Ebook: The Physics of Complex Systems (New Advances and Perspectives)

It is widely known that complex systems and complex materials comprise a major interdisciplinary scientific field that draws on mathematics, physics, chemistry, biology, and medicine as well as such social sciences as economics. The role of statistical physics in this new field has been expanding. Statistical physics has shown how phenomena and processes in different research areas that have long been assumed to be unrelated can have a common description. Through the application of statistical physics, methods developed for studying order phenomena in simple systems and processes have been generalized to more complex systems (e.g., polymers, biological macromolecules, and glasses) and processes (e.g., chaos, turbulence, economics, jamming, and biological functions). The two conceptual pillars in this approach are scaling and universality.

This volume contains all the lectures presented at the CLV Course of the International School of Physics “Enrico Fermi” held on 1–11 July 2003 in Varenna, Italy. They focus on recent advances and perspectives in the physics of complex systems and provide both an overview of the field and a more detailed examination of the new ideas and unsolved problems that are currently attracting the attention of researchers. 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, this collection is pedagogically focused so that the material will be accessible to a wider audience. We hope that this published form of the lectures will augment the pedagogical utility of the presentations. Bear in mind that the field of complex systems is very broad and that no single volume can be truly comprehensive.

This book should be a useful reference work for anyone interested in this area, whether beginning graduate student or advanced research professional. It provides up-to-date reviews of cutting-edge topics compiled by leading authorities and is designed to both broaden the reader’s competence within their own field and encourage the exploration of new problems in related fields.

The present subfield configuration of the physics of complex systems is suggested by the topic groupings used in this volume. These groupings provide a kind of “backbone” for the course and include i) scaling behavior, ii) supramolecular systems, polymers, associating polymers, polyelectrolytes and gels, iii) granular matter, iv) biological materials and systems, v) high-temperature superconductivity, vi) phase separation and out-ofequilibrium dynamics, vii) glass transition, supercooled fluids, and viii) geometrically constrained dynamics.

To facilitate the free interchange of ideas, 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. The Course schedule was such that extra time was allowed for informal discussion. Student participants were given special encouragement to participate in the poster sessions. Both the seminar contributions and the posters are included in this volume.

The book opens with an M. H. Cohen tribute to Enrico Fermi on the occasion of the 50th anniversary of the Varenna school (July 1953–July 2003). M. H. Cohen also reviews in detail the interplay between simplicity and complexity.

The opening lectures of B. Widom concern the hydrophobic effect, interfaces, and contact lines in three-phase coexistence. D. R. Nelson reports on recent developments in the Thomson problem in viruses, vesicles, and colloidosomes, and on the unzipping experiments carried out on single DNA molecules. S. Havlin and A. Bunde contribute a detailed examination of fractal correlations in medicine, biology, climate models, and global warming. E. I. Shakhnovic contributes a more specialized review of the field of protein folding, evolution, and design, including the most recent experimental work.

G. Parisi and C. Tsallis review important topics of general interest in statistical physics. Parisi also provides both an overview and a detailed examination of combinatorial optimization and Tsallis does the same for non-extensive statistical mechanics. K. A. Mueller considers intrinsic heterogeneous high-temperature superconductors from the point of view of complexity.

P.-G. de Gennes reports on the development of physical models and techniques used in the study of cellular adhesion. L. Blum discusses phase behavior in polyelectrolites and T. Schneider phase behavior in superconductivity. J. K. Percus reviews dynamical properties of fluids under tight confinement. Electrostatics in biological systems is discussed by M. Barbosa and F. Brochard considers properties of artificial cells.

The theory and applications associated with granular materials provide very precise tools for many of the topics discussed in the lectures, e.g., structural arrest at the glass transition, gelification, and non-equilibrium pattern formation. A. Coniglio proposes a statistical mechanics approach, based on clustering and frustration, that highlights similarities between the jamming of granular materials and glassy systems. H. L. Swinney reports on original studies of spatial patterns and shocks in granulary media. Related to this area is the contribution of H. J. Herrmann.

More detailed aspects of the glassy state are treated in complementary lectures. K. Binder discusses the statistical mechanics of glass and the glass transition. S. H. Chen, using mode coupling theory, discusses the critical slowdown in attractive glassy systems characterized by the existence of two types of structurally arrested states.

The Course faculty included 13 lecturers and 10 invited seminar speakers. Most of the students and young researchers attending the Course presented original contributions in the poster session.

The aim of the Course was not only to present reviews of all the various subareas, but also to stimulate the search for a unified approach in complex systems and complex materials by gathering together participants from a variety of specialized backgrounds. We all worked very hard, attending nearly 60 hours of lectures, seminars, and discussions during the two-week period. We hope this effort was rewarding for everyone attending.

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 during meals, coffee breaks, and the extended free period following lunch. 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.

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 Professor F. Bassani for his encouragement and advice during the preparation for the School. We also thank the General Committee of the Italian Physical Society (SIF), the European Commission, the Unesco-Roste, the National Organization for the New Technologies the Energy and the Environment (ENEA), the Istituto Nazionale di Fisica della Materia (INFM), the MIUR-PRIN02 project Unifying Concepts in Jamming, the US and European divisions of the Office of Naval Research (ONR), the Fondazione Bonino-Pulejo for their generous financial support. Last, but certainly not least, we offer our appreciation to B. Alzani, C. Vasini and M. Missiroli 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, due to the finite size of the auditorium, we were not able to admit to the Enrico Fermi School. Secondly, we wish to thank Ente Villa Monastero for making their beautiful buildings and gardens available to us “invaders.” Lastly, we thank the citizens of Varenna for their warmth and hospitality.

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

F. Mallamace and H. E. Stanley

1. Introduction

2. Static adhesion

3. Patch growth: a simple example

4. Tear-out processes

5. Extension towards less soft objects

6. Conclusions

1. Introduction

2. Molten silicondioxide and its mixtures with other oxides: the case of strong glass formers

3. Search for a characteristic length of the glass transition via confinement effects

4. The infinite-range Potts glass with p > 4 states: A scenario for the structural glass transition?

5. Final comments

1. Introduction

2. Experiment

3. SANS data analysis

4. Scaling plot of SANS intensity distribution

5. Results and discussion

6. Conclusions

1. Introduction

2. Phenomenology of the glass transition

3. A lattice glass model

4. A few experimental facts about granular media

5. Approaches á la Edwards to a Statistical Mechanics for granular media

6. Models for granular media

7. A mean-field study of hard spheres under gravity on a random graph

8. A hard-sphere binary mixture under gravity

9. Conclusions

1. Introduction

2. Friction and contact dynamics of grains in densely packed form

3. Evolution of percolating force chains in compressed granular media

4. Conclusions

1. Introduction

2. Patterns in vertically oscillated granular layers

3. Molecular Dynamics simulations

4. Localized structures and lattice dynamics

5. Continuum description

6. Shock waves in granular materials

7. Discussion

1. Introduction

2. General considerations

3. A well-understood problem: bipartite matching

4. Constraint optimization

5. An intermezzo on random graphs

6. Coloring a graph

7. Analytic computations

8. Conclusions

1. Introduction

2. Mathematical properties

3. Connection to thermodynamics

4. Applications

5. Final remarks

1. Introduction

2. Revisiting N-continuous density-functional theory; chemical reactivity and “atoms” in “molecules”

3. Excitation spectra in DFT

4. Noninteracting electron ensembles of given density

1. The hydrophobic effect

2. Interfaces and contact lines in three-phase coexistence

Introduction

1. One dimension

2. Single file, non-passing

3. Passing region

Introduction

1. Transient pores

2. Lipidic tubes

1. Introduction

2. Theory of electrolytes

3. Onsager bounds

4. The mean spherical approximation

5. The BIMSA for dimers

6. The polyelectrolyte MSA with the triplet exclusion chain approximation

7. Conclusions

1. Description

2. DNA in the presence of monovalent counterions and surfactants

3. DNA in the presence of multivalent ions

4. Conclusions

1. Introduction

2. Theory of virus shapes

3. Grain boundary scars

1. Introduction

2. Simple models provide valuable insights into protein folding

3. News from experiment

4. Detailed all-atom simulations —where theory meets experiments

5. Analysis of the folding nucleus at atomic resolution

6. From ensemble to single molecules —pulling and stretching

7. Bringing evolution into picture —conservation and designability

8. Bringing structure into the picture: designability

1. Introduction

2. Local distortions

3. Pairing

4. Pseudogap

5. Concluding comments

1. Introduction

2. Long-term correlated signals

3. Mean return interval R_q

4. Distribution function P_q(r) of the return intervals

5. Clustering of the return intervals

6. Conditional distribution function P_q(r|r₀)

7. Evaluation of observational and reconstructed datasets

8. Conclusion

1. Introduction

2. Income distribution in Australia

3. Wealth distribution from interacting additive stochastic processes

4. Conclusion

1. Introduction

2. Experiment

3. Results and discussion

4. Conclusions