Real and Complex Dynamical Systems, to reinforce contact between the two aspects of the theory and to make recent progress in each accessible to a larger group of mathematicians.

Molecular magnetism is a new field of research dealing with the synthesis and study of the physical properties of molecular assemblies involving open-shell units. It is essentially interdisciplinary, joining together organic, organometallic and inorganic chemists, as well as theoreticians, physicists and materials scientists.At the core of research into molecular magnetism lie design and synthesis of new molecular assemblies exhibiting bulk properties such as long-range magnetic ordering or bistability with an hysteresis effect, which confers a memory effect on the system. In such terms, magnetism may be considered a supramolecular function.The first eight contributions to this volume present the state of the art in organic supramolecular chemistry, emphasising interlocked systems and molecular trees. The following six articles are devoted to molecular materials constructed from organic radicals and transition metal units. Molecular bistability is then focused on, followed by metal-organic and coordination magnetic materials. A new approach to nano-sized particles closes the work.

Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.

The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre- quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.

This book of the proceedings of the 1997 NATO Advanced Study Institute (ASI) on Direct Methods for Solving Macromolecular Structures was assembled from the lecturers' contributions and represents a comprehensive and in-depth overview of crystallographic structure determination methods for macromolecules. While having a focus based on the direct methods, the Institute adopted an inclusive and broad perspective. Thus, both direct and experimental phasing techniques are presented in this book, highlighting their complementarities and synergies. As weil, methodologies spanning the full crystallographic image reconstruction process - from low resolution envelope definition to high resolution atomic refinement- are discussed. The first part of the book introduces the array of tools currently used in structure determination, whether originating from a mathematical, computational or experimental framework. This section of the book displays the variety and ingenuity of old and new phasing approaches developed to solve increasingly complex structures. Some of the contributions focus on recent developments and/or implementations that have given older approaches a new life. A case in point is the re-implementation of Buerger's superposition approach, which is now solving protein structures. Another beautiful example is found in the introduction to the traditional multiple isomorphous replacement approach where new techniques, such as site-directed mutagenesis and the use of inert gases in the preparation of heavy atom derivatives, are described. Equally impressive are the presentations of newer approaches, which take advantage of advances on the experimental front (e. g.

The first references to statistical extremes may perhaps be found in the Genesis (The Bible, vol. I): the largest age of Methu'selah and the concrete applications faced by Noah-- the long rain, the large flood, the structural safety of the ark --. But as the pre-history of the area can be considered to last to the first quarter of our century, we can say that Statistical Extremes emer- ged in the last half-century. It began with the paper by Dodd in 1923, followed quickly by the papers of Fre-chet in 1927 and Fisher and Tippett in 1928, after by the papers by de Finetti in 1932, by Gumbel in 1935 and by von Mises in 1936, to cite the more relevant; the first complete frame in what regards probabilistic problems is due to Gnedenko in 1943. And by that time Extremes begin to explode not only in what regards applications (floods, breaking strength of materials, gusts of wind, etc. ) but also in areas going from Proba- bility to Stochastic Processes, from Multivariate Structures to Statistical Decision. The history, after the first essential steps, can't be written in few pages: the narrow and shallow stream gained momentum and is now a huge river, enlarging at every moment and flooding the margins. Statistical Extremes is, thus, a clear-cut field of Probability and Statistics and a new exploding area for research.