Bücher der Reihe NATO Science Series C

As recent developments have shown, supersymmetric quantum field theory and string theory are intimately related, with advances in one area often shedding light on the other. The organising ideas of most of these advances are the notion of duality and the physics of higher dimensional objects or p-branes. The topics covered in the present volume include duality in field theory, in particular in supersymmetric field theory and supergravity, and in string theory. The Seiberg-Witten theory and its recent developments are also covered in detail. A large fraction of the volume is devoted to the current state of the art in M-theory, in particular its underlying superalgebra as well as its connection with superstring and N = 2 strings. The physics of D-branes and its essential role in the beautiful computation of the black hole entropy is also carefully covered. Finally, the last two sets of lectures are devoted to the exciting matrix approach to non-perturbative string theory.

The Mediterranean is one of the most studied regions of the world. In spite of this, a considerable spread of opinions exists about the geodynamic evolution and the present tectonic setting of this zone. The difficulty in recognizing the driving mechanisms of deformation is due to a large extent to the complex distribution in space and time of tectonic events, to the high number of parameters involved in this problem and to the scarce possibility of carrying out quantitative estimates of the deformation implied by the various geodynamic hypotheses. However, we think that a great deal of the present ambiguity could be removed if there were more frequent and open discussions among the scientists who are working on this problem. The meeting ofERICE was organized to provide an opportunity in this sense. In making this effort, we were prompted by the conviction that each step towards the understanding of the Mediterranean evolution is of basic importance both for its scientific consequences and for the possibleimplicationsfor society. It is well known, for instance, that the knowledge ofongoing tectonic processes in a given region and of their connection with seismic activity may lead to the recognition of middle- long term precursors of strong earthquakes. The few cases of tentative earthquake prediction in the world occurred where information on large scale seismotectonic behavior was available. This led to identify the zones prone to dangerous shocks, where observations of short-term earthquake precursors were then concentrated.

The study of defects and disorder in solids remains a central topic in solid state science. Developments in the field continue to be promoted by new experimental and theoretical techniques, while further impetus for the study of disorder in solids is provided by the growing range of applications of solid state materials in which disorder at the atomic level plays a crucial rOle. In this book we attempt to present a survey of fundamental and applied aspects of the field. We consider the basic aspects of defective crystalline and amorphous solids. We discuss recent studies of structural, electronic, transport, thermodynamic and spectroscopic properties of such materials. Experimental and theoretical methodologies are reviewed, and detailed consideration is given to materials such as fast ion conductors and amorphous semiconductors that are of importance in an applied context. Any survey of this large field is necessarily selective. We have chosen to emphasise insulating (especially oxidic) and semi-conducting materials. But many of the approaches and techniques we describe apply generally across the entire field of solid state science. This volume is based on a NATO ASI held at the Residencia Santa Teresa de Jesus, Madrid in September 1991. The Editor is grateful to the NATO Scientific Affairs Division for their sponsorship of this School. Thanks are also due to all who participated in and lectured at the school, but especially to the organising committee of A. V. Chadwick, G. N. Greaves, M. Grigorkiewicz, J. H. Harding and S. Kalbitzer. C. R. A.

The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject. The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex. With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes. For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.

Since the discovery that polymer single crystals are composed of chain folded macromolecules in 1957, the crystallization of polymers has attracted considerable interest and still provides fascinating and fruitful areas of research. Only a few books have been fully devoted to the crystallization of polymers in the past. This book contains the proceedings of the NATO ARW devoted to the `Crystallization of Polymers' which took place in September 1992 at the University of Mons-Hainaut (Belgium). In view of the variety of papers devoted to the crystallization of polymers, this book will be used in the next few years as a reference book for scientists concerned in the field of polymer physical chemistry. Crystallization of Polymers is mainly devoted to the experimental and theoretical study of the crystallization of synthetic polymers. As a kinetic study of the growth of polymer crystals should always be preceded by a morphological or a structural investigation, the structure, the morphology of polymer crystals and more particularly the lamellar and supralamellar organizations, as well as the nature of the crystal amorphous interface are reviewed and discussed.

I am pleased to participate in this Summer School and look forward to sharing some ideas with you over the next few days. At the outset I would like to describe the approach I will take in 1 presenting the material. I aim to present the material in a non- rigorous way and hopefully in an intuitive manner. At the same time I will draw attention to some of the major technical problems. It is pitched at someone who is unfamiliar with the area. The results presented here are unfamiliar to actuaries and insurance mathematicians although they are well known in some other fields. During the next few minutes I will make some preliminary comments. The purpose of these comments is to place the lectures in perspective and motivate the upcoming material. After this I will outline briefly the topics to be covered during the rest of this lecture and in the lectures that will follow. One of the central themes of these lectures is RISK-SHARING. Risk-sharing is a common response to uncertainty. Such uncertainty can arise from natural phenomena or social causes. One particular form of risk-sharing is the insurance mechanism. I will be dealing with models which have a natural application in the insurance area but they have been applied in other areas as well. In fact some of the paradigms to be discussed have the capacity to provide a unified treatment of problems in diverse fields.

In the last five years or so there has been an important renaissance in the area of (mathematical) modeling, identification and (stochastic) control. It was the purpose of the Advanced Study Institute of which the present volume constitutes the proceedings to review recent developments in this area with par- ticular emphasis on identification and filtering and to do so in such a manner that the material is accessible to a wide variety of both embryo scientists and the various breeds of established researchers to whom identification, filtering, etc. are important (such as control engineers, time series analysts, econometricians, probabilists, mathematical geologists, and various kinds of pure and applied mathematicians; all of these were represented at the ASI). For these proceedings we have taken particular care to see to it that the material presented will be understandable for a quite diverse audience. To that end we have added a fifth tutorial section (besides the four presented at the meeting) and have also included an extensive introduction which explains in detail the main problem areas and themes of these proceedings and which outlines how the various contributions fit together to form a coherent, integrated whole. The prerequisites needed to understand the material in this volume are modest and most graduate students in e. g. mathematical systems theory, applied mathematics, econo- metrics or control engineering will qualify.

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.