This volume contains the lectures presented at the CXXXIV Course of the Enrico Fermi School held 9–19 July 1996 in Varenna, Italy. The Course focuses on the physics of complex systems, and provides both an overview of the field and a more detailed examination of those topics within the field that are currently of greatest interest to researchers.

It is widely known that the properties of complex systems play an important role in a variety of different and overlapping areas in physics, chemistry, biology, mathematics, and technology. The research field of complex systems is very broad, so no volume can be comprehensive. Although all of the lecturers have made important contributions within their individual areas, and most have made significant contributions to the field as a whole, in this collection they have kept talks pedagogically focused, thereby making the material accessible to a wider audience. We hope that this published form of the lectures will augment the pedagogical utility of the presentations.

This book should be a useful reference work for people interested in this area, whether beginning graduate students or advanced research professionals. Up-to-date reviews of cutting-edge topics are provided, reviews compiled by leading authorities and designed to both broaden the reader's limits of competence within the reader's own field and encourage the exploration of new problems in related fields.

An overview of the present status of the physics of complex systems is provided by the way the general topics of the volume are grouped. These groupings provide a “backbone” for the Course, and include i) scaling behavior, ii) supramolecular systems, iii) aggregation, aggregation kinetics and disorderly growth mechanisms, iv) granular matter, v) polymers, associating polymers, polyelectrolytes and gels, vi) amphiphiles, emulsions, colloids, membranes and interface phenomena, vii) molecular motors, viii) phase separation and out-of-equilibrium dynamics, ix) turbulence, chaos and chaotic dynamics, x) glass transition, supercooled fluids, and xi) geometrically-constrained dynamics.

To facilitate the free interchange of new perspectives in the field, the lecturers and seminar leaders also made themselves available as course participants. Their active presence made possible a constant updating of the topics under discussion, and kept the focus clearly on a “state-of-the-art” level. Student participants were given special encouragement to participate in the poster sessions. Many of the seminar and poster contributions are included in this volume.

The opening lectures of P.-G. de Gennes concern both the theory and applications of granular matter. Applications of nonequilibrium pattern formation and spatiotemporal chaos are reviewed in some detail by F.T. Arecchi. S. Havlin's review provides a detailed examination of fractal correlation in medicine and biology, and, in a similar vein, A. Libchaber reports recent developments on the physics of proteins (assembly, force generation and motion). Detailed and original studies about developments of physical models and techniques applied to the study of biological systems are reported in the contributions of M. F. Shlesinger and his collaborators. Phase transitions appear through the discussion of H. N. W. Lekkerkerker on the phase transitions in colloidal solutions and the presentations of R. Bansil and F. Brochard.

Scaling concepts provide very precise tools for many of the topics discussed at the School; their applications are reviewed by F. Family in the dynamics of surfaces and interfaces. Dynamical properties of complex fluids, and, in particular, Brownian motion are reviewed by R. Klein for colloidal suspensions in the hydrodynamic regime. Y. Klafter and N. Ostrowsky give detailed information on Brownian motion in confined systems. In this connection S. V. Buldyrev and R. N. Mantegna report on such new and interesting applications as scaling concepts in economics (a model of company growth) and finance (providing analogies with turbulence).

Beginning with first principles, J. P. Hansen considers the structure and dynamics of suspensions. Microemulsion systems and the role of surfactants are discussed by S. H. Chen, with an emphasis on such leading properties of these systems as percolation and surface curvature in the bicontinuous phase. Other important topics in this area are presented in separate discussions of H. Hoffmann, A. Robledo and P. Tartaglia.

Aspects of the glassy state and of the glass transition are treated in several complementary lectures. In particular, a discussion on cluster and frustration is provided by A. Coniglio. G. Parisi discusses the critical slowing-down in glassy systems and C. A. Angell reviews several important impending achievements within the fields of strong and fragile liquids and two-state complexity in glass-forming systems, including biomolecules. Related to this area are the contributions of F. Sciortino, A. Bunde and S. Yip.

The Course faculty included 15 lecturers and 18 invited seminar speakers. Most of the students and young researchers attending the Course presented original contributions in the poster session. The Course schedule was such that extra time was allowed for informal discussion.

Three “ground rules” were adopted: i) each session was to consider coherent arguments, ii) lecturers could be interrupted at any time during the talks for questions, and iii) speakers, young researchers, and students were encouraged to mix in the dining rooms, the coffee breaks, and the long after-lunch pause. The outcome was as we had hoped: numerous spontaneous discussions and lively debates took place in an honest, friendly atmosphere of work. Many of these discussions occurred in the beautiful gardens of Villa Monastero and Villa Cipressi. Judging from the positive and often enthusiastic reactions of the lecturers and participants during and after the Course, the event was extraordinarily successful in achieving its intended objectives.

This Course was the first International Summer School on the broad subject of complex systems. The aim was not only to present reviews of all the various phenomena, but also to stimulate the search for a unified approach to the area by gathering together participants from a variety of specialized backgrounds. We all worked very hard (perhaps too hard!), attending nearly 60 hours of lectures, seminars and discussions within a period of only two weeks. We hope this effort was rewarding for everyone attending.

It is fortunate that we are able to present in this volume the final versions of nearly all the lectures and seminars presented at the Course. So much of importance and of high quality was presented that the material defies condensation or hierarchical ordering: the participants – experienced scientists, postdocs, and graduate students – have contributed with skill and enthusiasm.

We are grateful for the invaluable contributions and suggestions of G. Maino and M. F. Shlesinger, scientific secretaries for the School. We give special thanks to Profs. R. A. Ricci and G. Benedek for their encouragement and advice during the preparation for the School. We also thank the General Committee of the Italian Physical Society (SIF), the Italian National Council of Research (CNR), the National Group of Condensed Matter (GNSM-CNR), the National Organization for the New Technologies the Energy and the Environment (ENEA), the USA and the European offices of the Office of Naval Research (ONR) for their generous financial support. Last, but certainly not least, we offer our appreciation to E. Mazzi, P. Rucci and C. Vasini of the SIF for their valuable and excellent cooperation before, during, and after the School period, and for their heroic work in producing the present volume.

Before concluding, some personal remarks. First, we sincerely apologize to all the students whom we were not able to accept for the Enrico Fermi School, due to the finite size of the auditorium. Second, we wish to thank the Ente Villa Monastero for making available to us invaders such beautiful buildings and gardens. And, lastly, we thank the good citizens of Varenna sul Lago di Como for the warmth and hospitality shown us throughout our two-week stay as guests of the most beautiful villages on the face of the Earth.

We offer this volume to the reader in the hope that it will provide something of the enjoyment and reward that we and the other participants in the School experienced.

Francesco Mallamace and H. Eugene Stanley