The contributions published in this volume are the re- sults of the NATO Advanced Research Workshop "Improvement of Joint Interpretation of Geophysical and Geological Data", which took place in Gradisca d'Isonzo in October 1987 and February 1988. Modern computer techniques were applied for geoscien- tific studies in a new dimension. 45 scientists from 7 Euro- pean countries, Canada and the united states of America par- ticipated in the workshop. Interactive discussions and modeling improved the understanding of the very complex structure of the investigated area. We thank all contributors, but especially those pub- lishing in this volume, for their active participation to ensure the success of the meetings. Not to forget to mention the groups of assistants from the Istituto di Minere e Geo- fisica Applicata of the University of Trieste and from the Institute of Geophysics of the Freie Universitat Berlin. Many thanks for their help around the clock. However, a major prerequisite for this success was given by the hospitality of the international Centre for Applied Sciences (ICAS) in the wonderful restored ancient pallazzi Torriani and Pretuna of the town of Gradisca d'Isonzo. Thus, we are thankful to the president of ICAS, Dr. H.R. Dahlafi, and to the town of Gradisca d'Isonzo, especially to the mayor, Signore Travan. The studies carried out in Gradisca d'Isonzo had been supported by a grant of the NATO Scientific Affairs Division and we express our thanks to Dr. L. da Cunha as a steady partner in the background.

Mathematical modelling is ubiquitous. Almost every book in exact science touches on mathematical models of a certain class of phenomena, on more or less speci?c approaches to construction and investigation of models, on their applications, etc. As many textbooks with similar titles, Part I of our book is devoted to general qu- tions of modelling. Part II re?ects our professional interests as physicists who spent much time to investigations in the ?eld of non-linear dynamics and mathematical modelling from discrete sequences of experimental measurements (time series). The latter direction of research is known for a long time as "system identi?cation" in the framework of mathematical statistics and automatic control theory. It has its roots in the problem of approximating experimental data points on a plane with a smooth curve. Currently, researchers aim at the description of complex behaviour (irregular, chaotic, non-stationary and noise-corrupted signals which are typical of real-world objects and phenomena) with relatively simple non-linear differential or difference model equations rather than with cumbersome explicit functions of time. In the second half of the twentieth century, it has become clear that such equations of a s- ?ciently low order can exhibit non-trivial solutions that promise suf?ciently simple modelling of complex processes; according to the concepts of non-linear dynamics, chaotic regimes can be demonstrated already by a third-order non-linear ordinary differential equation, while complex behaviour in a linear model can be induced either by random in?uence (noise) or by a very high order of equations.

Thisvolumecontainsacollectionofpapersbyinternationalexpertsingeoph- ical ?uid dynamics, based upon presentations at a colloquium held in memory of Pedro Ripa on the ?rst anniversary of his untimely death. They review or present recent developments in hydrodynamic stability theory, Hamiltonian ?uid mechanics, balanceddynamics, waves, vortices, generaloceanographyand the physical oceanography of the Gulf ofCalifornia; all of them subjects in which Professor Ripamadeimportant contributions. His work, but also his friendly spiritandkindnesswerehighly regardedandappreciatedby colleagues and students alike around the world. This book is a tribute to his scienti?c legacy and constitutes a valuable reference for researchers and graduate s- dents interested in geophysical and general ?uid mechanics. Earlyin his career asa physicaloceanographer, Pedro Ripa made two la- mark contributions to geophysical ?uid dynamics. In 1981, he showed that the conservation of the potential vorticity is related to the invariance of the eq- tions of motion under the symmetry transformationsof the labels that identify the ?uid particles. That is, potential vorticity conservation is a consequence, via Noether's theorem, of the particle re-labelling symmetry. Two years later he published a paper entitled "General stability conditions for zonal ?ows in a one-layer model on the beta-plane or the sphere," where he established nec- sary conditions for stability in the shallow water equations, nowadays known as "Ripa's Theorem. " This is one of the very few Arnol'd-like stability con- tions that goes beyond two-dimensional or quasi-geostrophic ?ow, and stands alongside other famous stability criteria in making the foundations of the ?eld.

Surface Acoustic Waves in Inhomogeneous Media covers almost all important problems of the interaction of different types of surface acoustic waves with surface inhomogeneities. The problems of surface acoustic wave interaction with periodic topographic gratings widely used in filters and resonators are under careful consideration. The most important results of surface wave scattering by local defects such as grooves, random roughness, elastic wedges are given. Different theoretical approaches and practical rules for solving the surface wave problems are presented.

Written as both a textbook and a handy reference, this text deliberately avoids complex mathematics assuming only basic familiarity with geodynamic theory and calculus. Here, the authors have brought together the key numerical techniques for geodynamic modeling, demonstrations of how to solve problems including lithospheric deformation, mantle convection and the geodynamo. Building from a discussion of the fundamental principles of mathematical and numerical modeling, the text moves into critical examinations of each of the different techniques before concluding with a detailed analysis of specific geodynamic applications. Key differences between methods and their respective limitations are also discussed - showing readers when and how to apply a particular method in order to produce the most accurate results. This is an essential text for advanced courses on numerical and computational modeling in geodynamics and geophysics, and an invaluable resource for researchers looking to master cutting-edge techniques. Links to supplementary computer codes are available online.

This volume is concerned primarily with the chemical and physical effects of shock waves on typical materials. It compares naturally occurring materials with similar materials produced by shock compression in the laboratory, providing clues about the environment and events that produced the natural materials.

This volume contains the reviews and poster papers presented at the workshop Solar Convection and Oscillations and their Relationship: SCORe '96, held in Arhus, Denmark, May 27 - 31, 1996. The aim of this workshop was to bring together experts in the fields of convection and helioseismology, and to stimulate collaborations and joint research. The participation to this workshop was purposely kept limited in order to provide optimal conditions for informal discussions. In autumn of 199,5 the long-awaited GONG network of solar telescopes became fully operational and the first data already show significant improvement over existing datasets on solar oscillations. Furthermore, in December of 1995 the satellite SOHO was launched which, together with GONG, provides a major step forward in both the quantity and the quality of available solar oscillation data. It is with this in mind that we decided to organize the workshop to prepare for the optimal use of this wealth of data, with which to deepen our understanding of solar structure and specifically, of one of the longest-standing problems in solar and stellar modelling: the treatment of convection.

This book presents a historical perspective on plate tectonics. In doing so it discusses the foundations of rigid plate tectonics and the limitations of this approach. This classic approach explains the data at a level of 95 % precision. The authors explain data anomalies as a result of the discrepancies between spatial geodetical data and rigid kinematics in oceans. Data and its interpretation from various disciplines are pulled together in this book.

Nineteen contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision. An essential resource for researchers and graduates in applied mathematics, computer science and geophysics who are interested in the state-of-the-art developments in multivariate approximation.

A review of such natural disasters as floods and landslides, highlighting the possibility of safe and correct land planning and management by means of a global approach to territory. Since the events deriving from slope and fluvial dynamics are commonly triggered by the same factor, occur at the same time and are closely related, this book analyses floods and slope stability phenomena as different aspects of the same dynamic system: the drainage basin.

Structural geology has developed at a very rapid pace in recent years. Evolution of Geological Structures in Micro- to Macro-Scales, covering a wide spectrum of current research in structural geology from the grain scale to the scale of orogenic belts and from the brittle to the ductile field, provides an overview of newly emerging concepts in a single volume. The book covers a wide range of advances in such broad fields as hydraulic factures, normal faults, overthrusts, ductile shear zones, rock fabrics, folds, superposed folds and basement structures.

The book contains the notes of the lectures presented by outstanding experts at the 7th EADN School on plasma astrophysics. It is an up-to-date review of a number of basic topics in the physics of cosmic plasmas. The subject is treated both from a theoretical point of view and from that of the observational and diagnostic tools that provide us with the physically relevant data. The reader will have at hands a comprehensive and rather complete presentation of the subject, thanks also to the parallel development of the theoretical and experimental aspects. The book addresses graduate students and researchers in different areas who want to have a rapid and up-to-date introduction to this subject.

It is now possible to determine concentrations of trace constituents and pollutants in the lower atmosphere from space, a development which heralds a new era for tropospheric chemistry.

The authors describe how to develop and validate methods for determining tropospheric trace constituents from satellite data, to encourage the use of these data by atmospheric chemists, and to explore the undoubted synergism which will develop between satellite and ground-based measurements, and will eventually give rise to a permanent observation system for the troposphere. The book comprises several comprehensive overviews, prepared by acknowledged experts in the field, together with a series of individual reports from investigators whose work represents the cutting edge of the subject. A variety of results, giving global distributions of several species and their modelling are reported. Most results stem from ESA satellite data, but there is also an account of the North American work in this field which has mainly concentrated on global distributions of ozone.

It is fair to say that the field, as it develops, will revolutionize the way in which atmospheric chemistry is done. This timely book provides a good introduction for anyone with an interest in the future of the troposphere.

The reasons for writing this book are very simple. We use and teach com puter aided techniques of mathematical simulation and of pattern recogni tion. Life would be much simpler if we had a suitable text book with methods and computer programmes which we could keep referring to. Therefore, we have presented here material that is essential for mathematical modelling of some complex geological situations, with which earth scientists are often confronted. The reader is introduced not only to the essentials of computer modelling, data analysis and pattern recognition, but is also made familiar with the basic understanding with which they can plunge into when solving related and more complex problems. This book first makes a case for seismic stratigraphy and then for pattern recognition. Chapter 1 provides an extensive review of applications of pattern recognition methods in oil exploration. Simulation procedures are presented with examples that are fairly simple to understand and easy to use on the computer. Several geological situations can be formulated and simulated using the Monte Carlo method. The binary lithologic sequences, discussed in Chapter 2, consist of alternating layers of any two of sand, shale and coal."

It has always been ESO's aim to operate the VLT in an interferometric mode (VLTI) which allows the coherent combination of stellar light beams col lected by the four 8-m telescopes and by several smaller auxiliary telescopes. In December 1993, in response to financial difficulties, the ESO Council de cided to postpone implement at ion of the VLTI, Coude trains and associated adaptive optics for all the UTs but included provisions for continuing tech nological and development programmes devoted to the aim of reintroducing these capabilities at the earliest possible date. The desirability of carrying out the full VLTI programme as originally envisaged at the earliest possible moment has not, however, diminished, es pecially in view of VLTI's exceptional capabilities and resulting potential for new and exciting discoveries. In recent years, interferometric projects have begun to playa central role in ground-based high-resolution astronomy, and numerous instruments have been completed or are in the process of construc tion. Several large-aperture interferometers will probably co me on-line near the turn of the century. The impending presence of these new instruments represents an important incentive both for clarifying the scientific cases for various VLTI implementation plans and for ensuring VLTI's competitiveness in the international context over the next 1O 20 years."

Perilous Planet Earth places our concern about the threat to Earth from asteroids and comets within an historical context, looking at the evidence for past events within the geological and historical records. The book looks at the way in which prevailing views about modes of global change have changed dramatically over the years. It also considers the way in which catastrophic events are now seen to have influenced the course of evolution in the distant past, as well as the rise and fall of civilisations in more recent times. Professor Palmer argues that the better we understand our past, the greater the likelihood that we will be able to take appropriate action to preserve our civilisation for the future. Written in an engaging style that avoids jargon, the book will appeal to general readers and academics with an interest in evolution, geology, astronomy, social anthropology and history.

Lunar Gravimetry: Revealing the Far-Side provides a thorough and detailed discussion of lunar gravity field research and applications, from the initial efforts of the pre-Apollo and Luna eras to the dedicated gravity mapping experiments of the third millennium. Analysis of the spatial variations of the gravity field of the Moon is a key selenodetic element in the understanding of the physics of the Moon's interior. Remarkably, more than forty years after the initial steps in lunar exploration by spacecraft, the global gravity field still remains largely unknown, due to the limitations of standard observations techniques. As such, knowledge of the high-accuracy and high-resolution gravity field is one of the remaining unsolved issues in lunar science.

Beyond the four centuries of sunspot observation and the five decades during which artificial satellites have monitored the Sun that is to say for 99.99999% of the Sun 's existence our knowledge of solar history depends largely on analogy with kindred main sequence stars, on the outcome of various kinds of modelling, and on indirect measures of solar activity. They include the analysis of lunar rocks and meteorites for evidence of solar flares and other components of the solar cosmic-ray (SCR) flux, and the measurement of cosmogenic isotopes in wood, stratified ice and marine sediments to evaluate changes in the galactic cosmic-ray (GCR) flux and thus infer changes in the sheltering magnetic fields of the solar wind. In addition, shifts in the global atmospheric circulation which appear to result from cyclic fluctuations in solar irradiance have left their mark in river sediments and in the isotopic composition of cave deposits. In this volume the results these sources have already produced have been summarised, paying special attention to those that reflect processes in different parts of the Sun 's interior and that display periodicities and trends which may enable us to forecast future large-scale environmental changes.

The "European Experiment on the Transport and Transformation of Environmentally Relevant Trace Constituents over Europe" (EUROTRAC) was established in 1986 to tackle the scientific problem and combine the expertise, knowledge and resources in Europe, in order to apply them over a large region covering the greater part of the continent. EUROTRAC is a coordinated multidisciplinary scientific research project involving field measurements, laboratory studies, instrument development and development of comprehensive computer models for the simulation of the physical and chemical processes in the lower atmosphere.

This book provides an in-depth coverage of modern research on dynamical systems. The first part discusses stellar dynamics, integrable systems, the transition to chaos and instabilities in stellar dynamics as well as the dynamics of spiral galaxies. Models are given and compared with observations. The second part is devoted to the direct method of N-body simulations, to gas dynamics simulations and to galaxy formation.
Special care is taken to give to a pedagogical presentation of the material which makes this a unique text well suited for graduate courses in astrophysics.

This book begins with a very readable survey "The Sun Today" by J.-C. Pecker. It is followed by thorough reviews from leading experts covering theory and observations. The focus shifts from the solar core, studied via neutrino emissions and helioseismology, through the interface regions where it is believed the large-scale magnetic fields are generated, to the corona, where most of the high temperature phenomena characteristic of this region may be studied directly. As energetic particles play such a vigorous role in this part of the sun, a separate session was devoted to their transport and storage in the corona.

In the dozen years since the first edition appeared, there has been a great advance in understanding of the Earth's deep interior. This is not because there have been breakthroughs in understanding, or even many changes of ideas, but largely because of many small advances, often the result of improved tech niques. This has led to a complete revision of the book. For instance, we have a much better idea of how the cloud of gas that formed the Solar Nebula evolved into the Sun and the planets, and of the chemical processes that accompanied its evolution and determined the mix of elements in the Earth. We have a better understanding of convection and how plates are an essential part of it, and how it is accompanied by chemical processes that have extracted the materials to build continents. Although the major variation within the Earth is radial, improved geophysical and geochemical techniques have made progress in investigating and under standing the lateral heterogeneities, and it is encouraging that when geochemists and geophysicists talk about lateral heterogeneities they can sometimes be referring to the same thing. Plumes have become very fashionable as the cause of hot-spot magmatism and associated geochemical anomalies, probably origi nating at the base of the mantle (though clear evidence for their existence is lacking)."

Nuclear astrophysics as it stands today is a fascinating science. Even though, compared to other scientific fields, it is a young discipline which has developed only in this century, it has answered many questions concerning the under standing of our cosmos. One of these great achievements was the concept of nucleosynthesis, the creation of the elements in the early universe in interstellar matter and in stars. Nuclear astrophysics has continued, to solve many riddles of the evolution of the myriads of stars in our cosmos. This review volume attempts to provide an overview of the current status of nuclear astrophysics. Special emphasis is given to the interdisciplinary nature of the field: astronomy, nuclear physics, astrophysics and particle physics are equally involved. One basic effort of nuclear astrophysics is the collection of ob servational facts with astronomical methods. Laboratory studies of the nuclear processes involved in various astrophysical scenarios have provided fundamen tal information serving both as input for and test of astrophysical models. The theoretical understanding of nuclear reaction mechanisms is necessary, for example, to extrapolate the experimentally determined reaction rates to the thermonuclear energy range, which is relevant for the nuclear processes in our cosmos. Astrophysical models and calculations allow us to simulate how nuclear processes contribute to driving the evolution of stars, interstellar matter and the whole universe. Finally, elementary particle physics also plays an important role in the field of nuclear astrophysics, for instance through weak interaction processes involving neutrinos."

The?rsteditionofthistextappearedin1994.Shortlyafterthethirdprinting, our editor suggested that we attempt a second edition because new devel- mentsinstellarstructureandevolutionhadmadeouroriginalworkoutdated. We (the original authors, CJH and SDK) reluctantly agreed but with res- vations due to the e?ort involved. Our initial reluctance disappeared when we were able to convince (cajole, twist the arm of, etc.) our new coauth- colleague Virginia Trimble to join us. (Welcome Virginia!) We (i.e., all three of us) hope that you agree that the present edition is a great improvement compared to the 1994 e?ort. Our objectives in this edition are the same ones we set forth in 1994: Whatyouwill?ndisatextdesignedforourtargetaudience:thety- cal senior undergraduate or beginning graduate student in astronomy or astrophysics who wishes an overview of stellar structure and e- lution with just enough detail to understand the general picture. She or he can go on from there to more specialized texts or directly to the research literature depending on talent and interests. To this end, this text presents the basic physical principles without chasing all the (interesting!) details. For those of you familiar with the ?rst edition, you will ?nd that some things have not been changed substantially (F = ma is still F = ma), while othersde?nitelyhave.Forexample,Chapter2hasbeencompletelyrewritten.