This volume contains the texts of the principal survey papers presented at ALGORITHMS -and ORDER, held· at Ottawa, Canada from June 1 to June 12, 1987. The conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the University of Ottawa, and the Natural Sciences and Engineering Research Council of Canada. We are grateful for this considerable support. Over fifty years ago, the Symposium on Lattice Theory, in Charlottesville, U.S.A., proclaimed the vitality of ordered sets. Only twenty years later the Symposium on Partially Ordered Sets and Lattice Theory, held at Monterey, U.S.A., had solved many of the problems that had been originally posed. In 1981, the Symposium on Ordered Sets held at Banff, Canada, continued this tradition. It was marked by a landmark volume containing twenty-three articles on almost all current topics in the theory of ordered sets and its applications. Three years after, Graphs and Orders, also held at Banff, Canada, aimed to document the role of graphs in the theory of ordered sets and its applications. Because of its special place in the landscape of the mathematical sciences order is especially sensitive to new trends and developments. Today, the most important current in the theory and application of order springs from theoretical computer seience. Two themes of computer science lead the way. The first is data structure. Order is common to data structures.

The ihsan Ketin NATO Advanced Study Institute on the Tectonic Evolution of the Tethyan Region was conceived in 1982 in Veszprem, Hungary, when three of the organizers (B. C. B. , L. H. R. and A. M. C. 9. ) had come together for a meeting on the tectonics of the Pannonian basin. All three of us had experience in the Tethyan belt and all three of us had been for some time deploring the lack of communication among workers of this immense orogenic belt. Much new work had been completed in such previously little-known areas as Turkey, Iran, Afghanistan, the People's Republic of China, the entire Himalayan region, as well as new work in the European parts of the chain. Also, ironically, parts of the belt had just been closed to field work for political reasons, so it seemed as if the time was right to sit back and consider what had been done so far. Because the Istanbul group had had an interest in the whole of the Tethyan belt and because that ancient city was more centrally locElted with excellent opportunities to see both Palaeo- and Neo-Tethyan rocks in a weekend excursion, we thought that Istanbul was a natural place for such a meeting, not mentioning its own considerable attractions for the would-be contributors. A happy coincidence was that Prof.

The idea for organizing an Advanced Study Institute devoted largely to neutron star timing arose independently in three places, at Istanbul, Garching and Amster­ dam; when we became aware of each other's ideas we decided to join forces. The choice of a place for the Institute, in Turkey, appealed much to us all, and it was then quickly decided that Qe§me would be an excellent spot. When the preparations for the Institute started, early in 1987, we could not have guessed how timely the subject actually was. Of course, the recently dis­ covered QPO phenomena in accreting neutron stars and half a dozen binary and millisecond radio pulsars known at the time formed one of the basic motivations for organizing this Institute. But none of us could have guessed that later in 1987 we were to witness the wonderful discovery of the binary and millisecond radio pulsars in globular clusters and, -as if Nature wished to give us a special present for this the discovery in March 1988 of a millisecond pulsar in an eclipsing binary Institu- system, the first eclipsing radio pulsar ever found, and the second fastest in the sky! The discussion of this pulsar, its formation and fate was one of the highlights of this meeting, especially since its discoverers were among the participants of the Institute and could provide us with first-hand information.

Proceedings of the NATO Advanced Study Institute, Banff Centre, Canada, April 27-May 5, 1988

For many years, the two subjects of (1) postglacial rebound and its potential for generating earthquakes and (2) the seismicity of passive continental ml!rgins have been of interest and concern to earth scientists on both sides of the North Atlantic. New data and theoretical interpretations have given rise to vigorous discussions on how much the two phenomena inter-relate and whether a significant controlling factor on seismicity in northeastern North America and Scandinavia is the crustal uplift that has been occurring since the latest ice age. The lack of a good understanding of these phenomena presented a particular problem for engineering seismologists attempting to prepare accurate seismic hazard estimates for facili­ ties both on land (e. g. , nuclear power stations and radioactive waste repositories) and offshore (e. g. , petroleum production facili­ ties) . The NATO Advanced Research Workshop programme provided an opportuni ty to bring together a group of relevant geophysicists, geologists and geodesists from both sides of the North Atlantic, and a workshop on "Causes and Effects of Earthquakes at Passive Margins and in Areas of Postglacial Rebound on both Sides of the North Atlantic" was held in Vordingborg, Denmark, 9-13 May 1988. The sup­ port of the NATO Science Committee is gratefully acknowledged.

People who attended the NATO Advanced Study Institute (ASI) entitled NEW THEORETICAL CONCEPTS FOR UNDERSTANDING ORGANIC REAC­ TIONS held at Sant Feliu de Gufxols on the Costa Brava of Spain had a unique experience. They have seen the evolution of the field from qualitative arguments through the generation of Potential Energy Surfaces (PES) to the use of PES in molecular dynamics. The excellent lectures that were dedicated to the various aspects of Potential Energy Surfaces clearly revealed a colossal amount of ma­ terial that represents our current understanding of the overall problem. It is our hope that the present volume will recreate the excitement in the readers that we all experienced during the meeting in Spain. One can say, without too much exaggeration, that chemistry has become and exercise on potential energy surfaces (PES). Structural (position of the energy minima), spectroscopic (vicinity around the minima), and reactivity (reaction path along the surface) properties may be determined from the analysis of PES. New theoretical tools, together with recent developments in computer technology and programming, have allowed to obtain a better knowledge of these surfaces, and to extract further chemical information from them, so new horizons have been added to Theoretical Organic Chemistry.

The increasing production of industrial goods, heat, and energy, as well as traffic, has led to the release of considerable amounts of toxic trace metals to the atmosphere. The result is elevated concentrations of toxic metals in local populations and eco­ systems. Recently the problem of atmospheric long-range transport of trace metals has also been recognized. Significant amounts of these pollutants are disposed and deposited both on regional and global scales. In the atmosphere they may influence the chemical reactions. Of particular interest is their catalytic effect on the oxidation prosesses taking place in water droplets or on the surface of wet particles (e. g. the oxidation of sulphur dioxide to sulphate), however, the main environmental impact starts when the atmospheric trace metals are deposited on ground and vegetation and subsequently brought into the water circulation. During the later years significant progress has been made in the development of equipment to reduce and control the atmospheric emissions of toxic trace metals. This particularly applies to electrostatic precipitators and wet scrubbers for the collection of fine particles. The main objective of the workshop was to survey present knowledge concerning the sources, atmospheric fluxes, sinks and chemical impact of the atmospheric trace metals, and to review the developments of emission control equipment and the perspectives to reduce the potential risks from toxic metals. During the first two days of the meeting, 15 invited review papers were presented.

There are only few topics in organometallic chemistry, which have stimulated research activities in as many areas, as transition-metal carbene (alkylidene) complexes. About 25 years after the first planned synthesis of a carbene complex in E.O. Fischer's laboratory in Munich the NATO Advanced Research Workshop on Transition-Metal Carbene Complexes was the first meeting which,brought together scientists from different disciplines to discuss inorganic, organic, theoretical structural catalysis-related aspects of metal carbene chemistry. The 70th birthday of Professor E.O. Fischer was a good occasion for this enterprise. The organizers of the meeting (K.D. Dotz, Marburg; F.R. KreiBl, Munchen; U. Schubert, Wurzburg) were encouraged by the fact that most of the leading scientists in this area were able to participate in the workshop. The very high standard of the contributions is reflected in this book, which contains papers from the majority of the participants. The Proceedings show the state of the art in metal carbene chemistry and will hopefully be a landmark in the development of this area of chemistry. Generous financial support for the workshop and for the preparation of this book was provided by the Scientific Affairs Division of NATO and some companies. The organizers also acknowledge the efforts of the staff of the Bildungs­ zentrum der Hans-Seidel-Stiftung in Wild bad Kreuth for creating a pleasant and stimulating atmosphere during the conference.

Quantum mechanical calculations in physics, chemistry and biology are widely recognized as useful interpretative and predictive tools. Unfortunately, they are plagued by unfavorable convergence limitations due to the use of finite linear combinations of basis functions. With the current computer technologies, there is a possible way out to the situation by solving numerically the corresponding wave equations. The present interest and need for numerical determination of electronic structure of atoms, diatomic and poly atomic molecules led us to organize a NATO-ARW devoted to these questions. The aim of the meeting was to provide a review of the state of the art about techniques and applications. The organizing committee consisted of Drs. G. Berthier, P. Claverie, M. Defranceschi, J. Delhalle, H.J. Monkhorst and P. Pyykk6. It was a great sorrow for us to be informed in January 88 of the death of Professor P. Claverie who supported so enthusiastically the idea of having such a meeting organized. The NATO Advanced Research Worshop on : " Numerical Determination of the Electronic Structure of Atoms, Diatomic and Poly atomic Molecules" was held at Versailles (France) from April 17th till April 22th, 1988.

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.

This volume certainly is a Conference Proceedings, the Proceedings of the NATO Advanced Research Workshop (ARW) on "Unsaturated Flow in Hydrologic Modeling" held at "Les Villages du Soleil" near ArIes, France from June 13 to 17, 1988. Let me therefore acknowledge properly, at the very beginning, the gratitude of all the participants to the NATO Science Committee for its generous support and worthwhile goal of bringing together scientists of many countries to communicate and share their experiences. Particular thanks are extended to the director of the program, Dr. Luis Vega da Cunha for his interest and understanding. On the other hand this volume is also, and probably more so, a Textbook that fills a gap in the field of unsaturated flow. Many treatises on the subject present the theory in its different aspects. Hardly any explain in details how the different pieces can be put together to address realistic problems at the basin scale. The various invited contributions to the ARW were structured in a subject progression much as chapters are organized in a book. The intent of the ARW was to assess the current state of knowledge in "Unsaturated Flow" and its use in "Hydrologic Modeling Practice". In a sense the interest in fundamentals of unsaturated flow in this ARW was not just for the sake of knowledge but also and primarily for the sake of action. Can such fundamental knowledge be utilized for better management of the water resource? was the basic question.

A NATO Advanced Study Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987. This meeting was jointly supported by NATO and the Natural Sciences and Engineering Research Council of Canada, and was sponsored in part by the Canadian Mathematical Society. This book is the volume of proceedings for that meeting. Algebraic K-theory is essentially the study of homotopy invariants arising from rings and their associated matrix groups. More importantly perhaps, the subject has become central to the study of the relationship between Topology, Algebraic Geometry and Number Theory. It draws on all of these fields as a subject in its own right, but it serves as well as an effective translator for the application of concepts from one field in another. The papers in this volume are representative of the current state of the subject. They are, for the most part, research papers which are primarily of interest to researchers in the field and to those aspiring to be such. There is a section on problems in this volume which should be of particular interest to students; it contains a discussion of the problems from Gersten's well-known list of 1973, as well as a short list of new problems.

This edition is the labor of many enthousiastic scientists who were invited to teach at a NATO Advanced Study Institute on the "Spectroscopy of Inorganic Bioactivators" which took place on August 20 -30, 1988 at Club Poseidon, Loutraki, Greece. In this book the subjects were taught through several well prepared lectures. These lectures stretch the fact that scientific knowledge is the painfully gathered product of many wonderful human minds. I made an attempt to divide the lectures into separate chapters, however, there is interaction among the lectures, as I hope the book will show. First, there is introductory on an lecture supercomputing and super computers and their applications to solving structures of biological molecules followed by a state-of-the-art x-ray diffraction method at pi co second times. Important new advances have been made in x-ray diffraction analysis at picosecond times, in Hadamard spectroscopy, in micro-Raman spectroscopy in the Near Infrared region (1. 01 ~m) and remote sensing by Fourier Transform Infrared Spectroscopy. The chapters that follow include applications of spectroscopic technique to vii viii biologically important molecules, such as, DNA, proteins, membranes, and metal ion-biological molecule interactions. I would like to express my thanks to all the authors for their contributions and their cooperation in submitting their manuscript. I also thank the NATO Science Committee for making this possible. The field looks very promising for significant and exciting developments in the application of spectroscopy to bioactivators.

The NATO Advanced Research Workshop on "Paleoclimatology and Paleometeorology: Modem and Past Patterns of Global Atmospheric Transport" (held at Oracle, Arizona, USA from November 17-19, 1987) brought together atmospheric chemists, physicists, and meteorologists who study the origin and transport of modem-day mineral and biological aerosols with geologists and paleobotanists who study the sedimentary record of eolian and hydrologic processes along with modelers who study and conceptualize the processes influencing atmospheric transport at present and in the past. Presentations at the workshop provided a guide to our present knowledge of the entire spectrum of processes and phenomena important to the generation, transport, and deposition of eolian terrigenous material that ultimately becomes part of the geologic record and the modeling techniques that used to represent these processes. The presenta­ tions on the geologic record of eolian deposition documented our present understanding of the na~e and causes of climate change on time scales of the last glacial ages (tens of thousands of years) to time scales over which the arrangement of continents, mountains, and oceans has changed sub­ stantially (tens of millions of years). There has been a growing recognition of the importance of global climatic changes to the future well-being of humanity. In particular, the climatic response to human alterations to the earth's surface and chemical composition has led to concern over the agricultural, ecological, and societal impacts of such potential global changes.

The quest for high resolution has preoccupied radio astronomers ever since radio waves were first detected from space fifty years ago. This venture was par­ ticularly stimulated by the discovery of quasars, and led to the development of interferometer techniques using baselines of transglobal dimensions. These meth­ ods have become known as Very Long Baseline Interferometry (VLBI). Arrays of radio telescopes situated all over the Earth (or even in space) are regularly used for researches in radio astronomy, reaching resolutions as small as a fraction of a milli arcsecond. The technique also allows the measurement of the positions of the radio telescopes to a few millimeters and so VLBI has become a major tool in geodesy and the study of the rotation of the Earth. VLBI has now passed the pioneer stage and is becoming a standard facility available to astronomers and geodesists, requiring the coordination of the operations of indpendently owned radio telescopes around the world. In Europe observatories from England, Federal Republic of Germany, France, Italy, Poland, Sweden and The Netherlands are coordinated in their VLBI activity by the European VLBI Network Consortium (EVN). The Programme Committee of the EVN allocates time to scientific projects on a routine basis three times a year. The Unites States has a similar arrangement of a network of independent radio observatories, and joint experiments using 'Global Network' are often made.

This book which is the outcome of a NATO-Advanced Study Institute on Mod­ elling the Ocean Circulation and Geochemical Tracer Transport is concerned with using models to infer the ocean circulation. Understanding our climate is one of the major problems of the late twentieth century. The possible climatic changes resulting from the rise in atmospheric carbon dioxide and other trace gases are of primary interest and the ocean pla. ys a ma. jor role in determining the magnitude, temporal evolution and regional distribution of those changes. Because of the poor observational basis the ocean general circulation is not well understood. The World Ocean Circulation Experiment (WOCE) which is now underway is an attempt to improve our knowledge of ocean dynamics and thermodynamics on global scales relevant to climate change. Despite those efforts, the oceanic data base is likely to remain scarce and it is crucial to use appropriate methods in order to extract the maximum amount of information from observations. The book contains a thorough analysis of methods to combine data of val'ious types with dynamical concepts, and to assimilate data directly into ocean models. The properties of geocl;temical tracers such as HC, He, Tritium and Freons and how they may be used to impose integral constraints on the ocean circulation are discussed.

It has been widely recognized recently that in order to make scientific progress on large and important problems (eg, carbon dioxide effects on climate, viability of various sites for nuclear waste disposal etc.), it is necessary to integrate knowledge from wide ranging sets of disciplines. This is certainly true in the climate sciences, for progress in understanding the cause of the ice ages or the effects of industrial pollution on the future climate or even the likelihood of severe climatic consequences in the aftermath of nuclear war. All require state-of -the -art input from many geoscience disci­ plines climatology, oceanography, meteorology, chemistry, ecology, glaciology, geology, astronomy, space technology, computer technology, mathematics etc. Major international meetings have called for interaction of such geo-science disciplines to solve real world problems. To move beyond the rhetorical level, the NATO Special Programme on Global Transport Mechanisms in the Geo-Sciences whose activities started in 1983, deci­ ded to organise his closing symposium on such a topic which focus on the relationship between climate and geo-sciences. This symposium was held at the end of May 1988 at the Universite Catholique de Louvain, Louvain-Ia-Neuve, Belgium. One hundred-and-thirty participants from the 16 NATO countries and a number of non-NATO countries assembled for the Symposium. Another feature was the attendance by special invitation of 16 pro­ mising young scientists who might well become leading scientists on climate and geo-sciences in their respective countries in the next century.

It has been widely recognized recently that in order to make scientific progress on large and important problems (eg, carbon dioxide effects on climate, viability of various sites for nuclear waste disposal etc.), it is necessary to integrate knowledge from wide ranging sets of disciplines. This is certainly true in the climate sciences, for progress in understanding the cause of the ice ages or the effects of industrial pollution on the future climate or even the likelihood of severe climatic consequences in the aftermath of nuclear war. All require state-of -the -art input from many geoscience disci­ plines climatology, oceanography, meteorology, chemistry, ecology, glaciology, geology, astronomy, space technology, computer technology, mathematics etc. Major international meetings have called for interaction of such geo-science disciplines to solve real world problems. To move beyond the rhetorical level, the NATO Special Programme on Global Transport Mechanisms in the Geo-Sciences whose activities started in 1983, deci­ ded to organise his closing symposium on such a topic which focus on the relationship between climate and geo-sciences. This symposium was held at the end of May 1988 at the Universite Catholique de Louvain, Louvain-Ia-Neuve, Belgium. One hundred-and-thirty participants from the 16 NATO countries and a number of non-NATO countries assembled for the Symposium. Another feature was the attendance by special invitation of 16 pro­ mising young scientists who might well become leading scientists on climate and geo-sciences in their respective countries in the next century.

Frechet spaces have been studied since the days of Banach. These spaces, their inductive limits and their duals played a prominent role in the development of the theory of locally convex spaces. Also they are natural tools in many areas of real and complex analysis. The pioneering work of Grothendieck in the fifties has been one of the important sources of inspiration for research in the theory of Frechet spaces. A structure theory of nuclear Frechet spaces emerged and some important questions posed by Grothendieck were settled in the seventies. In particular, subspaces and quotient spaces of stable nuclear power series spaces were completely characterized. In the last years it has become increasingly clear that the methods used in the structure theory of nuclear Frechet spaces actually provide new insight to linear problems in diverse branches of analysis and lead to solutions of some classical problems. The unifying theme at our Workshop was the recent developments in the theory of the projective limit functor. This is appropriate because of the important role this theory had in the recent research. The main results of the structure theory of nuclear Frechet spaces can be formulated and proved within the framework of this theory. A major area of application of the theory of the projective limit functor is to decide when a linear operator is surjective and, if it is, to determine whether it has a continuous right inverse.

The ASI workshop on "Selectivities in Lewis Acid Promoted Reactions" held in the Emmantina-Hotel in Athens-Glyfada, Greece, October 2-7, 1988 was held to bring some light into the darkness of Lewis acid induced processes. As such the workshop reflects some current trends in organic synthesis, where Lewis acids are becoming a powerful tool in many different modern reactions, e.g. Diels-Alder reactions, Ene reactions, Sakurai reactions, and in general silicon and tin chemistry. The objective of this meeting was to bring together most of the world experts in the field to discuss the major reactions promoted by Lewis acids. Organic synthesis will play a major role in this book connected with some fundamental mechanistic work on allylsilane and -tin chemistry. Both natural product synthesis and unnatural molecules are presented in the chapters. The book presents all the 15 invited lectures and the contributions of 15 posters. I am confident that the material presented in this book will stimulate the chemistry, which has been discussed on our meeting, around the world. The meeting and the book were only possible through a grant of the NATO Scientific Affairs Devision and financial support by the following companies: Kali Chemie (Hannover, W-Germany), E. Merck (Darmstadt, W-Germany), Sandoz (Basel, Switzerland), Schering (Berlin, W-Germany).

MOLECULAR WEIGHr CHANGES AND NE1WORK FORMATION BY SCISSION AND CROSSUNKING A. Charlesby 1 Introduction Main Chain Scission of Polymers ____________________________ _ ________________________ _ 1 Crosslinking ______ . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . _ . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . __ . . . . _ . . . . . . . . . . . _ . . . . . . . . ___ . . _. __ . . . . _. _. _____ . _____ . _ 4 5 Random Crosslinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enhanced Crosslinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Other Forms of Crosslinking . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . _. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Combined Crosslinking and Scission ___________ _________________ ______ _ ______________ . _. _. 11 Antioxidants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . __ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . __ . . . 12 Crosslinking of Polymers in Solution ________________________________ . . ______________ . . . . __ 12 References _. __ _ 13 HIGH ENERGY RADIATION-AND UV UGHr-INDUCED CROSSLINKING AND CHAIN SCISSION w. Schnabel Introduction 15 Importance of Radiation-Induced Crosslinking and Main-Chain Scission in Linear Polymers ___________________________ _________________ 15 TYPes of Radiation and Radiation Sources _. ___________________________ . . . . . . . . . _ . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . _. _. _ . . __ . . . 16 Absorption of Radiation . . _ . . . . _ . . . . . . _ . . _ . . __ . _ . . . . . . . . ____ . . . _ . . . . . . . . . . . . __ . . . . _ . . . . . . . . . _ . . . . _ . . . . . . _ . . . _ . . _ . . . . . . . . . . . . . . . . . . . . . _ . . . . . __ . . . . . . . . . . . _ . . . . . _____ . . . . . . . . . ___ . . . 16 General Aspects Concerning XL and CS in Linear Polymers ______________________ . _________ . _____ . _____ 22 Random and Specific Site Attacks . . . . . . . _. ____ . _ . . . _ . . . . . . . . . . __ . . . . . . . . . . . . . _ . . ___ . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . _ . . . . . _ . . . . . __ . . . . _ . . . . . . _ . . . . __ . ___ . . . . . . . . . . __ . . _ 22 Detection of XL and CS . . . _. _ . . . . . . . . . . . . . . . _. __ . . . _ . . . . . . . . . . . . ___ . . . . . . . __ . . . _ . . . _ . . . . . . . . ____ . . . . . . . . . . . . . . . . . . _ . . . . _ . . . . . _ . . . . . . . . . . . . . . . . . . . . __ . . . . . _ . . . . _ . . . . . _. _ . . . . _ . . . . . . . 22 Simultaneous XL and CS Mechanisms 25 Ion Beam-Induced Radiation Effects In Linear Polymers ____________________________________________________ .

Computer Modelling techniques have developed very rapidly during the last decade, and interact with many contemporary scientific disciplines. One of the areas of greatest activity has concerned the modelling of condensed phases, including liquids solids and amorphous systems, where simulations have been used to provide insight into basic physical processes and in more recent years to make reliable predictions of the properties of the systems simulated. Indeed the predictive role of simulations is increasingly recognised both in academic and industrial contexts. Current active areas of application include topics as diverse as the viscosity of liquids, the conformation of proteins, the behaviour of hydrogen in metals, the diffusion of molecules in porous catalysts and the properties of micelles. This book, which is based on a NATO ASI held at the University of Bath, UK, from September 5th-17th, 1988, aims to give a general survey of this field, with detailed discussions both of methodologies and of applications. The earlier chapters of the book are devoted mainly to techniques and the later ones to recent simulation studies of fluids, polymers (including biological molecules) and solids. Special attention is paid to the role of interatomic potentials which are the fundamental physical input to simulations. In addition, developments in computer hardware are considered in depth, owing to the crucial role which such developments are playing in the expansion of the horizons of computer modelling studies.

This volume contains the papers presented in the NATO Advanced Research Workshop "Activation of Hormone and Growth Factor Receptors: Molecular Mechanisms and Consequences" held in Nafplion, Greece on September 25-30, 1988. The objective of NATO ARW is to assess the state of-the-art in a given scientific area and to formulate recommendations for future research in emerging areas of science by promoting international scientific contacts. In the Nafplion meeting this objective was reached by an international group of speakers, senior Greek scientists and graduates involved in relevant research areas. The Workshop was made possible by the generous support of the Scientific Council of NATO. We thank Drs. G. Sinclair and L.V. daCunha, Directors of the NATO ARW's and ASI's (Advanced Study Institutes) respectively, for their wholehearted support and advice. The International Union of Biochemistry awarded additional travel grants leading to increased international participation. Furthermore, the Secretariat of Science and Technology, the Ministry of Culture and Sciences and the National Hellenic Research Foundation contributed financially and by supporting personnel. We sincerely thank all these organizations for their support. Our heartful thanks are also extended to the Mayor of the Municipality of Nafplion, Mr.

The second Erice course in the school of Particle-Astrophysics was held in May, 1988. The topic choosen was Dark Matter. This is one of the most exciting top­ ics at the interface of particle physics and astrophysics. It is developing rapidly now due to a coming together not only of the theoretical concepts from the early universe with the theoretical concepts of galaxy formation, but also the coming to­ gether of the theorists, experimentalists and observers. It is with Dark Matter, the combined interrelated topics of galaxy formation and the generation of large scale structure that we see a confrontation of the exotic ideas from the early universe, such as phase transitions and unification, coming face to face with the realities of traditional observational cosmology. These realities have recently been heightened by the tremendous number of new observations, demonstrating that large scale structure of the universe is far more complex than anybody had suspected. In particular, we now see large scale foam, apparent large scale velocity fields, indicating devations from the Hubble flow, large scales of the order 100 Mpc, and galaxy formation occurring at high red shifts much greater than unity. We also see an apparent correlation of clusters of galaxies that may even exceed the c- relation of galaxies despite their being on much larger scales with lower average densities.

This interdisciplinary meeting has brought together a group of astrophysicists with hands-on experience in the numerical computation of astrophysical fluid dynamics, in particular nonlinear stellar pulsations, and a group of applied mathematicians who are actively engaged with the development of novel and improved numerical methods. The goal of the workshop has been for the astrophysicists to discuss in detail the numerical problems encountered in the modelling of stellar pulsations and for the mathematicians to present a survey of recent developments in numerical techniques. This astrophysical-mathematical intercourse will help the astrophysicists in the future development of more reliable and efficient codes, on the one hand, and it has introduced the mathematicians to an unfamiliar area which is a tough testing ground for their techniques. Since the difficulties encountered are common to other fluid dynamics problems, and are in fact perhaps more severe, fluid dynamicists in other research areas may fmd the results of this workshop of interest as well. Much of our theoretical understanding of the intricate and interesting behavior of variable stars rests on our ability to perform accurate numerical hydrodynamical computations of stellar models. Extensive calculations of nonlinear radial stellar pulsations with the use of increasingly powerful computers are showing more and more clearly that the numerical codes in current use have serious deficiencies.

Proceedings of the NATO Advanced Study Institute on Polymer Colloids, Strasbourg, France, July 3-15, 1988

Proceedings of the NATO Advanced Research Workshop, Digne, France, September 16-22, 1988

Assembled here is a collection of articles presented at a NATO ADVANCED STU­ DY INSTITUTE held at Puerto de la Cruz, Tenerife, Spain during the period of July 10th to 21st, 1989. In addition to the editors of these proceedings Professor Larry L. Schumaker from Vanderbilt University, Nashville, Tennessee, served as a member of the international organizing committee. The contents of the contribu­ tions fall within the heading of COMPUTATION OF CURVES AND SURFACES and therefore address mathematical and computational issues pertaining to the dis­ play, modeling, interrogation and representation of complex geometrical objects in various scientific and technical environments. As is the intent of the NATO ASI program the meeting was two weeks in length and the body of the scientific activities was organized around prominent experts. Each of them presented lectures on his current research activity. We were fortunate to have sixteen distinguished invited speakers representing nine NATO countries: W. Bohm (Federal Republic of Germany), C. de Boor (USA), C.K. Chui (USA), W. Dahmen (Federal Republic of Germany), F. Fontanella (Italy), M. Gasca (Spain), R. Goldman (Canada), T.N.T. Goodman (UK), J.A. Gregory (UK), C. Hoffman (USA), J. Hoschek (Federal Republic of Germany), A. Le Mehaute (France), T. Lyche (Norway), C.A. Micchelli (USA), 1.1. Schumaker (USA), C. Traas (The Netherlands). The audience consisted of both young researchers as well as established scientists from twelve NATO countries and several non-NATO countries.

Proceedings of the NATO Advanced Research Workshop, Bremen, Germany, October 10-14, 1988

This volume contains the texts of the principal survey papers presented at ALGORITHMS -and ORDER, held· at Ottawa, Canada from June 1 to June 12, 1987. The conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the University of Ottawa, and the Natural Sciences and Engineering Research Council of Canada. We are grateful for this considerable support. Over fifty years ago, the Symposium on Lattice Theory, in Charlottesville, U.S.A., proclaimed the vitality of ordered sets. Only twenty years later the Symposium on Partially Ordered Sets and Lattice Theory, held at Monterey, U.S.A., had solved many of the problems that had been originally posed. In 1981, the Symposium on Ordered Sets held at Banff, Canada, continued this tradition. It was marked by a landmark volume containing twenty-three articles on almost all current topics in the theory of ordered sets and its applications. Three years after, Graphs and Orders, also held at Banff, Canada, aimed to document the role of graphs in the theory of ordered sets and its applications. Because of its special place in the landscape of the mathematical sciences order is especially sensitive to new trends and developments. Today, the most important current in the theory and application of order springs from theoretical computer seience. Two themes of computer science lead the way. The first is data structure. Order is common to data structures.

The ihsan Ketin NATO Advanced Study Institute on the Tectonic Evolution of the Tethyan Region was conceived in 1982 in Veszprem, Hungary, when three of the organizers (B. C. B. , L. H. R. and A. M. C. 9. ) had come together for a meeting on the tectonics of the Pannonian basin. All three of us had experience in the Tethyan belt and all three of us had been for some time deploring the lack of communication among workers of this immense orogenic belt. Much new work had been completed in such previously little-known areas as Turkey, Iran, Afghanistan, the People's Republic of China, the entire Himalayan region, as well as new work in the European parts of the chain. Also, ironically, parts of the belt had just been closed to field work for political reasons, so it seemed as if the time was right to sit back and consider what had been done so far. Because the Istanbul group had had an interest in the whole of the Tethyan belt and because that ancient city was more centrally locElted with excellent opportunities to see both Palaeo- and Neo-Tethyan rocks in a weekend excursion, we thought that Istanbul was a natural place for such a meeting, not mentioning its own considerable attractions for the would-be contributors. A happy coincidence was that Prof.

The idea for organizing an Advanced Study Institute devoted largely to neutron star timing arose independently in three places, at Istanbul, Garching and Amster­ dam; when we became aware of each other's ideas we decided to join forces. The choice of a place for the Institute, in Turkey, appealed much to us all, and it was then quickly decided that Qe§me would be an excellent spot. When the preparations for the Institute started, early in 1987, we could not have guessed how timely the subject actually was. Of course, the recently dis­ covered QPO phenomena in accreting neutron stars and half a dozen binary and millisecond radio pulsars known at the time formed one of the basic motivations for organizing this Institute. But none of us could have guessed that later in 1987 we were to witness the wonderful discovery of the binary and millisecond radio pulsars in globular clusters and, -as if Nature wished to give us a special present for this the discovery in March 1988 of a millisecond pulsar in an eclipsing binary Institu- system, the first eclipsing radio pulsar ever found, and the second fastest in the sky! The discussion of this pulsar, its formation and fate was one of the highlights of this meeting, especially since its discoverers were among the participants of the Institute and could provide us with first-hand information.

Proceedings of the NATO Advanced Study Institute, Banff Centre, Canada, April 27-May 5, 1988

For many years, the two subjects of (1) postglacial rebound and its potential for generating earthquakes and (2) the seismicity of passive continental ml!rgins have been of interest and concern to earth scientists on both sides of the North Atlantic. New data and theoretical interpretations have given rise to vigorous discussions on how much the two phenomena inter-relate and whether a significant controlling factor on seismicity in northeastern North America and Scandinavia is the crustal uplift that has been occurring since the latest ice age. The lack of a good understanding of these phenomena presented a particular problem for engineering seismologists attempting to prepare accurate seismic hazard estimates for facili­ ties both on land (e. g. , nuclear power stations and radioactive waste repositories) and offshore (e. g. , petroleum production facili­ ties) . The NATO Advanced Research Workshop programme provided an opportuni ty to bring together a group of relevant geophysicists, geologists and geodesists from both sides of the North Atlantic, and a workshop on "Causes and Effects of Earthquakes at Passive Margins and in Areas of Postglacial Rebound on both Sides of the North Atlantic" was held in Vordingborg, Denmark, 9-13 May 1988. The sup­ port of the NATO Science Committee is gratefully acknowledged.

People who attended the NATO Advanced Study Institute (ASI) entitled NEW THEORETICAL CONCEPTS FOR UNDERSTANDING ORGANIC REAC­ TIONS held at Sant Feliu de Gufxols on the Costa Brava of Spain had a unique experience. They have seen the evolution of the field from qualitative arguments through the generation of Potential Energy Surfaces (PES) to the use of PES in molecular dynamics. The excellent lectures that were dedicated to the various aspects of Potential Energy Surfaces clearly revealed a colossal amount of ma­ terial that represents our current understanding of the overall problem. It is our hope that the present volume will recreate the excitement in the readers that we all experienced during the meeting in Spain. One can say, without too much exaggeration, that chemistry has become and exercise on potential energy surfaces (PES). Structural (position of the energy minima), spectroscopic (vicinity around the minima), and reactivity (reaction path along the surface) properties may be determined from the analysis of PES. New theoretical tools, together with recent developments in computer technology and programming, have allowed to obtain a better knowledge of these surfaces, and to extract further chemical information from them, so new horizons have been added to Theoretical Organic Chemistry.

The increasing production of industrial goods, heat, and energy, as well as traffic, has led to the release of considerable amounts of toxic trace metals to the atmosphere. The result is elevated concentrations of toxic metals in local populations and eco­ systems. Recently the problem of atmospheric long-range transport of trace metals has also been recognized. Significant amounts of these pollutants are disposed and deposited both on regional and global scales. In the atmosphere they may influence the chemical reactions. Of particular interest is their catalytic effect on the oxidation prosesses taking place in water droplets or on the surface of wet particles (e. g. the oxidation of sulphur dioxide to sulphate), however, the main environmental impact starts when the atmospheric trace metals are deposited on ground and vegetation and subsequently brought into the water circulation. During the later years significant progress has been made in the development of equipment to reduce and control the atmospheric emissions of toxic trace metals. This particularly applies to electrostatic precipitators and wet scrubbers for the collection of fine particles. The main objective of the workshop was to survey present knowledge concerning the sources, atmospheric fluxes, sinks and chemical impact of the atmospheric trace metals, and to review the developments of emission control equipment and the perspectives to reduce the potential risks from toxic metals. During the first two days of the meeting, 15 invited review papers were presented.

There are only few topics in organometallic chemistry, which have stimulated research activities in as many areas, as transition-metal carbene (alkylidene) complexes. About 25 years after the first planned synthesis of a carbene complex in E.O. Fischer's laboratory in Munich the NATO Advanced Research Workshop on Transition-Metal Carbene Complexes was the first meeting which,brought together scientists from different disciplines to discuss inorganic, organic, theoretical structural catalysis-related aspects of metal carbene chemistry. The 70th birthday of Professor E.O. Fischer was a good occasion for this enterprise. The organizers of the meeting (K.D. Dotz, Marburg; F.R. KreiBl, Munchen; U. Schubert, Wurzburg) were encouraged by the fact that most of the leading scientists in this area were able to participate in the workshop. The very high standard of the contributions is reflected in this book, which contains papers from the majority of the participants. The Proceedings show the state of the art in metal carbene chemistry and will hopefully be a landmark in the development of this area of chemistry. Generous financial support for the workshop and for the preparation of this book was provided by the Scientific Affairs Division of NATO and some companies. The organizers also acknowledge the efforts of the staff of the Bildungs­ zentrum der Hans-Seidel-Stiftung in Wild bad Kreuth for creating a pleasant and stimulating atmosphere during the conference.

Quantum mechanical calculations in physics, chemistry and biology are widely recognized as useful interpretative and predictive tools. Unfortunately, they are plagued by unfavorable convergence limitations due to the use of finite linear combinations of basis functions. With the current computer technologies, there is a possible way out to the situation by solving numerically the corresponding wave equations. The present interest and need for numerical determination of electronic structure of atoms, diatomic and poly atomic molecules led us to organize a NATO-ARW devoted to these questions. The aim of the meeting was to provide a review of the state of the art about techniques and applications. The organizing committee consisted of Drs. G. Berthier, P. Claverie, M. Defranceschi, J. Delhalle, H.J. Monkhorst and P. Pyykk6. It was a great sorrow for us to be informed in January 88 of the death of Professor P. Claverie who supported so enthusiastically the idea of having such a meeting organized. The NATO Advanced Research Worshop on : " Numerical Determination of the Electronic Structure of Atoms, Diatomic and Poly atomic Molecules" was held at Versailles (France) from April 17th till April 22th, 1988.

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.

This volume certainly is a Conference Proceedings, the Proceedings of the NATO Advanced Research Workshop (ARW) on "Unsaturated Flow in Hydrologic Modeling" held at "Les Villages du Soleil" near ArIes, France from June 13 to 17, 1988. Let me therefore acknowledge properly, at the very beginning, the gratitude of all the participants to the NATO Science Committee for its generous support and worthwhile goal of bringing together scientists of many countries to communicate and share their experiences. Particular thanks are extended to the director of the program, Dr. Luis Vega da Cunha for his interest and understanding. On the other hand this volume is also, and probably more so, a Textbook that fills a gap in the field of unsaturated flow. Many treatises on the subject present the theory in its different aspects. Hardly any explain in details how the different pieces can be put together to address realistic problems at the basin scale. The various invited contributions to the ARW were structured in a subject progression much as chapters are organized in a book. The intent of the ARW was to assess the current state of knowledge in "Unsaturated Flow" and its use in "Hydrologic Modeling Practice". In a sense the interest in fundamentals of unsaturated flow in this ARW was not just for the sake of knowledge but also and primarily for the sake of action. Can such fundamental knowledge be utilized for better management of the water resource? was the basic question.

A NATO Advanced Study Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987. This meeting was jointly supported by NATO and the Natural Sciences and Engineering Research Council of Canada, and was sponsored in part by the Canadian Mathematical Society. This book is the volume of proceedings for that meeting. Algebraic K-theory is essentially the study of homotopy invariants arising from rings and their associated matrix groups. More importantly perhaps, the subject has become central to the study of the relationship between Topology, Algebraic Geometry and Number Theory. It draws on all of these fields as a subject in its own right, but it serves as well as an effective translator for the application of concepts from one field in another. The papers in this volume are representative of the current state of the subject. They are, for the most part, research papers which are primarily of interest to researchers in the field and to those aspiring to be such. There is a section on problems in this volume which should be of particular interest to students; it contains a discussion of the problems from Gersten's well-known list of 1973, as well as a short list of new problems.

This edition is the labor of many enthousiastic scientists who were invited to teach at a NATO Advanced Study Institute on the "Spectroscopy of Inorganic Bioactivators" which took place on August 20 -30, 1988 at Club Poseidon, Loutraki, Greece. In this book the subjects were taught through several well prepared lectures. These lectures stretch the fact that scientific knowledge is the painfully gathered product of many wonderful human minds. I made an attempt to divide the lectures into separate chapters, however, there is interaction among the lectures, as I hope the book will show. First, there is introductory on an lecture supercomputing and super computers and their applications to solving structures of biological molecules followed by a state-of-the-art x-ray diffraction method at pi co second times. Important new advances have been made in x-ray diffraction analysis at picosecond times, in Hadamard spectroscopy, in micro-Raman spectroscopy in the Near Infrared region (1. 01 ~m) and remote sensing by Fourier Transform Infrared Spectroscopy. The chapters that follow include applications of spectroscopic technique to vii viii biologically important molecules, such as, DNA, proteins, membranes, and metal ion-biological molecule interactions. I would like to express my thanks to all the authors for their contributions and their cooperation in submitting their manuscript. I also thank the NATO Science Committee for making this possible. The field looks very promising for significant and exciting developments in the application of spectroscopy to bioactivators.

The NATO Advanced Research Workshop on "Paleoclimatology and Paleometeorology: Modem and Past Patterns of Global Atmospheric Transport" (held at Oracle, Arizona, USA from November 17-19, 1987) brought together atmospheric chemists, physicists, and meteorologists who study the origin and transport of modem-day mineral and biological aerosols with geologists and paleobotanists who study the sedimentary record of eolian and hydrologic processes along with modelers who study and conceptualize the processes influencing atmospheric transport at present and in the past. Presentations at the workshop provided a guide to our present knowledge of the entire spectrum of processes and phenomena important to the generation, transport, and deposition of eolian terrigenous material that ultimately becomes part of the geologic record and the modeling techniques that used to represent these processes. The presenta­ tions on the geologic record of eolian deposition documented our present understanding of the na~e and causes of climate change on time scales of the last glacial ages (tens of thousands of years) to time scales over which the arrangement of continents, mountains, and oceans has changed sub­ stantially (tens of millions of years). There has been a growing recognition of the importance of global climatic changes to the future well-being of humanity. In particular, the climatic response to human alterations to the earth's surface and chemical composition has led to concern over the agricultural, ecological, and societal impacts of such potential global changes.

The quest for high resolution has preoccupied radio astronomers ever since radio waves were first detected from space fifty years ago. This venture was par­ ticularly stimulated by the discovery of quasars, and led to the development of interferometer techniques using baselines of transglobal dimensions. These meth­ ods have become known as Very Long Baseline Interferometry (VLBI). Arrays of radio telescopes situated all over the Earth (or even in space) are regularly used for researches in radio astronomy, reaching resolutions as small as a fraction of a milli arcsecond. The technique also allows the measurement of the positions of the radio telescopes to a few millimeters and so VLBI has become a major tool in geodesy and the study of the rotation of the Earth. VLBI has now passed the pioneer stage and is becoming a standard facility available to astronomers and geodesists, requiring the coordination of the operations of indpendently owned radio telescopes around the world. In Europe observatories from England, Federal Republic of Germany, France, Italy, Poland, Sweden and The Netherlands are coordinated in their VLBI activity by the European VLBI Network Consortium (EVN). The Programme Committee of the EVN allocates time to scientific projects on a routine basis three times a year. The Unites States has a similar arrangement of a network of independent radio observatories, and joint experiments using 'Global Network' are often made.

This book which is the outcome of a NATO-Advanced Study Institute on Mod­ elling the Ocean Circulation and Geochemical Tracer Transport is concerned with using models to infer the ocean circulation. Understanding our climate is one of the major problems of the late twentieth century. The possible climatic changes resulting from the rise in atmospheric carbon dioxide and other trace gases are of primary interest and the ocean pla. ys a ma. jor role in determining the magnitude, temporal evolution and regional distribution of those changes. Because of the poor observational basis the ocean general circulation is not well understood. The World Ocean Circulation Experiment (WOCE) which is now underway is an attempt to improve our knowledge of ocean dynamics and thermodynamics on global scales relevant to climate change. Despite those efforts, the oceanic data base is likely to remain scarce and it is crucial to use appropriate methods in order to extract the maximum amount of information from observations. The book contains a thorough analysis of methods to combine data of val'ious types with dynamical concepts, and to assimilate data directly into ocean models. The properties of geocl;temical tracers such as HC, He, Tritium and Freons and how they may be used to impose integral constraints on the ocean circulation are discussed.

It has been widely recognized recently that in order to make scientific progress on large and important problems (eg, carbon dioxide effects on climate, viability of various sites for nuclear waste disposal etc.), it is necessary to integrate knowledge from wide ranging sets of disciplines. This is certainly true in the climate sciences, for progress in understanding the cause of the ice ages or the effects of industrial pollution on the future climate or even the likelihood of severe climatic consequences in the aftermath of nuclear war. All require state-of -the -art input from many geoscience disci­ plines climatology, oceanography, meteorology, chemistry, ecology, glaciology, geology, astronomy, space technology, computer technology, mathematics etc. Major international meetings have called for interaction of such geo-science disciplines to solve real world problems. To move beyond the rhetorical level, the NATO Special Programme on Global Transport Mechanisms in the Geo-Sciences whose activities started in 1983, deci­ ded to organise his closing symposium on such a topic which focus on the relationship between climate and geo-sciences. This symposium was held at the end of May 1988 at the Universite Catholique de Louvain, Louvain-Ia-Neuve, Belgium. One hundred-and-thirty participants from the 16 NATO countries and a number of non-NATO countries assembled for the Symposium. Another feature was the attendance by special invitation of 16 pro­ mising young scientists who might well become leading scientists on climate and geo-sciences in their respective countries in the next century.

It has been widely recognized recently that in order to make scientific progress on large and important problems (eg, carbon dioxide effects on climate, viability of various sites for nuclear waste disposal etc.), it is necessary to integrate knowledge from wide ranging sets of disciplines. This is certainly true in the climate sciences, for progress in understanding the cause of the ice ages or the effects of industrial pollution on the future climate or even the likelihood of severe climatic consequences in the aftermath of nuclear war. All require state-of -the -art input from many geoscience disci­ plines climatology, oceanography, meteorology, chemistry, ecology, glaciology, geology, astronomy, space technology, computer technology, mathematics etc. Major international meetings have called for interaction of such geo-science disciplines to solve real world problems. To move beyond the rhetorical level, the NATO Special Programme on Global Transport Mechanisms in the Geo-Sciences whose activities started in 1983, deci­ ded to organise his closing symposium on such a topic which focus on the relationship between climate and geo-sciences. This symposium was held at the end of May 1988 at the Universite Catholique de Louvain, Louvain-Ia-Neuve, Belgium. One hundred-and-thirty participants from the 16 NATO countries and a number of non-NATO countries assembled for the Symposium. Another feature was the attendance by special invitation of 16 pro­ mising young scientists who might well become leading scientists on climate and geo-sciences in their respective countries in the next century.

Frechet spaces have been studied since the days of Banach. These spaces, their inductive limits and their duals played a prominent role in the development of the theory of locally convex spaces. Also they are natural tools in many areas of real and complex analysis. The pioneering work of Grothendieck in the fifties has been one of the important sources of inspiration for research in the theory of Frechet spaces. A structure theory of nuclear Frechet spaces emerged and some important questions posed by Grothendieck were settled in the seventies. In particular, subspaces and quotient spaces of stable nuclear power series spaces were completely characterized. In the last years it has become increasingly clear that the methods used in the structure theory of nuclear Frechet spaces actually provide new insight to linear problems in diverse branches of analysis and lead to solutions of some classical problems. The unifying theme at our Workshop was the recent developments in the theory of the projective limit functor. This is appropriate because of the important role this theory had in the recent research. The main results of the structure theory of nuclear Frechet spaces can be formulated and proved within the framework of this theory. A major area of application of the theory of the projective limit functor is to decide when a linear operator is surjective and, if it is, to determine whether it has a continuous right inverse.

The ASI workshop on "Selectivities in Lewis Acid Promoted Reactions" held in the Emmantina-Hotel in Athens-Glyfada, Greece, October 2-7, 1988 was held to bring some light into the darkness of Lewis acid induced processes. As such the workshop reflects some current trends in organic synthesis, where Lewis acids are becoming a powerful tool in many different modern reactions, e.g. Diels-Alder reactions, Ene reactions, Sakurai reactions, and in general silicon and tin chemistry. The objective of this meeting was to bring together most of the world experts in the field to discuss the major reactions promoted by Lewis acids. Organic synthesis will play a major role in this book connected with some fundamental mechanistic work on allylsilane and -tin chemistry. Both natural product synthesis and unnatural molecules are presented in the chapters. The book presents all the 15 invited lectures and the contributions of 15 posters. I am confident that the material presented in this book will stimulate the chemistry, which has been discussed on our meeting, around the world. The meeting and the book were only possible through a grant of the NATO Scientific Affairs Devision and financial support by the following companies: Kali Chemie (Hannover, W-Germany), E. Merck (Darmstadt, W-Germany), Sandoz (Basel, Switzerland), Schering (Berlin, W-Germany).

MOLECULAR WEIGHr CHANGES AND NE1WORK FORMATION BY SCISSION AND CROSSUNKING A. Charlesby 1 Introduction Main Chain Scission of Polymers ____________________________ _ ________________________ _ 1 Crosslinking ______ . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . _ . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . __ . . . . _ . . . . . . . . . . . _ . . . . . . . . ___ . . _. __ . . . . _. _. _____ . _____ . _ 4 5 Random Crosslinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enhanced Crosslinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Other Forms of Crosslinking . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . _. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Combined Crosslinking and Scission ___________ _________________ ______ _ ______________ . _. _. 11 Antioxidants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . __ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . __ . . . 12 Crosslinking of Polymers in Solution ________________________________ . . ______________ . . . . __ 12 References _. __ _ 13 HIGH ENERGY RADIATION-AND UV UGHr-INDUCED CROSSLINKING AND CHAIN SCISSION w. Schnabel Introduction 15 Importance of Radiation-Induced Crosslinking and Main-Chain Scission in Linear Polymers ___________________________ _________________ 15 TYPes of Radiation and Radiation Sources _. ___________________________ . . . . . . . . . _ . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . _. _. _ . . __ . . . 16 Absorption of Radiation . . _ . . . . _ . . . . . . _ . . _ . . __ . _ . . . . . . . . ____ . . . _ . . . . . . . . . . . . __ . . . . _ . . . . . . . . . _ . . . . _ . . . . . . _ . . . _ . . _ . . . . . . . . . . . . . . . . . . . . . _ . . . . . __ . . . . . . . . . . . _ . . . . . _____ . . . . . . . . . ___ . . . 16 General Aspects Concerning XL and CS in Linear Polymers ______________________ . _________ . _____ . _____ 22 Random and Specific Site Attacks . . . . . . . _. ____ . _ . . . _ . . . . . . . . . . __ . . . . . . . . . . . . . _ . . ___ . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . _ . . . . . _ . . . . . __ . . . . _ . . . . . . _ . . . . __ . ___ . . . . . . . . . . __ . . _ 22 Detection of XL and CS . . . _. _ . . . . . . . . . . . . . . . _. __ . . . _ . . . . . . . . . . . . ___ . . . . . . . __ . . . _ . . . _ . . . . . . . . ____ . . . . . . . . . . . . . . . . . . _ . . . . _ . . . . . _ . . . . . . . . . . . . . . . . . . . . __ . . . . . _ . . . . _ . . . . . _. _ . . . . _ . . . . . . . 22 Simultaneous XL and CS Mechanisms 25 Ion Beam-Induced Radiation Effects In Linear Polymers ____________________________________________________ .

Computer Modelling techniques have developed very rapidly during the last decade, and interact with many contemporary scientific disciplines. One of the areas of greatest activity has concerned the modelling of condensed phases, including liquids solids and amorphous systems, where simulations have been used to provide insight into basic physical processes and in more recent years to make reliable predictions of the properties of the systems simulated. Indeed the predictive role of simulations is increasingly recognised both in academic and industrial contexts. Current active areas of application include topics as diverse as the viscosity of liquids, the conformation of proteins, the behaviour of hydrogen in metals, the diffusion of molecules in porous catalysts and the properties of micelles. This book, which is based on a NATO ASI held at the University of Bath, UK, from September 5th-17th, 1988, aims to give a general survey of this field, with detailed discussions both of methodologies and of applications. The earlier chapters of the book are devoted mainly to techniques and the later ones to recent simulation studies of fluids, polymers (including biological molecules) and solids. Special attention is paid to the role of interatomic potentials which are the fundamental physical input to simulations. In addition, developments in computer hardware are considered in depth, owing to the crucial role which such developments are playing in the expansion of the horizons of computer modelling studies.

This volume contains the papers presented in the NATO Advanced Research Workshop "Activation of Hormone and Growth Factor Receptors: Molecular Mechanisms and Consequences" held in Nafplion, Greece on September 25-30, 1988. The objective of NATO ARW is to assess the state of-the-art in a given scientific area and to formulate recommendations for future research in emerging areas of science by promoting international scientific contacts. In the Nafplion meeting this objective was reached by an international group of speakers, senior Greek scientists and graduates involved in relevant research areas. The Workshop was made possible by the generous support of the Scientific Council of NATO. We thank Drs. G. Sinclair and L.V. daCunha, Directors of the NATO ARW's and ASI's (Advanced Study Institutes) respectively, for their wholehearted support and advice. The International Union of Biochemistry awarded additional travel grants leading to increased international participation. Furthermore, the Secretariat of Science and Technology, the Ministry of Culture and Sciences and the National Hellenic Research Foundation contributed financially and by supporting personnel. We sincerely thank all these organizations for their support. Our heartful thanks are also extended to the Mayor of the Municipality of Nafplion, Mr.

The second Erice course in the school of Particle-Astrophysics was held in May, 1988. The topic choosen was Dark Matter. This is one of the most exciting top­ ics at the interface of particle physics and astrophysics. It is developing rapidly now due to a coming together not only of the theoretical concepts from the early universe with the theoretical concepts of galaxy formation, but also the coming to­ gether of the theorists, experimentalists and observers. It is with Dark Matter, the combined interrelated topics of galaxy formation and the generation of large scale structure that we see a confrontation of the exotic ideas from the early universe, such as phase transitions and unification, coming face to face with the realities of traditional observational cosmology. These realities have recently been heightened by the tremendous number of new observations, demonstrating that large scale structure of the universe is far more complex than anybody had suspected. In particular, we now see large scale foam, apparent large scale velocity fields, indicating devations from the Hubble flow, large scales of the order 100 Mpc, and galaxy formation occurring at high red shifts much greater than unity. We also see an apparent correlation of clusters of galaxies that may even exceed the c- relation of galaxies despite their being on much larger scales with lower average densities.

This interdisciplinary meeting has brought together a group of astrophysicists with hands-on experience in the numerical computation of astrophysical fluid dynamics, in particular nonlinear stellar pulsations, and a group of applied mathematicians who are actively engaged with the development of novel and improved numerical methods. The goal of the workshop has been for the astrophysicists to discuss in detail the numerical problems encountered in the modelling of stellar pulsations and for the mathematicians to present a survey of recent developments in numerical techniques. This astrophysical-mathematical intercourse will help the astrophysicists in the future development of more reliable and efficient codes, on the one hand, and it has introduced the mathematicians to an unfamiliar area which is a tough testing ground for their techniques. Since the difficulties encountered are common to other fluid dynamics problems, and are in fact perhaps more severe, fluid dynamicists in other research areas may fmd the results of this workshop of interest as well. Much of our theoretical understanding of the intricate and interesting behavior of variable stars rests on our ability to perform accurate numerical hydrodynamical computations of stellar models. Extensive calculations of nonlinear radial stellar pulsations with the use of increasingly powerful computers are showing more and more clearly that the numerical codes in current use have serious deficiencies.

Proceedings of the NATO Advanced Study Institute on Polymer Colloids, Strasbourg, France, July 3-15, 1988

Proceedings of the NATO Advanced Research Workshop, Digne, France, September 16-22, 1988

Assembled here is a collection of articles presented at a NATO ADVANCED STU­ DY INSTITUTE held at Puerto de la Cruz, Tenerife, Spain during the period of July 10th to 21st, 1989. In addition to the editors of these proceedings Professor Larry L. Schumaker from Vanderbilt University, Nashville, Tennessee, served as a member of the international organizing committee. The contents of the contribu­ tions fall within the heading of COMPUTATION OF CURVES AND SURFACES and therefore address mathematical and computational issues pertaining to the dis­ play, modeling, interrogation and representation of complex geometrical objects in various scientific and technical environments. As is the intent of the NATO ASI program the meeting was two weeks in length and the body of the scientific activities was organized around prominent experts. Each of them presented lectures on his current research activity. We were fortunate to have sixteen distinguished invited speakers representing nine NATO countries: W. Bohm (Federal Republic of Germany), C. de Boor (USA), C.K. Chui (USA), W. Dahmen (Federal Republic of Germany), F. Fontanella (Italy), M. Gasca (Spain), R. Goldman (Canada), T.N.T. Goodman (UK), J.A. Gregory (UK), C. Hoffman (USA), J. Hoschek (Federal Republic of Germany), A. Le Mehaute (France), T. Lyche (Norway), C.A. Micchelli (USA), 1.1. Schumaker (USA), C. Traas (The Netherlands). The audience consisted of both young researchers as well as established scientists from twelve NATO countries and several non-NATO countries.

Proceedings of the NATO Advanced Research Workshop, Bremen, Germany, October 10-14, 1988