The second edition of this volume has been extensively revised. A different version of Chap. 7, reflecting recent significant progress in understanding of spatiotempo ral chaos, is now provided. Much new material has been included in the sections dealing with intermittency in birth-death models and noise-induced phase transi tions. A new section on control of chaotic behavior has been added to Chap. 6. The subtitle of the volume has been changed to better reflect its contents. We acknowledge stimulating discussions with H. Haken and E. Scholl and are grateful to our colleagues M. Bar, D. Battogtokh, M. Eiswirth, M. Hildebrand, K. Krischer, and V. Tereshko for their comments and assistance. We thank M. Lubke for her help in producing new figures for this volume. Berlin and Moscow A. s. Mikhailov April 1996 A. Yu. Loskutov Preface to the First Edition This textbook is based on a lecture course in synergetics given at the University of Moscow. In this second of two volumes, we discuss the emergence and properties of complex chaotic patterns in distributed active systems. Such patterns can be produced autonomously by a system, or can result from selective amplification of fluctuations caused by external weak noise."

Our aim in this book is to present and enlarge upon those aspects of parallel computing that are needed by practitioners of computational science. Today al most all classical sciences, such as mathematics, physics, chemistry and biology, employ numerical methods to help gain insight into nature. In addition to the traditional numerical methods, such as matrix inversions and the like, a whole new field of computational techniques has come to assume central importance, namely the numerical simulation methods. These methods are much less fully developed than those which are usually taught in a standard numerical math ematics course. However, they form a whole new set of tools for research in the physical sciences and are applicable to a very wide range of problems. At the same time there have been not only enormous strides forward in the speed and capability of computers but also dramatic new developments in computer architecture, and particularly in parallel computers. These improvements offer exciting prospects for computer studies of physical systems, and it is the new techniques and methods connected with such computer simulations that we seek to present in this book, particularly in the light of the possibilities opened up by parallel computers. It is clearly not possible at this early stage to write a definitive book on simulation methods and parallel computing."

For more than 100 years the Beilstein Handbook has been publishing checked and evaluated data on organic compounds. It has become the major reference book for the chemical and physical properties of organic com pounds. The prediction of these physical properties was the subject of the Beilstein workshop. The ability to predict physical properties is for several reasons of great interest to the Beilstein Institute. It is of primary importance to be able to check the abstracted data for accuracy and to eliminate simple mistakes like typing errors. Presently all the work whether manuscript writing or evaluation of data is carried out manually. This is very time consuming, with the entry of Beilstein into electronic data gathering and publication, the opportunity for computerized consistency checking has become available. Contrary to belief, when one examines the Beilstein Handbook or Chemical Abstracts there is a dearth of chemical information. There are a great many compounds but few are well defined resulting in large gaps in the information available to the chemist. These information gaps could be filled by using algorithmic methods to estimate the properties of interest. An important question to answer is "What is the chemist's reaction to estimated data?" Will he accept it for use, within limits defined by the method, or will it be unacceptable and therefore detrimental for the data base. However if one could partly fill gaps in the data base the increase in the power of the search techniques would be marked."

Considering aspects of symmetry rules in chemistry, one is faced with con tradictory terms as for example, "90 % concertedness" sometimes being used in literature. To accept conservation of orbital symmetry to be as controlled as inversion by alternative principles seems far more promising. The intention of this book is aimed at introducing a qualitative understanding of phase rela tions in electromagnetic interactions. Avoiding one-sided dogmatism we tried to demonstrate the importance of alternative principles as guidelines to the evolution of alternative order in chemical systems. Passing through the jungle of information it became extremly important to control again and again our insights into the ordering phenomena by experi ments under conditions as coherent as possible. We became more aware of the fact that chemistry - the science of "becoming" in complex systems - can not be understood by mechanistic details, i. e. THROUGHPUT-studies alone, because the mechanism is only true for the special system under inves tigation and does not offer a tool for the evolution of opposite order. We had to accept chemistry as a mediator between molecular physics and general epistemology. This quite unusual combination was directed by excel lent teachers and the realizations were made possible by enthusiastic, open minded coworkers (see references). The next target we will strive for on this journey will be to quantify the alternative principles, that means obtaining the order parameters of H. Haken (e. g. in asymmetric synthesis).

This book contains the proceedings of the international workshop on Many-Atom Interactions in Solids, which was held June 5-9, 1989, in Pajulahti, Finland. The purpose of the workshop was to bring together physicists, chemists and materials scientists working in the field of interatomic interactions and their applications in computer simulations of condensed matter. The workshop attracted a good fraction of the active groups in the field, and created lively discussion and interchange of ideas. The contributions in this volume have been grouped by the editors into review type articles and more specific applications to different topics. The order of the articles does not follow the order of the presentations in the workshop. The editors wish to express their gratitude first of all to all the workshop par ticipants for creating an enjoyable and fruitful workshop and to the contributors for their efforts in putting together these proceedings. We hope that this volume will be a useful resource for practitioners in and newcomers to this exciting field. We would like to thank Jens N!l1rskov for his help in planning the scientific pro gramme and Eija Jarvinen for taking care of most of the practical arrangements of the workshop. The workshop was made possible by financial support from the Finnish Ministry of Education, the Research Institute for Theoretical Physics (Helsinki), NORDITA (Copenhagen), and Helsinki University of Technology.

Chemistry is the science of substances (today we would say molecules) and their transformations. Central to this science is the complexity of shape and function of its typical representatives. There lies, no longer dependent on its vitalistic antecedents, the rich realm of molecular possibility called organic chemistry. In this century we have learned how to determine the three-dimensional structure of molecules. Now chemistry as whole, and organic chemistry in particular, is poised to move to the exploration of its dynamic dimension, the busy business of transformations or reactions. Oh, it has been done all along, for what else is synthesis? What I mean is that the theoretical framework accom panying organic chemistry, long and fruitfully laboring on a quantum chemical understanding of structure, is now making the first tentative motions toward building an organic theory of reactivity. The Minkin, Simkin, Minyaev book takes us in that direction. It incorporates the lessons of frontier orbital theory and of Hartree-Fock SCF calculations; what chemical physicists have learned about trajectory calculations of selected reactions, and a simplified treatment of all-important solvent effects. It is written by professional, accomplished organic chemists for other organic chemists; it is consistently even-toned in its presentation of contending approaches. And very much up to date. That this contemporary work should emerge from a regional university in a country in which science has been highly centralized and organic chemistry not very modern, invites reflection."

In this text experts review experimental studies that directly reveal the relationship between the atomic structure and physical behavior of high-Tc superconductors. The thorough discussion centers on twins, twin boundaries, the vortex lattice, and magnetic and mechanical properties in connection with structural imperfections. Particular attention is paid to the role of the oxygen atom in the Y-Ba-Cu-O and La-Cu-O species. The experimental methods evaluated include electron and X-ray diffraction, electron microscopy, and M-ssbauer spectroscopy. This book makes extraordinarily valuable data obtained at the Institute of Solid State Physics at Chernogolovka accessible to the wider international community of researchers in superconductivity.

As a general rule any interdisciplinary subject and that includes Computational Theoretical Organic Chemistry (CTOC) incorporates people from the two overlaping areas. In this case the overlaping areas are Computational Theoretical Chemistry and Organic Chemistry. Since CTOC is a relatively young science, people continue to shift from their major discipline to this area. At this particular time in history we have to accept in CTOC people who were trained in Computational Theoretical Chemistry and do not know very much about Organic Chemistry, but more often the opposite case is operative Experimental Organic Chemistry who have not been exposed to Computational Theoretical Chemistry. This situation made NATO Advanced Study Institute in the field of CTOC necessary. The inhomogenity outlined above was present in the NATO Advanced Study Institute, held at Menton in July 1980, and to some degree it is noticable from the content of this volume. This book contains 20 contributions. The first contribution is an Introduc tion chapter in which the initiated experimental chemists are briefed about the subject matter. The last chapter describes very briefly the "Computational Laboratory" that was designed to help people with an experimental back ground in order to obtain some first hand experience. Between the first and the last chapters there are 18 contributions. These contributions were arranged in a spectrum from the exclusively method oriented papers to the applications of existing computational methods to problems of interest in Organic Chemistry."

This book is intended to collect in one place as much information as possible on the use of EPR spectroscopy in the analysis of systems in which two or more spins are magnetically coupled. This is a field where research is very active and chemists are elbow-to-elbow with physicists and biologists in the forefront. Here, as in many other fields, the contributions coming from different disciplines are very important, but for active researchers it is sometimes difficult to follow the literature, due to differences in languages, and sources which are familiar to, e. g. , a physicist, are exotic to a chemist. Therefore, an effort is needed in order to provide a unitary description of the many different phenomena which are collected under the title. In order to define the arguments which are treated, it is useful to state clearly what is not contained here. So we do not treat magnetic phenomena in conductors and we neglect ferro- and antiferromagnetic resonance. The basic foundations of EPR spectroscopy are supposed to be known by the reader, while we introduce the basis of magnetic interactions between spins. In the first two chapters we review the foundations of exchange interactions, trying to show how the magnetic parameters are bound to the electronic structure of the interacting centers.

The present book is an attempt to outline some, certainly not all, mathematical aspects of modern organic chemistry. We have focused our attention on topological, graph-theoretical and group-theoretical features of organic chemistry, Parts A, B and C. The book is directed to all those chemists who use, or who intend to use mathe matics in their work, and especially to graduate students. The level of our exposition is adjusted to the mathematical background of graduate students of chemistry and only some knowledge of elementary algebra and calculus is required from the readers of the book. Some less well-known. but still elementary mathematical facts are collected in Appendices 1-4. This, however, does not mean that the mathematical rigor and numerous tedious, but necessary technical details have been avoided. The authors' intention was to show the reader not only how the results of mathematical chemistry look, but also how they can be obtained. In accordance with this, Part 0 of the book contains a few selected advanced topics which should give the reader the flavour of the contemporary research in mathe matical organic chemistry. One of the authors (I.G.) was an Alexander von Humboldt fellow in 1985 when the main part of the book was written. He gratefully acknowledges the financial support of the Alexander von Humboldt Foundation which enabled his stay at the Max-Planck-Institut fUr Strahlenchemie in M iilheim and the writing of this book."

The quantum theory of magnetism is a well-developed part of contemporary solid-state physics. The basic concepts of this theory can be used to describe such important effects as ferromagnetic ordering oflocalized magnetic moments in crystals and ferromagnetism of metals produced by essentially delocalized electrons, as well as various types of mutual orientation of atomic magnetic moments in solids possessing different crystal lattices and compositions. In recent years, the spin-fluctuational approach has been developed, which can overcome some contradictions between "localized" and "itinerant" models in the quantum mechanics of magnetic crystals. These are only some of the principal achievements of quantum magnetic theory. Almost all of the known magnetic properties of solids can be qualitat ively explained on the basis of its concepts. Further developments should open up the possibility of reliable quantitative description of magnetic properties of solids. Unfortunately, such calculations based on model concepts appear to be very complicated and, quite often, not definite enough. The rather small number of parameters of qualitative models are usually not able to take into account the very different types of magnetic interactions that appear in crystals. Further development of magnetic theory requires quantitative information on electronic wave function in the crystal considered. This can be proved by electronic band structure and cluster calculations. In many cases the latter can be a starting point for quantitative calculations of parameters used in magnetic theory."

The aim of this book is to give a simple, short, and elementary introduction to the second quantized formalism as applied to a many-electron system. It is intended for those, mainly chemists, who are familiar with traditional quantum chemistry but have not yet become acquainted with second quantization. The treatment is, in part, based on a series of seminars held by the author on the subject. It has been realized that many quantum chemists either interested in theory or in applications, being educated as chemi ts and not as physicists, have never devoted themselves to taking a course on the second quantized approach. Most available textbooks on this topic are not very easy to follow for those who are not trained in theory, or they are not detailed enough to offer a comprehensive treatment. At the same time there are several papers in quantum chemical literature which take advantage of using second quantization, and it would be worthwhile if those papers were accessible for a wider reading public. For this reason, it is intended in this survey to review the basic formalism of second quantization, and to treat some selected chapters of quantum chemistry in this language. Most derivations will be carried out in a detailed manner, so the reader need not accept gaps to understand the result.

Solid-State NMR is a branch of Nuclear Magnetic Resonance which is presently experiencing a phase of strongly increasing popularity. The most striking evidence is the large number of contributions from Solid-State Resonance at NMR meetings, approaching that ofliquid state resonance. Important progress can be observed in the areas of methodological developments and applications to organic and inorganic matter. One volume devoted to more or less one of each of these areas has been published in the preceding three issues. This volume can be considered an addendum to this series. Selected methods and applications of Solid-State NMR are featured in three chapters. The first one treats the recoupling of dipolar interactions in solids, which are averaged by fast sample rotation. Following an introduction to effective Hamiltonians and Floquet theory, different types of experiment such as rotary resonance, dipolar chemical shift correlation spectroscopy, rotational resonance and multipulse recoupling are treated in the powerful Floquet formalism. In the second chapter, the different approaches to line narrowing of quadrupolar nuclei are reviewed in a. consistent formulation of double resonance (DaR) and dynamic angle spinning (DAS). Practical aspects of probe design are considered as well as advanced 2D experiments, sensitivity enhancement techniques, and spinning sideband manipulations. The use of such techniques dramatically increases the number of nuclei which can be probed in high resolution NMR spectroscopy. The final chapter describes new experimental approaches and results of structural studies of noncrystalline solids."

I feel very honored that I have been asked to write a Foreword to this book. The subject of the book - "Coupled cluster theory" - has been around for about half a century. The basic theory and explicit equations for closed-shell ground states were formulated before 1970. At the beginning of the seventies the rst ab initio calcu- tion were carried out. At that time speed and memory of computers were very limited compared to today's standards. Moreover, the size of one-electron bases employed was small, so that it was only possible to achieve an orientation in methodical aspects rather than to generate new signi cant results. Extensive use of the coupled-cluster method started at the beginning of the eighties. With the help of more powerful computers the results of coupled-cluster approaches started to yield more and more interesting results of relevance to the interpretation of experimental data. New ideas in methodology kept appearing and computer codes became more and more ef cient. This exciting situation continues to this very day. Remarkably enough, even the - quired equations can now be generated by a computer with the help of symbolic languages. The size of this monograph and the rich variety of articles it contains attests to the usefulness and viability of the couple-cluster formalism for the h- dling of many-electron correlation effects. This represents a vivid testimony of a tremendous work that has been accomplished in coupled-cluster methodology and its exploitation.

1. A.-R. Grimmer, Berlin, FRG; B. Bl}mich, Aachen, FRG: Introduction to Solid-State NMR 2. F. Laupretre, Paris, France: High-Resolution 13C NMRInvestigations of Local Dynamics in Bulk Polymers at Temperatures Below andAbove the Glass-Transition Temperature 3. D. Raftery, Philadelphia, PA;B.F. Chmelka, Santa Barbara, CA: Xenon NMR Spectroscopy 4. G. Fleischer, Leipzig, FRG; F. Fujara, Mainz, FRG: NMR as a Generalized Incoherent Scattering Experiment 5. P. Bl}mler, B. Bl}mich, Mainz, FRG: NMR Imaging of Solids

For chemists, biochemists, physicists and materials scientists, pressure as an experimental variable represents a tool that provides unique information about the microscopic properties of the materials being studied. In addition to its use as a research tool for investigating the energetics, structure, dynamics and kinetics of molecular transformations of materials, pressure is also being used to modify the properties of materials to preserve or improve their properties. The contributions collected here cover the main areas of high pressure research, including applications in materials science, condensed matter physics, chemistry and biochemistry. In addition, some papers offer more specialised aspects of high pressure studies. The book makes clear the impressive range of fundamental and applied problems that can be studied by high pressure techniques and also points towards a major growth of high pressure science and technology in the new millennium.

By incorporating biologically-inspired functions into ICT, various types of new-generation information and communication systems can be created. Just some example of areas already benefiting from such design inspiration are network architectures, information processing, molecular communication, and complex network modeling for solving real world-problems. This book provides the theoretical basis for understanding these developments and explains their practical applications. Highlighted inserts appears throughout to help readers to understand the very latest topics in these emerging research fields. The book ends with a more philosophical discussion on how new ICT solutions can be found by looking at analogous systems in biology. This new way of thinking may help researchers and practitioners to apply innovative ideas in developing next-generation technologies.

Understanding molecular orbitals (MOs) is a prerequisite to appreciating many physical and chemical properties of matter. This extensively revised second edition of A Pictorial Approach to Molecular Bonding presents the author's innovative approach to MOs, generating them pictorially for a wide variety of molecular geometries. A major enhancement to the second edition is the PC- and Macintosh-compatible Nodegame software, which is coordinated with the text and aids in pictorially teaching molecular orbital theory using generator orbitals.

Fundamentals of Continuum Mechanics of Soils provides a long-needed general scheme for the study of the important yet problematic material of soil. It closes the gap between two disciplines, soil mechanics and con- tinuum mechanics, showing that the familiar concepts of soil mechanics evolve directly from continuum mechanics. It confirms concepts such as pore pressures, cohesion and dependence of the shear stress on consolidation, and rejects the view that continuum mechanics cannot be applied to a material such as soil. The general concepts of continuum mechanics, field equations and constitutive equations are discussed. It is shown how the theory of mixtures evolves from these equations and how, along with energetics and irrevers- ible thermodynamics, it can be applied to soils. The discussion also sheds light on some aspects of mechanics of materials, especially compressible materials. Examples are the introduction of the Hencky measure of strain, the requirement of dual constitutive equations, and the dependence of the spent internal energy on the stored internal energy. Researchers in engineering mechanics and material sciences may find that the results of experiments on soils can be generalized and extended to other materials. The book is a reference text for students familiar with the fundamentals of mechanics, for scholars of soil engineering, and for soil scientists. It is also suitable as an advanced undergraduate course in soil mechanics.

This book consists of two parts, the first dealing with dissipative structures and the second with the structure and physics of chaos. The first part was written by Y. Kuramoto and the second part by H. Mori. Throughout the book, emphasis is laid on fundamental concepts and methods rather than applications, which are too numerous to be treated here. Typical physical examples, however, including nonlinear forced oscilla tors, chemical reactions with diffusion, and Benard convection in horizontal fluid layers, are discussed explicitly. Our consideration of dissipative structures is based on a phenomenolog ical reduction theory in which universal aspects of the phenomena under consideration are emphasized, while the theory of chaos is developed to treat transport phenomena, such as the mixing and diffusion of chaotic orbits, from the viewpoint of the geometrical phase space structure of chaos. The title of the original, Japanese version of the book is Sanitsu Kozo to Kaosu (Dissipative Structures and Chaos). It is part of the Iwanami Koza Gendai no Butsurigaku (Iwanami Series on Modern Physics). The first Japanese edition was published in March 1994 and the second in August 1997. We are pleased that this book has been translated into English and that it can now have an audience outside of Japan. We would like to express our gratitude to Glenn Paquette for his English translation, which has made this book more understandable than the original in many respects."

The state-of-the-art in contemporary theoretical chemistry is presented in this 4-volume set with numerous contributions from the most highly regarded experts in their field. It provides a concise introduction and critical evaluation of theoretical approaches in relation to experimental evidence.

Predicting molecular structure and energy and explaining the nature of bonding are central goals in quantum chemistry. With this book, the editors assert that the density functional (DF) method satisfies these goals and has come into its own as an advanced method of computational chemistry. The wealth of applications presented in the book, ranging from solid state sys tems and polymers to organic and organo-metallic molecules, metallic clus ters, and biological complexes, prove that DF is becoming a widely used computational tool in chemistry. Progress in the methodology and its imple mentation documented by the contributions in this book demonstrate that DF calculations are both accurate and efficient. In fact, the results of DF calculations may pleasantly surprise many chem ists. Even the simplest approximation of DF, the local spin density method (LSD), yields molecular structures typical of ab initio correlated methods. The next level of theory, the nonlocal spin density method, predicts the energies of molecular processes within a few kcallmol or less. Like the Hartree-Fock (HF) and configuration interaction (CI) methods, the DF method is based only on fundamental physical constants. Therefore, it does not require semiempirical parameters and can be applied to any molecular system and to metallic phases. However, DF's greatest advantage is that it can be applied to much larger systems than those approachable by tradition al ab initio methods, especially when compared with correlated ab initio methods."

Solid-State NMR is a branch of Nuclear Magnetic Resonance which is presently experiencing a phase of strongly increasing popularity. The most striking evidence is the large number of contributions from Solid-State Resonance atNMR meetings, approaching that ofliquid state resonance. Important progress can be observed in three areas: Methodological developments, applications to inorganic matter, and applications to organic matter. These developments are intented to be captured in three volumes in this series, each of them being devoted to more or less one of these areas. The present volume on Solid-State NMR III is devoted mainly to organic matter. The recent developments of deuteron NMR and their applications are reviewed in the first chapter. Crosspolarization, MAS, and dynamic angle spinning are being explored for enhancement of information and sensitivity. In addition to the analysis of classical relaxation times and modern 2D spectra, detailed dynamic information becomes accessible from investigations of the relaxation time anisotropies. The second chapter examines cross-polarization in static and rotating solids under conditions of spin diffusion and thermal motion. The underlying dipole-dipole interaction is further exploited by the techniques described in the third chapter for studies of polymer-polymer miscibility. Short range techniques are discriminated from long-range techniques based on spin diffusion. The use ofthese techniques is illustrated by a case study ofPMMAJPVF blends. The last chapter addresses novel z methods and applications of two-dimensional exchange NMR for investigations of relative molecular orientations, polymer morphology, molecular dynamics, and macroscopic molecular order."

The contributions to this book cover a wide range of applications of Soft Computing to the chemical domain. The early roots of Soft Computing can be traced back to Lotfi Zadeh's work on soft data analysis [1] published in 1981. 'Soft Computing' itself became fully established about 10 years later, when the Berkeley Initiative in Soft Computing (SISC), an industrial liaison program, was put in place at the University of California - Berkeley. Soft Computing applications are characterized by their ability to: * approximate many different kinds of real-world systems; * tolerate imprecision, partial truth, and uncertainty; and * learn from their environment. Such characteristics commonly lead to a better ability to match reality than other approaches can provide, generating solutions of low cost, high robustness, and tractability. Zadeh has argued that soft computing provides a solid foundation for the conception, design, and application of intelligent systems employing its methodologies symbiotically rather than in isolation. There exists an implicit commitment to take advantage of the fusion of the various methodologies, since such a fusion can lead to combinations that may provide performance well beyond that offered by any single technique.