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During the last decade, various powerful experimental tools have been developed, such as small angle X-ray and neutron scattering, X-ray and neutron reflection from interfaces, neutron spin-echo spectroscopy and quasi-elastic multiple light scattering and large scale computer simulations. Due to the rapid progress brought about by these techniques, one witnesses a resurgence of interest in the physicochemical properties of colloids, surfactants and macromolecules in solution. Although these disciplines have a long history, they are at present rapidly transforming into a new, interdisciplinary research area generally known as complex liquids or soft condensed matter physics: names that reflect the considerable involvement of the chemical and condensed matter physicists. This book is based on lectures given at a NATO ASI held in the summer of 1991 and discusses these new developments, both in theory and experiment. It constitutes the most up-to-date and comprehensive summary of the entire field.

Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated direction exist. The clue is to ask the right question. Classical geometry is a typical example in which the factorization of a motion into reflections or, more generally, of a collineation into central collineations, supplies valuable information on the geometric and algebraic structure. This mode of investigation has gained momentum since the end of last century. The tradition of geometric-algebraic interplay brought forward two branches of research which are documented in Parts I and II of these Proceedings. Part II deals with the theory of reflection geometry which culminated in Bachmann's work where the geometric information is encoded in properties of the group of motions expressed by relations in the generating involutions. This approach is the backbone of the classification of motion groups for the classical unitary and orthogonal planes. The axioms in this char- acterization are natural and plausible. They provoke the study of consequences of subsets of axioms which also yield natural geometries whose exploration is rewarding. Bachmann's central axiom is the three reflection theorem, showing that the number of reflections needed to express a motion is of great importance.

Pulsating and eccentric binary stars play a fundamentally important role in deciphering the mass distribution within stars. The present volume reviews the fundamental concepts of both radial and nonradial oscillations in the stars, including the Sun. Helio- and astroseismological results are reviewed, from the basics to the most recent developments. A new theory is presented, which seems to explain the mechanism of the light and radial velocity variations of recently discovered Ap stars. This textbook covers almost all kinds of variable stars of widely different characteristics. It will serve as a reference text for a very long time to come, not only for specialists but also for undergraduate students of physics and astronomy.

This NATO Advanced Study Institute provided an up dated understanding, from a fundamental and deep point of view, of the progress and current problems in the early universe, cosmic microwave background radiation, large scale structure, dark matter problem, and the interplay between them. The focus was placed on the Cosmic Microwave Background Radiation. Emphasis was given to the mutual impact of fundamental physics and cosmology, both at theoretical and experimental-or observational-levels, within a deep and well defined programme, and a global unifying view, which, in addition, provides of careful inter-disciplinarity. Special Lectures were devoted to neutrinos in astrophysics and high energy astrophysics. In addition, each Course of this series, introduced and promoted topics or subjects, which, although not being of purely astrophysical or cosmological nature, were of relevant physical interest for astrophysics and cosmology. Deep understanding, clarification, synthesis, careful interdisciplinarity within a fundamental physics framework, werethe maingoals ofthe course. Lectures ranged from a motivation and pedagogical introduction for students and participants not directly working in the field to the latest developmentsand most recent results. All Lectures were plenary, had the same duration and were followed by a discussion. The Course brought together experimentalists and theoretical physicists, astrophysicists and astronomers from a variety of backgrounds, including young scientists at post-doctoral level, senior scientists and advanced graduatestudentsas well.

This volume contains a series of lectures delivered at the 2nd course of the International School of Astrophysics at the "Ettore Majorana" Centre for Scientific Culture in Erice (Sicily) from June 22 to July 9, 1974. The course was jointly planned by L. Woltjer and myself and was fully supported by a grant from the NATO Advanced Study Institute Programme. It was organized with the aim of providing students and young researchers with an up to date account of the structure and evolution of galaxies and was attended by 94 participants from 20 countries. The study of galaxies is one of the most important areas of contemporary astrophysics both for its intrinsic interest and because it is a prerequisite to a quantitative understanding of the structure of the universe. Recently, a qualitatively new under­ standing has become available through both observational andtheore­ tical progress. On the observational side, new techniques applied at the large optical telescopes and, in particular, the impressive results obtained wi. th the high resolution radio telescopes have made it possible to obtain a detailed mapping of the structure of galaxies other than our own. At the same time, new theoretical insights and the availability of powerful computers to construct models holds out the hope that a full understanding of the structur. es of galaxies may be within our reach.

The ~irst international con~erence on differential games was held at Amherst, Massachusetts, in September 1969. A second meeting, partially supported by N.A.T.O., was held in Varenna, Italy, in June 1970. At these conferences many new theoretical results and applications, especially in economic problems, were presented. The present volume consists o~ the lectures presented at a N.A.T.O. Advanced Study Institute on the "Theory and Applications of Differential Games" held at the University of Warwick, Coventry, England, from 27th August to 6th September, 1974. The main contributions during the first week consisted of a survey of two person zero sum differential games by L. D. Berkovitz and four integrated lectures by R. J. Elliott and N. J. Kalton, who have made important contributions to the concept of "value" of a differential game. Applications were featured during the second week and included tactical air games, pursuit and evasion problems, as well as computational aspects. A closing lecture with historical perspectives was given by Rufus Issacs, the recognised pioneer of differential games theory.

The International Summer School on Statistical Distributions in Scientific Work was held in Trieste during July 1980 for a period of three weeks. The emphasis was on research, review, and exposition concerned with the interface between modem statistical distribution theory and real world problems and issues involving science, technology, and management. Both theory and applications received full attention at the School. The program consisted of a Short Intensive Preparation Course, a NATO Advanced Study Institute, and a Research Conference. While the relative composi­ tion of these activities varied somewhat in terms of instruction, exposition, research­ review, research, and consultation, the basic spirit of each was essentially the same. Every participant was both a professor and a student. The summer school was sponsored by the NATO Advanced Study Institutes Program; Consiglio Nazionale delle Ricerche, Italy; Regione Autonoma Friuli Ven­ ezia Giulia, Italy; National Institutes of Health, USA; Office of Naval Research, USA; The Pennsylvania State University; Universita di Roma; Universita di Trieste; International Statistical Ecology Program; International Transfer of Science and Technology, Belgium; and the participants and their home institutions and organiza­ tions. Research papers, research-review expositions and instructional lectures were spe­ cially prepared for the program. These materials have been refereed and revised, and are now available in a series of several edited volumes and monographs.

This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al­ gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet­ ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups.

edited by c. H. Lineweaver, J. G. Bartlett, A. Blanchard Observatoire Astronomique de Strasbourg, Strasbourg, France M. Signore Ecole normale superieure, Paris, France and J. Silk Departments of Astronomy and Physics, University of California at Berkeley, Berkeley, CA, U. S. A. Kluwer Academic Publishers Dordrecht / Boston / London Published in cooperation with NATO Scientific Affairs Division ISBN-13:978-94-010-6512-2 e-ISBN-13:978-94-009-0051-6 DOI:10. 107/ 978-94-009-0051-6 Softcover reprint of the hardcover 1st edition 1997 Dedication We dedicate these proceedings to the people who paid for it: taxpayers of the NATO alliance. Table of Contents PREFACE IX LIST OF PARTICIPANTS XI LISTOF CONTRIBUTORS Xlll I. Introduction, Mathematical Tools and Background An Introduction to CBR Studies: Spectrum, Degree-Scale Fluctuations, Foregrounds and Interferometry R. B. Partridge ElementsofGeneral Relativity, Cosmology and the Cosmic Microwave Background Jose L. Sanz 33 Statisticsand Random Functions in Astrophysics BernhardIT. Jones 67 Structure Formation Joseph Silk III II. eMB Anistropies CalculationofCosmic Background Radiation Anisotropies and Implications Emory F. Bunn 135 The CMB Anistropy Experiments: Cosmic Microwave Background George F. Smoot 185 viii III. CMB Spectrum The CMBR-Spectrum: ATheoretical Introduction Albert Stebbins 241 The CMB Spectrum George F. Smoot 271 IV. Astroparticle Physics Inflation and the Cosmic Background Radiation: What Every Cosmologist Needs to Know Michael S. Turner 309 Primordial Chemistry and Cosmic Background Radiation M. Signori, P. Encrenaz, R. MaoJi, B. Melchiorri, F. Melchiorri and D. Puy 345 The Cosmic Background Radiation and Elementary Particles Pierre Salati 365 V.

This volwne is the proceedings of the third school in particle astrophysics that Schramm and Galeotti have organized at Erice. The focus of thirs third school was the Generation of Cosmological Large-Scale Structure. It was held in November of 1996. The fIrst school in the series was on "Gauge Theory and the Early Universe" in May 1986, the second was on "Dark Matter in the Universe" in May 1988. All three schools have been successful under the auspices of the NATO Advanced Study Institute. This volume is thus the third in the series of the proceedings of these schools. The choice of the topic for this third school was natural, since the problem of generating a large-scale structure has become the most pressing problem in cosmology today. In particular, it is this generation of structure that is the interface between astronomical observations and particle models for the early universe. To date, all models for generating structures inevitably require new fundamental physics beyond the standard, SU x SU X U , model of high energy physics. The 3 2 I seeds for generating structures usually invoke unifIcation physics, and the matter needed to clump and form them seems to require particle properties that have not been seen in laboratories to date.

The theory of simple and complex fluids has made considerable recent progress, due to the emergence of new concepts and theoretical tools, and also to the availability of a large body of new experimental data on increas­ ingly complex systems, as well as far-reaching methodological developments in numerical simulations. This AS! aimed at providing a comprehensive overview of the most significant theoretical developments, supplemented by a few presentations of cutting-edge simulation and experimental work. The impact of the Institute in the overall landscape of Statistical Mechanics received an important recognition with its inclusion in the list of satellite events of STATPHYS20, the triennal international conference on Statistical Physics held in Paris in July 1998. These Proceedings contain the texts of the 13 Lecture Courses and 9 Invited Seminars delivered at Patti. Two clear trends emerge from these Proceedings: first, the diversity of new and unexpected theoretical results relating to classic models of liq­ uids, which have recently been subjected to fresh scrutiny; and secondly the parallel emergence of new concepts, models and methods, aimed at investigating complex fluids and phenomena, like the phase behaviour of fluids in pores, macromolecular assemblies, and the glass transition. Many of the new tools have their roots in traditional liquid state theory, and, in conjunction with fresh input from related fields, allow it wider applicability.

A few years ago, a real break-through happened in observational astronomy: the un­ derstanding of the effect of atmospheric turbulence on the structure of stellar images, and of ways to overcome this dramatic degradation. This opened a route to diffraction-limited observations with large telescopes in the optical domain. Soon, the first applications of this new technique led to some outstanding astrophysical results, both at visible and infrared wavelengths. Yet, the potential of interferometric observations is not fully foreseeable as the first long-baseline arrays of large optical telescopes are being built or cOIIllnissioned right now. In this respect a comparison with the evolution of radio-astronomy is tempting. From a situation where, in spite of the construction of giant antennas, low angular resolution was prevailing, the introduction of long baseline and very long baseline interferometry and the rapid mastering of sophisticated image reconstruction techniques, have brought on a nearly routine basis high dynamic range images with milliarcseconds resolution. This, of course, has completely changed our views of the radio sky.

The 1980 Maratea NATO Advanced Study Institute (= ASI) followed the lines of the 1976 Liege NATO ASI. Indeed, the interest of boundary problems for linear evolution partial differential equations and systems is more and more acute because of the outstanding position of those problems in the mathematical description of the physical world, namely through sciences such as fluid dynamics, elastodynamics, electro­ dynamics, electromagnetism, plasma physics and so on. In those problems the question of the propagation of singularities of the solution has boomed these last years. Placed in its definitive mathematical frame in 1970 by L. Hormander, this branch -of the theory recorded a tremendous impetus in the last decade and is now eagerly studied by the most prominent research workers in the field of partial differential equations. It describes the wave phenomena connected with the solution of boundary problems with very general boundaries, by replacing the (generailly impossible) computation of a precise solution by a convenient asymptotic approximation. For instance, it allows the description of progressive waves in a medium with obstacles of various shapes, meeting classical phenomena as reflexion, refraction, transmission, and even more complicated ones, called supersonic waves, head waves, creeping waves, ¿¿¿¿¿¿ The !'tudy of singularities uses involved new mathematical concepts (such as distributions, wave front sets, asymptotic developments, pseudo-differential operators, Fourier integral operators, microfunctions, ¿¿¿ ) but emerges as the most sensible application to physical problems. A complete exposition of the present state of this theory seemed to be still lacking.

The Supramolecular Compounds refer to organised multi-molecular assemblies and associated phenomena. The stability and the properties of these compounds strongly involve structural three-dimensional (3D) information. The crystal itself can be considered as a giant supermolecule. Thus, a thorough understanding of crystal structures and crystal growth provides a unique information on the intermolecular interactions. Indeed, each crystal reflects in a particular way the recognition properties of molecules. More so, modern crystallography allows to study in detail two­ or three-component crystalline solids in which the recognition processes can be seen from the structural standpoint. Crystallography of smaller and smaller single crystals, faster and faster experiments, time-resolved x-ray crystallography, are extremely potent source of physico-chemical information. The present Advanced Study Institute (A.S.I.) - which was planned five years ago as the 22nd Course of the International School of Crystallography (director: T. L. BLUNDELL), 1-11 June 1995, E. Majorana Centre, Erice, Italy - is probably the first international meeting specifically devoted to the Crystallography of Supramolecular Compounds. The presence of crystallographers, chemists and physicists enhanced the coherence of the typical sequence: Conception and Design - Synthesis - Structure and Visualisation - Properties. The interactive and interdisciplinary character of this research is central to the development of general structural models for a large spectrum of compounds: ionophores, cryptates, fullerenes, calixarenes, cyclodextrins, cyclotriveratrylenes, pillar type compounds, zeolites, hydrates, solvates and others.

This volume contains a series of lectures presented at the 4th Course of the International School of Astrophysics, held in Erice (Sicily) from July 9 - July 20, 1977 at the "E. Majorana" Centre for Scientific Culture. The course was fully supported by a grant from the NATO Advanced Study Institute Programme. It was attended by 82 participants from 15 countries. Even though the infrared portion of the electromagnetic spectrum covers an extensive interval from the red region of the optical spectrum (10,000 A) to the microwave radio region (1 mm), its role in astronomy has been minimal until the last two decades. Until very recently, the only objects observed were the sun, the moon and the planets. A primary reason for this late development was the lack of sensitive detectors and the necessary cryogenic technology that must accompany their use. Recent progress in this technology has been paralleled by an ever increasing interest of astronomers in infrared observations, leading to a number of ex­ tremely important results in different branches of astronomy. This becomes evident when one realizes that in many astrophysical conditions most of the energy is found to be channeled into the infrared portion of the electromagnetic spectrum. Stars were detected that yield most of their radiation in the infrared; these objects present a new view of stellar evolution, both in the birth and death stages.

This volume is the documentation of the second Course on 'Neutron Stars, Active Galactic Nuclei and Jets', held at Erice in September 1988. This second Course was devoted to our knowledge about neutron-star sources. The poster spoke of: pulsars, accreting X-ray sources and jet englnes, perhaps also UHE pulsars, X­ ra~' bursters and black-hole candidat.es. Neutron stars have even been proposed as the primary cosmic-ray boosters. Most of theil' properties are stil1 controversial, such as their birth mechanism (neutrino versus magnetic piston), internal structure (neutrons, quarks, strange particles), magnetic, thermal and spin histories, wind generation (hydrogen versus pair plasma, radiation versus centrifugal pressure), magnetospheric structure and accretion modes (along field lines versus quasi-Keplerian). The listed controversies have largely survived through the Course and entered into the proceedings. Several lecturers speak of 'magnetic-field decay' in neutron stars, of the 'recycling' of old pulsars, and of 'accretion-induced collapse' of white dwarfs as though such processes were textbook knowledge. Terms and abbreviations like RPSR (=recycled pulsar), spinup line, AIC, and ADC (=accretion disk corona) help to foster the assumptions. It is not clear to me at this time whether any of these notions has an application to reality.

This book contains the transcripts of the invited lectures presented at the NATO Advanced Study Institute on "Numerical Solution of Partial Differential Equations". The Study Institute was held at the Netherlands-Norwegian Reactor School, Institutt for Atomenergi, Kjeller, Norway, 20th - 24th August 1973. The members of the Scientific Advisory Committee were: A. R. Mitchell, University of Dundee, Scotland I. HoI and, University of Trondheim, Norway T. Havie, UniverSity of Trondheim, Norway The members of the Organizing Committee were: E. Andersen, Institutt for Atomenergi, Kjeller, Norway G. E. Fladmark, Institutt for Atomenergi, Kjeller, Norway J. G. Gram, Institutt for Atomenergi, Kjeller, Norway The aim of the Study Institute was to bring together mathe­ maticians and engineers working with numerical methods. The papers presented covered both theory and application of methods for solution of partial differential equations. The topics were finite element methods, finite difference methods, and methods for solution of linear and nonlinear systems of equations with application to continuum mechanics and heat transfer. The total number of participants was 68. Their names are given at the end of the book. The publication of these proceed­ ings could be realized through the kind cooperation of the lec­ turers. The Advanced Study Institute was financially sponsored by NATO Scientific Affairs Division. The Organizing Committee wishes to express its gratitude for this support. Valuable assistance was given by Mrs. G.

This volume contains the proceedings of an Advanced Study and Re­ search Institute on Theoretical Approaches to Scheduling Problems. The Institute was held in Durham, England, from July 6 to July 17, 1981. It was attended by 91 participants from fifteen different countries. The format of the Institute was somewhat unusual. The first eight of the ten available days were devoted to an Advanced Study Insti­ tute, with lectures on the state of the art with respect to deter­ ministic and stochastic scheduling models and on the interface between these two approaches. The last two days were occupied by an Advanced Research Institute, where recent results and promising directions for future research, especially in the interface area, were discussed. Altogether, 37 lectures were delivered by 24 lecturers. They have all contributed to these proceedings, the first part of which deals with the Advanced Study Institute and the second part of which covers the Advanced Research Institute. Each part is preceded by an introduction, written by the editors. While confessing to a natural bias as organizers, we believe that the Institute has been a rewarding and enjoyable event for everyone concerned. We are very grateful to all those who have contributed to its realization.

This volume is based on lectures and discussions presented at a NATO Advanced Study Institute on ELF and VLF Radio Wave Propagation, which was held in Norway April 1974. The study of propagation of electromagnetic waves with frequen­ cies below 100 kHz has long traditions in ionospheric physics. To-day, this frequency range is still of great importance, both to the physicist, who uses the waves as diagnostic tools to study the earth's environment and to the engineer who exploits the characteris­ tics of these waves to improve communications, navigation and timing systems. In recent years the active interest in the field has led to very rapid progress in the development of propagation theory as well as in the application of this theory to the solution of practical problems. The intention of the Organizing Committee for this Conference was to bring together theoreticians and experi­ mentalists working on the various aspects of wave propagation, in order to stimulate a fruitful discussion and exchange of ideas.

Our Galactic center's proximity allows astronomers to study physical pro­ cesses within galactic nuclei at a level of detail that will never be possible in the more distant, but usually also more spectacular, extragalactic systems. Recent advances in instrumentation from the radio, through the submillime­ ter and infrared wavebands, and out to the X- and "'(-ray bands now allow observations of the Galactic Center over thirteen orders of magnitude in wave­ length. Our knowledge about the central few hundred parsecs of our Galaxy has consequently increased vastly over the past decade. The same new instru­ ments provide high resolution, high quality measurements of nearby ''normal'' galactic nuclei; that is, nuclei whose modest energy output is comparable to that of our own (and most other) galaxies. Theorists, spurred in part by the new observations, have been able to refine models of the energetics, dynam­ ics, and evolution of the gas and stellar systems deep within galactic nuclei.

The Proceedings of the tenth Advanced Study Institute (ASI) on Tech­ niques and Concepts of High Energy Physics are dedicated to Jane and Bob Wilson. Jane joined Bob at St. Croix for the first session of this Institute, after Bob had stepped down as director of Fermilab, and was scheming to build a modest charm factory in the parking lot of Columbia University's Nevis Laboratory. Through the years, Bob has been a great friend of the School, and much of its success and flavor can be attributed to his guidance and support. The 1998 meeting was held once again at the Hotel on the Cay, and, as before, the work and the fun went on very enjoyably. We had a to­ tal of 76 participants from 23 countries, with the main financial support for the meeting provided by the Scientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was co-sponsored by the U. S. Department of Energy, by the Fermi National Accelerator Laboratory (Fermilab), by the U.S. National Science Foundation, and by the University of Rochester. As in the case of the previous ASIs, the scientific program was designed for advanced graduate students and recent PhD recipients in experimental particle physics. The present volume of lectures should complement and update the material published (by Plenum) for the first nine ASIs and prove to be of value to a wider audience of physicists.

by K. Lambeck, R. Sabadini and E. B08Chi Viscosity is one of the important material properties of the Earth, controlling tectonic and dynamic processes such as mantle convection, isostasy, and glacial rebound. Yet it remains a poorly resolved parameter and basic questions such as whether the planet's response to loading is linear or non-linear, or what are its depth and lateral variations remain uncertain. Part of the answer to such questions lies in laboratory observations of the rheology of terrestrial materials. But the extrapolation of such measurements from the laboratory environment to the geological environment is a hazardous and vexing undertaking, for neither the time scales nor the strain rates characterizing the geological processes can be reproduced in the laboratory. General rules for this extrapolation are that if deformation is observed in the laboratory at a particular temperature, deformation in geological environments will occur at a much reduced temperature, and that if at laboratory strain rates a particular deformation mechanism dominates over all others, the relative importance of possible mechanisms may be quite different at the geologically encountered strain rates. Hence experimental results are little more than guidelines as to how the Earth may respond to forces on long time scales.

This volume contains refereed papers and extended abstracts of papers presented at the NATO Advanced Research Workshop entitled 'Numerical Integration: Recent Developments, Software and Applications', held at Dalhousie University, Halifax, Canada, August 11-15, 1986. The Workshop was attended by thirty-six scientists from eleven NATO countries. Thirteen invited lectures and twenty-two contributed lectures were presented, of which twenty-five appear in full in this volume, together with extended abstracts of the remaining ten. It is more than ten years since the last workshop of this nature was held, in Los Alamos in 1975. Many developments have occurred in quadrature in the intervening years, and it seemed an opportune time to bring together again researchers in this area. The development of QUADPACK by Piessens, de Doncker, Uberhuber and Kahaner has changed the focus of research in the area of one dimensional quadrature from the construction of new rules to an emphasis on reliable robust software. There has been a dramatic growth in interest in the testing and evaluation of software, stimulated by the work of Lyness and Kaganove, Einarsson, and Piessens. The earlier research of Patterson into Kronrod extensions of Gauss rules, followed by the work of Monegato, and Piessens and Branders, has greatly increased interest in Gauss-based formulas for one-dimensional integration.