Proceedings of the NATO Advanced Study Institute, Crete, Greece, July 14-24, 1985

Fractal geometry allows the description of natural patterns and the establishment and testing of models of pattern formation. In particular, it is a tool for geoscientists. The aim of this volume is to give an overview of the applications of fractal geometry and the theory of dynamic systems in the geosciences. The state of the art is presented and the reader obtains an impression of the variety of fields for which fractal geometry is a useful tool and of the different methods of fractal geometry which can be applied. In addition to specific information about new applications of fractal geometry in structural geology, physics of the solid earth, and mineralogy, proposals and ideas about how fractal geometry can be applied in the reader's field of studies will be put forward.

Researchers in the natural sciences are faced with problems that require a novel approach to improve the quality of forecasts of processes that are sensitive to environmental conditions. Nonlinearity of a system may significantly complicate the predictability of future states: a small variation of parameters can dramatically change the dynamics, while sensitive dependence of the initial state may severely limit the predictability horizon. Uncertainties also play a role. This volume addresses such problems by using tools from chaos theory and systems theory, adapted for the analysis of problems in the environmental sciences. Sensitive dependence on the initial state (chaos) and the parameters are analyzed using methods such as Lyapunov exponents and Monte Carlo simulation. Uncertainty in the structure and the values of parameters of a model is studied in relation to processes that depend on the environmental conditions. These methods also apply to biology and economics. For research workers at universities and (semi)governmental institutes for the environment, agriculture, ecology, meteorology and water management, and theoretical economists.

The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

This volume contains the proceedings of a conference held in Wiirzburg, August 20-24, 1990. The theme of the conference was Bifurcation and Chaos: Analysis, Algorithms, Ap plications. More than 100 scientists from 21 countries presented 80 contributions. Many of the results of the conference are described in the 49 refereed papers that follow. The conference was sponsored by the Deutsche Forschungsgemeinschaft, and by the Deutscher Akademischer Austauschdienst. We gratefully acknowledge the support from these agen cies. The science of nonlinear phenomena is evolving rapidly. Over the last 10 years, the emphasis has been gradually shifting. How trends vary may be seen by comparing these proceedings with previous ones, in particular with the conference held in Dortmund 1986 (proceedings published in ISNM 79). Concerning the range of phenomena, chaos has joined the bifurcation scenarios. As expected, the acceptance of chaos is less emotional among professionals, than it has been in some popular publications. A nalytical methods appear to have reached a state in which basic results of singularities, symmetry groups, or normal forms are everyday experience rather than exciting news. Similarly, numerical algorithms for frequent situations are now well established. Implemented in several packages, such algorithms have become standard means for attacking nonlinear problems. The sophisti cation that analytical and numerical methods have reached supports the vigorous trend to more and more applications. Pioneering equations as those named after Duffing, Van der Pol, or Lorenz, are no longer exclusively the state of art.

Today, climate-related processes and problems are referred to as Global Change by nearly everyone including scientists, politicians, and economists; citizens worldwide are anxious about the often ob served disorientation of our environment under the influence of man. Better information on the Earth's natural systems and their possible alterations is necessary. The topic itself is so wide that sound scien tific descriptions of it as a whole are rare. For the non-specialist infor mation from relevant fields is not easy to obtain; and often, the pro gnostic models presented are contradictory and even for specialists difficult to evaluate. Therefore, this book on Climate, Earth Processes and Earth History by Richard Huggett fills an important gap. It discusses the great, climate-related areas of the Earth's environment. The atmosphere, the hydrosphere, the sediments as products of weathering and geomorphic processes, the relief as landforms and soils, and the biosphere are thoroughly treated as the prominent sub systems which are greatly affected by climate. These subsystems not only control the visual and internal aspects of our landscapes, but they are themselves especially influenced by climatic changes which can be due to either changes in the natural system or anthropogenic changes. Thus, our landscapes will be subject to significant altera tions, if climatic variations exceed certain thresholds. The plan for the present book by Richard Huggett was originally discussed in regard to the Springer Series on Physical Environment.

The Geo-Sciences Panel is a synonym for the Special Programme on Global Transport Mechanisms in the Geo-Sciences. This Programme is one of the special programs established by the NATO Science Committee to promote the study of a specific topic using the usual NATO structures, namely, Advanced Research Workshops, Advanced Study Institutes, Conferences, Collaborative Research Grants, Research-Studies and Lecture Visits. The aim of the Programme is to stimulate and facilitate international col laboration among scientists of the member countries in selected areas of global transport mechanisms in the Earth's atmosphere, hydrosphere, lithosphere and asthenosphere, and the interactions between these global transport processes. Created in 1982, the Geo-Sciences Panel followed the Air Sea Interactions Panel which was very successful in reviewing mechanisms at the air-sea-ice interface. Initially the Geo-Sciences Panel recognized the importance of magma chambers, ore deposits, geochemical cycles, seismic activity and hydrological studies. However, the Panel was rap idly convinced that the climate system is one of the most important sys tems in which to promote research on global transport mechanisms. Consequently, the Panel welcomed the organization of a course on Physically Based Modelling and Simulation of Climate and Climatic Change. This course was launched in Belgium in 1984 during both the Liege colloquium on Coupled Ocean-Atmosphere tlodels and the Louvain-Ia Neuve General Assembly of the European Geophysical Society. Rapidly scientists recognized that this course was timely and would be well received by the climate community, especially by junior researchers in this multi- and inter-disciplinary field.