This book illustrates how models of complex systems are built up and provides indispensable mathematical tools for studying their dynamics. This second edition includes more recent research results and many new and improved worked out examples and exercises.

This book teaches how to use Mathematica to solve a wide variety of problems in mathematics and physics. It is based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students. The book is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs. The first part, in which the reader learns how to use a variety of Mathematica commands, contains examples, not long explanations; the second part contains attractive applications.

This book teaches how to use Mathematica to solve a wide variety of problems in mathematics and physics. It is based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students. The book is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs. The first part, in which the reader learns how to use a variety of Mathematica commands, contains examples, not long explanations; the second part contains attractive applications.

This book illustrates how models of complex systems are built up and provides indispensable mathematical tools for studying their dynamics. This second edition includes more recent research results and many new and improved worked out examples and exercises.

Universality is one of the fascinating features of condensed matter physies: it is the property whereby systems of radieally different composition and structure ex- hibit similar behavior. In the mid-1960s the word entered usage to express the fact that the equations of state of several substances could be mapped onto one another near the critical point: critieal universality. Renormalization group theory in the early 1970s provided both an explanation and a sharper definition of universality. Systems with similar behavior - universality classes - correspond to the same fixed point of a renormalization group transformation. A number of brilliant con- tributions showed how the same concepts could be applied to non-thermodynamie systems, such as the statisties of self-avoiding walks or of connected clusters on a lattice. A few years later it was realized that chaotie dynamieal systems mayaiso exhibit some degree of universality, the paradigmatic example being the period doubling cascade in the iterated maps of the unit interval into itself.

"Amphiphilic layers" play essential roles in the behaviour of a great variety of disperse systems such as micelles, microemulsions and vesicles. They can also exist as isolated mono- or bilayers, or constitute extended liquid crystalline structures. Although the properties of these different systems may at first sight seem unrelated, theoretical interpretations of them depend on several common concepts. This was the reason for bringing together scientists working in this area for the International Winter School on the Physics of Amphiphilic Layers, which was held at Les Houches, 10-18 February, 1987. The topics treated in the proceedings volume are mono- and bilayers, interactive forces between layers (with special emphasis on steric forces), ordered structures (in particular swollen lamellar phases and defects), vesicles, micelles (including polymer-like systems), microemulsions (especially random bicontinuous structures) and porous media. The importance of thermal fluctuations in the amphiphilic layers is stressed. Recent results are presented and literature references allow readers not familiar with the subject to find any background information they require.

Cellular automata are fully discrete dynamical systems with dynamical variables defined at the nodes of a lattice and taking values in a finite set. Application of a local transition rule at each lattice site generates the dynamics. The interpretation of systems with a large number of degrees of freedom in terms of lattice gases has received considerable attention recently due to the many applications of this approach, e.g. for simulating fluid flows under nearly realistic conditions, for modeling complex microscopic natural phenomena such as diffusion-reaction or catalysis, and for analysis of pattern-forming systems. The discussion in this book covers aspects of cellular automata theory related to general problems of information theory and statistical physics, lattice gas theory, direct applications, problems arising in the modeling of microscopic physical processes, complex macroscopic behavior (mostly in connection with turbulence), and the design of special-purpose computers.

This book is the proceedings of a workshop on problems at the interface between elementary particle and nuclear physics. It deals with experimental and theoretical developments in the investigation of hadrons and nuclei and in the study of their interactions at low and high energies, including nonperturbative quantum chromodynamics, quark confinement, hadron spectroscopy, hadronic interactions, strange particles, hypernuclei, structure functions of nucleons and nuclei, antiproton annihilation on nucleons and nuclei, quark-gluon plasmas and heavy-ion collisions. Plans for new accelerators are evaluated and some related topics in astrophysics, such as supernovae and neutrinos, are discussed.

Macroscopic physics provides us with a great variety of pattern-forming systems displaying propagation phenomena, from reactive fronts in combustion, to wavy structures in convection and to shear flow instabilities in hydrodynamics. These proceedings record progress in this rapidly expanding field. The contributions have the following major themes: - The problems of velocity selection and front morphology of propagating interfaces in multiphase media, with emphasis on recent theoretical and experimental results on dendritic crystal growth, Saffman-Taylor fingering, directional solidification and chemical waves. - The "unfolding" of large-scale, low-frequency behavior in weakly confined homogeneous systems driven far from equilibrium, and more specifically, the envelope approach to the mathematical description of textures in different cases: steady cells, propagating waves, structural defects, and phase instabilities. - The implications of the presence of global downstream transport in open flows for the nature, convective or absolute, of shear flow instabilities, with applications to real boundary layer flows or shear layers, as reported in contributions covering experimental situations of fundamental and/or engineering interest.

7 Les Houches The purpose of this workshop was to bring together, for the first time, active scientists from very different fields, such as physics, chemistry, physiology and the behavioural sciences, all having a common interest: The interac tion of static magnetic fields with biological and macromolecular matter. As physicists, biologists and medical scientists naturally have different scientific competences, attitudes and abilities, this appeared to be an enterprise of un certain issue. However, it turned out that all participants tried to find (and many succeeded in reaching) a mutual basis of understanding. Thanks to a fair number of outstanding, comprehensive talks and to very active discus sions, most of us, we believe, have substantially enlarged our insight into the actual hard facts within a research area that was considered for a long time - and still remains in many aspects - somewhat controversial. The perhaps most striking and useful reaction to magnetic fields at the supermolecular level is the alignment of biopolymers, proteins, viruses, large assemblies such as retinal rods and membranes when suspended in a solvent, usually water. The ease of alignment depends on the anisotropy of the dia magnetic susceptibility of the constituent groups and bonds and, in addition, on the extent of their mutual orientational order inside a macromolecular assembly. Here very strong fields above I-lOT appear to be necessary, in general, to achieve measurable alignment."

The Winter School held in Les Houches on March 12-21, 1985 was devoted to Semiconductor Heterojunctions and Superlattices, a topic which is recognized as being now one of the most interesting and active fields in semiconductor physics. In fact, following the pioneering work of Esaki and Tsu in 1970, the study of these two-dimensional semiconductor heterostructures has developed rapidly, both from the point of view of basic physics and of applications. For instance, modulation-doped heterojunctions are nowadays currently used to investigate the quantum Hall effect and to make very fast transistors. This book contains the lectures presented at this Winter School, showing in particular that many aspects of semiconductor heterojunctions and super lattices were treated, extending from the fabrication of these two-dimensional systems to their basic properties and applications in micro-and opto-electron ics. Among the subjects which were covered, one can quote as examples: molecular beam epitaxy and metallorganic chemical vapor deposition of semi conductor compounds; band structure of superlattices; properties of elec trons in heterojunctions, including the fractional quantum Hall effect; opti cal properties of two-dimensional heterostructures; quantum well lasers; and two-dimensional electron gas field effect transistors. It is clear that two-dimensional semiconductor systems are raising a great deal of interest in many industrial and university laboratories. From the number of applications which were received and from the reactions of the participants, it can certainly be asserted that this School corresponded to a need and came at the right time."

The trend towards miniaturisation of microelectronic devices and the search for exotic new optoelectronic devices based on multilayers confer a crucial role on semiconductor interfaces. Great advances have recently been achieved in the elaboration of new thin film materials and in the characterization of their interfacial properties, down to the atomic scale, thanks to the development of sophisticated new techniques. This book is a collection of lectures that were given at the International Winter School on Semiconductor Interfaces: Formation and Properties held at the Centre de Physique des Rouches from 24 February to 6 March, 1987. The aim of this Winter School was to present a comprehensive review of this field, in particular of the materials and methods, and to formulate recom mendations for future research. The following topics are treated: (i) Interface formation. The key aspects of molecular beam epitaxy are emphasized, as well as the fabrication of artificially layered structures, strained layer superlattices and the tailoring of abrupt doping profiles. (ii) Fine characterization down to the atomic scale using recently devel oped, powerful techniques such as scanning tunneling microscopy, high reso lution transmission electron microscopy, glancing incidence x-ray diffraction, x-ray standing waves, surface extended x-ray absorption fine structure and surface extended energy-loss fine structure. (iii) Specific physical properties of the interfaces and their prospective applications in devices. We wish to thank warmly all the lecturers and participants, as well as the organizing committee, who made this Winter School a success."

Based on a third-year course for French students of physics, this book is a graduate text in functional analysis emphasizing applications to physics. It introduces Lebesgue integration, Fourier and Laplace transforms, Hilbert space theory, theory of distribution a la Laurent Schwartz, linear operators, and spectral theory. It contains numerous examples and completely worked out exercises.