Nonextensivity in Seismic Complexity and Earthquake Networks

S. Abe
Tsukuba University, Japan

It is shown that both spatial and temporal geometric distances between two successive earthquakes obey Tsallisian q-statistics and well satisfy "duality". Based on the conjectured relationship between q-statistics and the concept of complex networks, the earthquake networks are defined and constructed by making use of the seismic data taken in Southern California and Japan. It is found that the networks are scale-free and represents the small-world structure in the static picture. On the other hand, in the dynamical picture, the networks are directed and do not represent the small worlds. Discovery of two novel scale-free laws are reported on the directed earthquake networks.

Vlasov analysis of metaequilibrium

C. Anteneodo and R.O. Vallejos
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil

The Hamiltonian Mean-Field model (HMF), an inertial $XY$ ferromagnet with infinite-range interactions, has been extensively studied in the last few years, especially due to its long-lived meta-equilibrium states, which exhibit breakdown of ergodicity, anomalous diffusion, aging, and non-Maxwell velocity distributions.
The most widely investigated meta-equilibrium states of the HMF arise from special (fully magnetized) initial conditions that evolve to a spatially homogeneous state with well defined macroscopic characteristics and whose lifetime increases with the system size, eventually reaching equilibrium. These metaequilibrium states have been observed for specific energies close below the critical value 0.75 corresponding to a ferromagnetic phase transition. Numerical experiments have also shown the disappearance of the family of homogeneous meta-equilibrium states below a certain energy.
We investigated the dynamical stability of these states. Since the -space dynamics is governed by a Vlasov equation in the thermodynamic limit, we applied a nonlinear stability test to (i) a selected set of spatially homogeneous solutions of Vlasov equation, qualitatively similar to those numerically observed and (ii) numerical coarse-grained distributions of the finite-N dynamics. Our analysis indicates that the disappearance of the homogenous family at 0.68 can be interpreted as a reflection of the loss of Vlasov stability at that critical energy.

Multifractal analysis of turbulence and granular flow

T.Arimitsu and N.Arimitsu
Tsukuba University, Japan

The probability density function (PDF) of velocity fluctuations ofgranular turbulence ("glanulence") observed by Radjai and Roux [1] intheir two-dimensional simulation of a slow granular flow under homogeneous quasistatic shearing is studied by the multifractal analysis (MFA) proposed by the present authors [2--5]. Radjai and Roux reported that there is an evident analogy between the scaling features of turbulence and of granulence in spite of the fundamentally different origins of fluctuations in these systems. MFA is a unified self-consistent approach for the systems with large deviations, which has been constructed based on the Tsallis-type distribution function [6]
that provides an extremum of the "extensive" Reny or the "non-extensive" Tsallis entropy [6] under appropriate constraints. It is shown by the present analysis that the system of granulence and of turbulence indeed have common scaling characteristics.
References:
[1] F.Radjiai and S.Roux, Phys. Rev. Lett. 89 (2002) 064302.
[2] T.A. and N.A., Phys. Rev. E 61 (2000) 3237.
[3] T.A. and N.A., J. Phys. A: Math. Gen. 33 (2001) L235.
[4] T.A. and N.A., Physica D 193 (2004) 218.
[5] T.A. and N.A., in "Highlights in Condensed Matter Physics", eds.A.Avella et al. (AIP Conf. Proceed. 695, 2003) p.135.
[6] C.Tsallis, J. Stat. Phys. 52 (1988) 479.

Chaotic Neuron Dynamics, Synchronization and Feature Binding: Quantum Aspects

F. T. Arecchi
Department of Physics, University of Firenze, Italy

A central issue of cognitive neuroscience is feature binding ,that is, how a large collection of coupled neurons combines external signals with internal memories into new coherent patterns of meaning. An external stimulus localized at some input spreads over a large assembly of coupled neurons, building up a collective state univocally corresponding to that stimulus. Thus, the synchronization of spike trainsof many individual neurons over a limited time span is the basis of a coherent perception.
Based on recent investigations, a novel conjecture for the dynamics of single neurons and, consequently, for neuron assemblies is formulated. Heteroclinic chaos (HC), that is ,the sequential approach to a saddle focus (SF) and a saddle node (SN),yields trains of equal spikes occurring at apparently erratic times .HC is proposed as the most suitable time code; a new quantitative indicator, called propensity ,is introduced to select the best neuron model.
In order to classify the set of different perceptions, the percept space is given a metric structure by introducing a distance measure between distinct percepts. The distance in percept spaceis conjugate to the duration of the perception in the sense that an uncertainty relation in percept space is associated with time limited perceptions. Thus coding of different percepts by synchronized spike trains entails fundamental quantum features . It is conjectured that they are related to the details of the perceptual chain rather than depending on Planck's action.

Generalization of the Pesin equality for weakly chaotic low dimensional maps

F. Baldovin
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil

The Pesin equality is a central result for nonlinear chaotic systems, linking an entropic functional to the dynamical behavior expressed by the sensitivity to initial conditions. We analyze analytically and numerically weak chaos regimes characterized by the vanishing of the largest Lyapunov exponent for dissipative and conservative maps. For the edge of chaos of unimodal maps it is possible to unambiguously relate the dynamical behavior to Tsallis' entropy. We discuss this connection in higher dimensions.

Aging in Subdiffusion Generated by a Deterministic Dynamical System

E. Barkai
Department of Chemistry and Biochemistry, University of Notre Dame, Usa

We investigate [1] aging behavior in a simple dynamical system: the Geisel--Thomae non-linear map. In the non aging regime this map is known to generates sub-diffusion deterministically. We show that the map exhibits aging behavior when proper initial conditions are choosen. Asymptotic behaviors of the aging diffusion process
are described using the stochastic framework of aging continuous time random walks [2]. We show numerically, how the deterministic aging process is described by an aging diffusion equation which is of fractional order. Our work demonstrates that aging behavior can be found in deterministic low dimensional dynamical systems. Interestingly, the aging behavior we obtain is similar to aging behaviour found for random walks in random environments.

[1] E. Barkai, Aging in Subdiffusion Generated by a Deterministic Dynamical System, Phys. Rev. Lett. 90, 104101 (2003).
[2] E. Barkai, Y. C. Cheng , Aging Continuous Time Random Walks, J. of Chemical Physics 118, 6167 (2003).

Superstatistics: Theory and applications

C. Beck
Queen Mary College, University of London, UK

Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatio-temporal inhomogenities of an intensive variable (e.g. the inverse temperature). They contain Tsallis statistics as a special case. I will briefly discuss the theory and some recent physical applications of superstatistical models. Particular attention is drawn to the large energy asymptotics of general superstatistics, for which a variational principle is developed (joint work with Hugo Touchette).

Fractal Growth of Carbon Schwarzites

G. Benedek

Dipartimento di Scienza dei Materiali, Universita' di Milano-Bicocca, Milano, Italy

Carbon schwarzites, which we have recently synthesized with the new technique of supersonic cluster beam deposition (SCBD), are the long-sought three-dimensional (3D) form of sp2 carbon, after graphite (2D), nanotubes (1D) and fullerenes (0D). It is shown that the potential energy of all forms of sp2 carbon are described by a Helfrich form valid for membranes, which implies that the stable forms of schwarzites, are minimal surfaces. SCBD schwarzitic films are shown to grow as fractal self-affine structures. The parametric conditions for the growth of either schwarzites or nanotubes or fullerenes are established. Since the minimality condition can be fulfilled at each step of the growth process, the latter actually occurs along the valley bottom of the energy landscape, and conversion to other forms of sp2 carbon are very unlikely.

Galilean-Invariant Multi-Speed Entropic Lattice Boltzmann Models

B. M. Boghosian
Department of Mathematics, Bromfield-Pearson Hall
Tufts University, Medford, MA 02155, USA

For certain choices of lattices and particle speeds, the requirement of Galilean invariance has been shown to completely determine the form of the H function used in entropic lattice Boltzmann models for the incompressible Navier-Stokes equations in D dimensions. In this presentation, we substantially generalize the construction of such Galilean-invariant entropic lattice Boltzmann models by allowing for multiple masses and speeds. We show that the required H function for these models must be determined by solving a certain functional differential equation. Remarkably, the solutions to this equation have the form of the Tsallis entropy, where q is determined by the solution to a certain transcendental equation, involving the dimension and symmetry properties of the lattice, as well as the masses and speeds of the particles. In addition, we describe a recently derived entropic lattice Boltzmann model for Burgers' equation in one dimension.

A Non-Gaussian Stock Market Model: the Pricing of Options and Debt

L. Borland
Evnine Vaughan Associates, San Francisco, CA USA

A non-Gaussian model of stock prices based on a statistical feedback processis proposed. Fluctuations evolve according to power-law distributions of (Tsallis) index q. Based on this model, many realistic features of markets are captured, including power-law distributions and volatility-clustering. Option pricing formulae are derived which match well to empirical prices, reproducing the observed volatility smile and skew. A non-Gaussian framework for the capital structure of companies is also derived, leading to formulae for the pricing of corporate debt. We find that both stock options and debt are well-priced using q circa 1.4.

Random walks, liquidity molasses and critical response in financial markets

JP Bouchaud
CEA, Orme Merisiers, F-91191 Gif Sur Yvette, France

Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: long-range correlated market orders that lead to super-diffusion (or persistence), and mean reverting limit orders that lead to sub-diffusion (or anti-persistence). We define and study a model where the price, at any instant, is the result of the impact of all past trades, mediated by a non constant `propagator' in time that describes the response of the market to a single trade. Within this model, the market is shown to be, in a precise sense, at a critical point, where the price is purely diffusive and the average response function almost constant. We show that the power-law decay of the bare impact function comes both from an excess flow of limit order opposite to the market order flow, and to a systematic anti-correlation of the bid-ask motion between trades, two effects that create a `liquidity molasses' which dampens market volatility.

Nonextensivity in the matter-radiation interaction, and the role of the Wheeler-Feynman identity.

A.Carati, M. Marino, L. Galgani
Dipartimento di Matematica, Università di Milano, Italy

If one considers a system of N particles with mutual retarded electromagnetic interactions, one immediately realizes that an analogue of the Olbers paradox is met, because the force acting on a given particle due to all the other (N-1) ones in principle diverges with N. However, for the case of dipoles on a regular lattice we prove that there exist normal modes, so that such a divergence does not appear. This is due to an apparently miracolous compensation, by which a part of total action due to the (N-1) particles exactly cancels the dissipative Radiation term due to the self-field of the considered particle. The proof of such a compensation actually amounts to proving an identity involving the semidifference of the retarded and the advanced fields (summed over all the particles) which had been assumed as a postulate by Wheeler and Feynman in their celebrated old work.

Dynamical instability, diffusion and the Fourier Heat law (*)

G. Casati

Center for Nonlinear and Complex systems, Universita' degli Studi dell' Insubria , Como, Italy

Given a particular classical, many-body Hamiltonian system, no transport theory can predict whether or not this specific Hamiltonian system yields an energy transport governed by the Fourier heat law. By using simple specific examples we analyze the relation between dynamical properties, correlations decay, diffusive behaviour and heat conduction. We show that, acting on the parameter which controls the strength of the on site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.
The connection with the survival probability and the so-called Loschmidt echo is briefly discussed.

(*)It seems there is no problem in modern physics for which there are on record as many false starts, and as many theories which overlook some essential feature, as in the problem of the thermal conductivity of nonconducting crystals
R.E. Peierls

Tumor Gompertzian growth by cellular energetic balance

P. Castorina, D. Zappalà
Dipartimento di Fisica e Astronomia and Infn sezione di Catania, Italy

A macroscopic model of the tumor Gompertzian growth is proposed. The new approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics, and related to the growth inhibitor factors. The model is successfully applied to the multicellular tumor spheroid data.

Symmetry breaking induced directed motions

C.-H. Chang
National Center for Theoretical Science, Taiwan

Many directed motion phenomena in microsystems are ascribed to symmetry breakings. Well known examples include the spatial symmetry breaking of ratchets in biological motors [1] and the temporal symmetry breaking of quantum pumping in quantum dots [2]. Since these two mechanisms are often mixed together in a real system, an interesting question emerges, namely, which kind of symmetry breaking is dominant and decides the directed motion of a system. This question will be illustrated in a simple model with an asymmetry potential and a driving force generated by deterministic chaotic maps [3]. Vector field analysis reveals that the driving force frequency is the most crucial parameter, which decides whether the directed motion is determined by the spatial or the temporal symmetry breakings.

[1] M.O. Magnasco, Phys. Rev. Lett. 71, 1477, (1993).
[2] M. Switkes, C.M. Marcus, K. Campman, A.C. Gossard, Science 283, 1905 (1999).
[3] C.-H. Chang, Phys. Rev. E (Rapid Comm.) 66, 015203(R), (2002).

Work and Heat Fluctuations in Systems with Deterministic and Stochastic Forces

E. G. D. Cohen and R. Van Zon
The Rockefeller University New York, NY, USA

In systems with purely deterministic or purely stochastic forces in a non-equilibrium stationary state, a conventional Fluctuation Theorem holds. However, if both deterministic and stochastic forces are present, the heat fluctuations are qualitatively different from the conventional ones, because of an interference of the two different kinds of forces. Two examples are discussed: that of a Brownian particle confined by a laser induced harmonic potential, which is pulled through the fluid at constant velocity and a parallel electrical circuit with a given current source. These lead to new Fluctuations Theorems which could be of relevance for the design of stable nano machines. A very recent experimental confirmation of these new Fluctuation Theorems has been obtained.

Granular Materials

A. Coniglio

Dipartimento di Scienze Fisiche, Universita' di Napoli "Federico II, Napoli, Italy

After a brief introduction to the complex phenomenology of granular materials, I will discuss a statistical mechanics approach to granular materials at rest,based on Edwards original proposal. The formalism allows to apply standard statistical mechanics techniques to simplified models for granular materials. Using this approach I will investigate by means of analytical and numerical methods the phenomenon of the jamming transition and segregation which occurs in granular systems.

Complexity in the Immune System

M W. Deem
Department of Physics & Astronomy, Rice University Houston, TX , USA

The adaptive vertebrate immune system is a wonder of modern evolution. Under most circumstances, the dynamics of the immune system is well-matched to the dynamics of pathogen growth during a typical infection. Some pathogens, however, have evolved escape mechanisms that interact in subtle ways with the immune system dynamics. In addition, negative interactions the immune system, which has evolved over 400 000 000 years, and vaccination, which has been practiced for only 200 years, are possible. For example, vaccination against the flu can actually increase susceptibility to the flu in the next year. As another example, vaccination against one of the four strains of dengue fever typically increases susceptibility against the other three strains. Immunodominance also arises in the immune system control of nascent tumors--the immune system recognizes only a small subset of the tumor specific antigens, and the rest are free to grow and cause tumor growth.

In this talk, I present a physical theory of original antigenic sin and immunodominance. How localization in the immune system leads to the observed phenomena is discussed.

1) M. W. Deem and H. Y. Lee, ``Sequence Space Localization in the Immune System Response to Vaccination
and Disease,'' Phys. Rev. Lett. 91 (2003) 068101.
2) J.-M. Park and M. W. Deem, ``Correlations in the T Cell Response to Altered Peptide Ligands,'' Physica A, to
appear. http://arxiv.org/abs/q-bio.BM/0404023

Energy Landscapes as complex networks

J. Doye
University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, UK

Typically a system on a complex energy landscape will spend the majority of the time vibrating within the basins of attraction surrounding the minima, punctuated by occasional transitions to other minima along transition state valleys. This suggests a dynamically-motivated description of the energy landscape in terms of a network of minima connected by transition states. This complete network has been obtained for small Lennard-Jones clusters and has properties typical of scale-free networks. This is fairly surprising, since it is a static network and
connections are based on the adjacency of basins in configuration space. We propose that this topology reflects the wide distribution of basin areas, and compare our results to model spatial networks obtained from Apollonian-like packings of circles and hyperspheres. A potential signature of the scale-free topology is a power-law distribution of the basin areas. We obtain this distribution from simulations for a binary Lennard-Jones liquid, and find just such a power-law behaviour. These results suggest that this scale-free pattern of connectivities may be a fundamental feature of the organization of complex energy landscapes.

Active Brownian Particles - Stochastic Dynamics of Swarm Systems

W. Ebeling , U. Erdmann and Lutz Schimansky-Geier
Humboldt-University Berlin

After summarizing basic features of nonlinear Brownian motion we we develope a model of the Brownian dynamics of swarms including noise. This model allows to model the stochastic motion of swarms of biological entities based on energy consumption and conversion into acceleration of motion. The model is applied to swarms with attracting forces leading to confinement. Further we include also hydrodynamic-type forces, which parallelize motions of neighbors. By means of analytical results we can distinguish between translational, rotational and amoebic modes of swarm motion. We study in detail the mean square displacement and the stochastic distribution functions.

References:

[1] F. Schweitzer, W. Ebeling, B. Tilch, Phys. Rev. Lett. 80, 5044 (1998); Phys. Rev. E 64, 02110/1-12
[2] U. Erdmann et al., Eur. Phys. J. B 15, 105 (2000); Phys.Rev. E 65, 061106 (2002); FNL 3, L145 (2003)
[3] M. Okubo, S.A. Levin, Diffusion and ecological problems: Modern perspectives, Berlin Springer 2001.

The physics approach to financial economics

D. Farmer
Santa Fe Institute, New Mexico, USA

Most models in economics are essentially qualitative, failing to produce sharply falsifiable predictions. This is because many of the underlying assumptions of these models are difficult to independently measure. Physicists have challenged the fundamental assumptions of mainstream economic models, and have pursued an alternative philosophy of data analysis. New empirical work has uncovered many interesting laws about markets. However, so far most physics models of economic phenomena suffer from the same lack of falsifiability as the economics models they are designed to replace. Even if many of us believe the underlying assumptions are more reasonable, the value of such models in producing quantitative predictions remains to be demonstrated. There are, however, some indications that this is changing. I will review recent progress in empirical analysis and modeling, including power law and long-memory properties of market data. There are reasons to be optimistic that we will soon obtain testable quantitative models, at least for a restrictive class of economic phenomena.

Monte Carlo simulations of opinion dynamics

S. Fortunato
University of Bielefeld, Germany

Sociophysics simulations are an attempt to describe multi-agents processes occurring in a society in terms of simple concepts and methods of statistical physics. We focus here on opinion dynamics, i. e. on the process that leads to the creation of well defined personal positions (e.g. political orientations) among the people of a community, due to local interactions between the agents. We shall introduce the most popular consensus models and illustrate their main features and predictions.

The metastable liquid-liquid phase transition: from water to colloids and liquid metals.

G. Franzese,
Departament de Física Fonamental, Universitat de Barcelona, Spain

The possibility of a liquid-liquid (LL) phase transition has been often taken into consideration only for anomalous liquids, i.e. liquids with a non-standard behavior for thermodynamics quantities. A typical example is water, where the anomalous increase of isobaric density for decreasing temperature has been shown to imply the theoretical existence of a LL critical point [1,2,3]. However, the opposite relation is not valid [4]: the existence of a LL critical point does not imply the anomalous density behavior [5]. We have shown this result by studying, with molecular dynamics simulations and integral equations approach, a system of particles interacting via an isotropic soft-core attractive potential. We find [6] large ranges of the parameters of the potential for which the system has a LL critical point, described by a mean-field equation à la van der Waals, and crystal polymorphism but no density anomaly. Of great interest is how the existence of a LL critical point in the metastable supercooled liquid phase affects the crystal nucleation [7]. Depending on the parameters of the potential, the system could resemble star-polymers solutions, colloids, protein solutions, or, to some extent, liquid metals.

[1] G. Franzese and H. E. Stanley, J. Phys.: Cond. Mat. 14, 2201 (2002).
[2] G. Franzese, M. I. Marqués, and H. E. Stanley, Phys. Rev. E 67, 011103 (2002).
[3] F. Sciortino, E. La Nave, P. Tartaglia, Phys. Rev. Lett. 91, 155701 (2003).
[4] G. Franzese. G. Malescio, A. Skibinsky, S.V. Buldyrev, and H. E. Stanley, Nature 409, 692 (2001).
[5] G. Franzese. G. Malescio, A. Skibinsky, S.V. Buldyrev, and H. E. Stanley, Phys. Rev. E 66, 051206 (2002).
[6] A. Skibinsky, S.V. Buldyrev, G. Franzese. G. Malescio, and H. E. Stanley, http://lanl.arXiv.gov/find/cond-mat/0309632
[7] M. H. J. Hagen, E. J. Meijer, G. C. A. M. Mooij, D. Frenkel, and H. N. W. Lekkerkerker, Nature 365, 425
(1993); P. Rein ten Wolde and D. Frenkel, Science 277, 1975 (1997).

Metastability and supersymmetry in disordered systems

I. Giardina
INFM and Università di Roma La Sapienza, Italy

The presence of metastable states is a well known feature of disordered systems and plays a crucial role in the slowing down of the dynamics and the occurrence of the glass transition. A deep understanding of the geometric structure of these states and its implications on the dynamical behaviour therefore represents a very important issue. I will show that when analysing the properties of metastable states, and in particular their entropic contribution, a supersymmetry is revealed at a formal level, which has a clear physical interpretation. Systems that have different structures of metastable states seem to behave differently in terms of this supersymmetry: for some of them the supersymmetry is obeyed, for others it is spontaneously broken. I will discuss the meaning of the supersymmetry breaking and its connection with the dynamics. Finally, I will show how the supersymmetry breaking affects some powerful techniques, as the cavity method, which have to be appropriately redefined.

Earthquakes temporal occurrence: statistical studies and Self-Organized Criticality

C. Godano
Università di Napoli, Federico II, Dipartimento di Scienze Ambientali, Caserta, Italy

The distribution of inter-occurrence time between seismic events is a quantity of great interest in seismic risk assessment. We evaluate this distribution for different models of earthquakes occurrence and follow two distinct approaches: The non homogeneous Poissonian and the non Poissonian one. In all cases we obtain either a power law or a power law damped by an exponential factor behaviour. This feature suggests the interpretation of the earthquake occurrence phenomenon as due to some non-linear dynamics. Here we propose that a modification of the Self-Organised Criticality approach could provide a correct modelling of the data.

The physics of complexity: modulation or renewal?

P. Grigolini
Istituto dei Processi Chimico Fisici del CNR
Area della Ricerca di Pisa and Dipartimento di Fisica "Enrico Fermi", Universita' di Pisa, Pisa, ITALY

We study a non-Poisson intermittent process, corresponding to the recent experimental observation of the stimulated fluorescence of the so called "blinking quantum dots" [1,2]. The distribution of sojourn times in the "light on" and "light off" states is an inverse power law with index 1.5. We make a comparison between the renewal and the modulation condition. The former is based on the assumption that the sojourn times are uncorrelated. The latter rests on a modulation prescription that is inspired to the dynamic approach recently proposed by Beck to derive non-extensive thermodynamics [3]. We show that the renewal hypothesis yields aging, in accordance with the result of the analysis of experimental data, recently done by Brokmann et al. [4]. We prove that this property provokes the breakdown of the approaches based on the master equation response to external perturbation, in agreement with the results of Sokolov, Blumen and Klafter [5]. The emission and absorption spectra require a new approach based on the continuous random walk rather than on the quantum master equations [6]. We also prove that the modulation condition does not produce aging effects, and is compatible with the quantum master equation approach.

[1] R. G. Neuhauser, K. T. Shimizu, W. K. Woo, S. A. Empedocles, and M. G. Bawendi, Phys. Rev. Lett 85, 3301 (2000).
[2] M. Kuno, D. P. Fromm, H. F. Hamann, A. Gallagher, and D. J. Nesbitt, J. Chem. Phys. 112, 3117 (2000).
[3] C. Beck, Phys. Rev. Lett. 87, 180601 (2001).
[4] X. Brokmann, J.-P. Hermier, G. Messin, P. Desbiolles, J.-P. Bouchaud, and M. Dahan, Phys. Rev. Lett. 90, 120601 (2003).
[5] I. M. Sokolov, A. Blumen and J. Klafter, Europhys. Lett. 56, 175 (2001).
[6] G. Aquino, L. Palatella and P. Grigolini, in press on Phys. Rev. Lett.

STOCHASTIC RESONANCE: Past --Present-Future

P. Hanggi
Institute of Physics University of Augsburg, Germany

Complex Systems Biology:
Universal Statistics in Gene Expressions, General Relationship between Phenotypic Fluctuations and Evolution Speed, and Origin of Heredity

K. Kaneko
University of Tokyo, Komaba

We intend to understand life as a `complex system', by unveiling universal features underlying all biological systems. For this purpose, we take a constructive approach, by setting up a simple system both experimentally and theoretically, and answer general questions on a biological system. After surveying this standpoint, I discuss some of recent studies along this line, both in theory and experiment.
First, I discuss universal statistical laws of chemical abundances in a cell that sustains recursive production. From theoretical studies of simple protocell models, discovered are a power law law in average gene expression and log-normal distribution of the abundances of each chemical. Experimental verification of these laws is also presented.
Second, to discuss relevance of this phenotypic fluctuations to evolution, we extend fluctuation-dissipation theorem in physics, to obtain universal relationship between phenotypic and genetic fluctuations. Proportionality between evolution speed and phenotypic fluctuation is derived, as is demonstrated experimentally.
The next problem we address concerns with search for some chemicals that suppress the above fluctuations. Taking a simple reaction network model, we show that molecules minority in number are preserved well by suppressing the fluctuations. These molecules control the behavior of a cell relatively strongly, and start to play the role of genetic information.
Origin of heredity and evolvability are discussed, based on this minority controlled state. Last, if time is allowed, differentiation of cells and robust development are explained from dynamical systems theory.

The importance of being central

V. Latora
Dipartimento di Fisica e Astronomia, Infn sezione di Catania, Università di Catania, Italy

The idea of the centrality of individuals and organizations in their social networks was one of the earliest to be pursued by social network analysts. In this talk we review the main measures of structural centrality that have been proposed over the years to quantify the importance of an individual in a social network. We also discuss a new measure of centrality we have
recently introduced and that is based on the concept of efficient propagation of information over the network. We show some applications to social systems, city planning, and to the immune system. We discuss how the issue of structural centrality is related to the protection of critical infrastructures from terroristic attacks, and to cascading effects in the Internet and in electric power grids. Our centrality measure has also been used to develop a method for finding community structures.

What entropy at the edge of chaos?

R. Tonelli, M. Lissia, C. Coraddu

Infn sezione di Cagliari, Italy

Asymptotically the Boltzmann-Gibbs entropy of chaotic systems increases linearly and the sensitivity to initial conditions
is exponential with time: Pesin equality relates these two behaviors. It has been proposed and there exist numerical
evidences that the same framework can be extended to the edge of chaos by using appropriate generalizations of the exponential and of the Boltzmann-Gibbs entropy. We study this conjecture within a specific class of generalized entropies and related exponential using the logistic map as a test case.

Financial networks from correlation-based clustering techniques

R.N. Mantegna
University of Palermo, Italy

We discuss a correlation-based clustering procedure performed on financial time series. Specifically, we consider (i) the filtering of economic information associated with the single linkage clustering procedure producing a minimal spanning tree and a hierarchical tree [1], (ii) the topological properties of the financial networks, (iii) the comparison between topological properties of real data and data obtained by widespread market models [2] and (iv) an extension of the single linkage clustering procedure providing a planar triangular fully connected graph [3].

[1] Rosario N. Mantegna, Hierarchical Structure in Financial Markets, Eur. Phys. J. B 11, 193-197 (1999).
[2] Giovanni Bonanno, Guido Caldarelli, Fabrizio Lillo and Rosario N. Mantegna, Topology of correlation based
minimal spanning trees in real and model markets Physical Review E 68, 046130 (2003).
[3] T. Di Matteo, T. Aste, M. Tumminello and R.N. Mantegna, Hierarchical modeling with Planar Triangular
Fully Connected Graphs, manuscript in preparation.

Transport of interacting particles in binary mixtures

F. Marchesoni*
Dipartimento di Fisica, Universitá di Camerino, Camerino, Italy

The motion of two interacting species of small particles, coupled differently to their environment, is studied both analytically and via numerical simulations. We find three ways of controlling the particle motion of one (passive) B species by means of another (active) A species: (i) dragging the target particles B by driving the auxiliary particles A, (ii) rectifying the motion of the B species on the asymmetric potential created by the A-B interactions, and (iii) dynamically modifying (pulsating) this potential by controlling the motion of the A particles. This allows easy control of the magnitude and direction of the velocity of the target particles by changing the ac drive(s).

*in collaboration with F. Nori and S. Savelev

Optimization by thermal cycling

A. Moebius1, K.H. Hoffmann2 and C. Shoen3

1Leibniz Institute for solid state and material research, Dresdren Germany
2 Institute of Physics, Chemnitz,
3 Max Planck Institute for solid state research, Stuttgart, Germany

Thermal cycling is an euristic optimization algorithm which consists of cyclically heating and quenching by Metropolis and local search procedure, respectively, where theamplitude slowly decreases. In recent years, it has been successfully applied to two combinatorial optimization tasks, the travelling salesman problem and the search for the low-energy states of the Coulomb glass. In these cases, the algorithm is far more efficient than the usual simulated annealing. When applied to an archive of samples instead of to a single one, it can compete with leading genetic local search algorithms.
However, in its original form the algorithm was designed only for the case of discrete variables. Here we demonstrate that its basic ideas can successfully be applied also to a problem with continuous variables, the search for low-energy states of Lennard-Jones clusters.

[1] A. Moebius, A. Neklioudov, A. Diaz-sanchez, K.H. Hoffmann, A. Fachat, M. Schreiber, Phys. Rev. Lett. 79, 4297 (1997).

Ubiquity of metastable-to-stable crossover in weakly chaotic dynamical systems

F. Baldovin1, L. G. Moyano1,2, A. P. Majtey2 , A. Robledo3 and C. Tsallis1

1Centro Brasileiro de Pesquisas Fisicas,Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro -- RJ,
2Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Cordoba, Argentina
3Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico 01000 D.F., Mexico

We present a comparative study of several dynamical systems of increasing complexity, namely, one, two and many globally-coupled standard maps, and the Hamiltonian Mean Field model (i.e., the classical inertial infinitely-ranged ferromagnetically coupled XY spin model). We emphasize the appearance, in all of these systems, of metastable states and their ultimate crossover to the equilibrium state. We comment on the underlying mechanisms responsible for these phenomena (weak chaos) and compare common characteristics. We point out that this ubiquitous behavior appears to be associated to the features of the nonextensive generalization of the Boltzmann-Gibbs statistical mechanics.

Complex networks in astrophysical and geophysical systems

M. Paczuski
Imperial College, London, UK

Complex networks have attracted a great deal of attention recently as descriptions of biological, social, and technological systems. In this talk I demonstrate that they also arise in ordinary physical systems, and lead to new insights. Complex networks arise as (1) physical descriptions of astrophysical plasmas as well as (2) in capturing spatio-temporal correlations of earthquakes. Our recent analysis of observational data of the solar corona reveals that the flux tubes (links) and footpoints (nodes), where they attach on the photosphere, embody a scale free network. The statistics of solar flares and of the magnetic network structure are unified through a self-organized critical model where the avalanches and network co-generate each other into a complex, critical state. By invoking a metric to quantify correlations between earthquakes, networks of earthquakes are made by linking highly correlated events. This metric provides a simple and straightforward alternative to the usual method of analyzing earthquake correlations using space-time windows set by the observer. It also introduces the possibility of using recently developed ideas in complex network theory to reveal new correlation structures of seismicity. We find, for instance, that the earthquake network is both scale free and highly clustered. New scaling laws are found for the distances between earthquakes and their aftershocks. The original Omori law with p=1 emerges as a robust feature of seismicity, holding up to years even for aftershock sequences initiated by intermediate magnitude events.

Quantum Transport In Molecular Devices: A Generalized Langevin-Schroedinger Approach and Beyond

U. Peskin
Department of Chemistry and The Lise Meitner Center for Computational Quantum Chemistry
Technion-Israel Institute of Technology, Haifa 32000, Israel

Electron transport processes through molecular systems has drawn much attention recently due to its potential applications in nano-scale molecular electronics. Electronic tunneling is one of the most important transport mechanism is such systems and characterization of the molecular parameters controlling tunneling rates is of major importance. Particularly interesting in this context is the role of electronic-nuclear coupling in controlling and gating electron transfer through molecules, as suggested by recent experiments measuring intra-molecular electron transfer in donor-bridge-acceptor complexes, and in metal-molecule-metal junctions. Our work aims at a qualitative understanding of the mechanisms of dissipative tunneling and a quantitative prediction of tunneling rates in molecular systems. We study electronic tunneling through a dissipative molecular barrier beyond the weak electronic nuclear coupling limit using an analytically solvable model. The frequency of coherent tunneling oscillations in a symmetric donor-bridge-acceptor system is shown to increase with the intensity of electronic-nuclear coupling at the molecular bridge. This is attributed to the opening of vibronic tunneling pathways with lower effective energy barriers for through-bridge tunneling. The sensitivity of the calculated tunneling frequency to the intensity of the electronic-nuclear coupling at the bridge implies that this coupling enhances electronic tunneling by several orders of magnitude in realistic conditions. Therefore, chemical modifications aiming to control the elasticity (nuclear response) of the molecular bridge are expected to have a significant effect on electronic tunneling rates and can be used for controlling electron transport through molecules.

Statistical Physics for cosmic structures

L. Pietronero
Università di Roma, La Sapienza, Roma , Italy

Clustering and Pattern Formation in Interacting Particle Dynamics

A. Provata
Institute of Physical Chemistry , National Center for Scientific Research "Demokritos" 15310 Athens, Greece

We present a hierarchy of non-linear dynamical systems with increasing complexity and examine their spatiotemporal behavior when they are implemented on low dimensional lattices. More specifically we concentrate on two models a) the Lattice Lotka Volterra model (LLV) which presents conservative dynamics at the mean field level and b) the Lattice Limit Cycle (LLC) model which presents dissipative dynamics at the mean-field level. Both models involve three types of interacting particles but the former involves two-particle interactions while the latter four-particle interactions. Both models lead to spontaneous segregation when they are realised on low dimensional lattices via Kinetic Monte Carlo simulations.
The spontaneously formed clusters have fractal boundaries and their fractal properties depend a) on the specific model, b) the parameters and c) the distance from the bifurcation point in the case of the LLC model. For appropriate boundary conditions, dynamical patterns appear such as stripes and helices. The propagation of fronts between different competing clusters has been studied and is shown to belong to the same universality class as the Eden model.

Complexity, Metastability and Nonextensivity in Hamiltonian dynamics

A. Rapisarda
Dipartimento di Fisica e Astronomia and Infn sezione di Catania, Italy

We will review the dynamical anomalies found in a paradigmatic Hamiltonian model of fully coupled classical spins, showing the most recent findings and the connections with Tsallis q-statistics and glasses [1-4].

[1] A.Pluchino, V. Latora and A. Rapisarda, Phys. Rev. E 69 (2004) 056113.
[2] A.Pluchino, V. Latora and A. Rapisarda, Physica D 193 (2004) 315.
[3] A.Pluchino, V. Latora and A. Rapisarda, Physica A 338 (2004) 60.
[4] A.Pluchino, V. Latora and A. Rapisarda, Continnum Mechanics and Thermodynamics 16 (2004) 245.

Can magnetic inhomogeneity be described with nonextensive thermodynamics?

M.S. Reis1, V.S. Amaral1, J.P. Araujo2 and I.S. Oliveira3
1Departamento de Fisica and CICECO, Universidade de Aveiro, 3810-193 Aveiro Portugal
2IFIMU, Departamento de Fisica, Universidade do Porto, 4150 Porto Portugal
3Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud 150 - Urca, 22290-180 Rio de Janeiro-RJ Brazil

In recent publications we developed the main features of a generalized magnetic system, in the sense of the non-extensive Tsallis thermostatistics. Mean-field-non-extensive models[1] could predict transitions of first and second order, as well as several magnetic anomalies, as a direct consequence of the non-extensivity (through the value of q, the entropic parameter of Tsallis thermostatistics). The theoretical results predicted satisfactorily the peculiar magnetic properties of manganites, that are intrinsically inhomogeneous, and have micro-clusters with fractal shapes, randomly distributed in the material. These features are experimentally confirmed, and are the fundamental ingredients to justify the use of the nonextensive formalism. In the present work, we show the strict correlation between a inhomogeneous magnetic system, described within the Maxwell-Boltzmann statistics, and a homogeneous magnetic system, described within the Tsallis statistics. We could found classes of q(H; T) that characterize the kind of inhomogeneity present in the system (for instance, temperature, magnetic ¯eld, magnetic moment and others). In addition, the description of manganites using Griffiths phase[2] can be recovered with the use of the non-extensive formalism.

[1] M.S. Reis et al., Phys. Rev. B 68 (2003) 014404; ibid66 (2002) 134417; Europhys. Letters 58 (2002) 42.
[2] M.B. Salamon et al., Phys. Rev. Lett. 88 (2002) 197203.

Environmental atmospheric turbulence at Florence airport

S. Rizzo1, A. Rapisarda2,

1 ENAV spa Firenze, Dipartimento di Fisica e Astronomia Università di Catania, salvrizz@tiscali.it
2 Dipartimento di Fisica e Astronomia and Infn Università di Catania

We present an analysis of a time series of wind strength measurements recorded at Florence airport in the period October 2002 - March 2003. The data were taken simultaneously by two runway head anemometers, located at a distance of 900 m, at a frequency of 3.3?10-3Hz. The data show strong correlations over long time spans of a few tens of hours. We performed an analysis of wind velocity as it is usually done for turbulence laboratory experiments[1,2]. Wind velocity returns and wind velocity differences were considered. The pdfs of these quantities exhibit strong non-Gaussian fat tails. The distribution of the standard deviations of the fluctuations can be successfully reproduced by a Gamma distribution while the Log-normal one fails completely. Following Beck and Cohen superstatistics approach [3], we extract the Tsallis entropic index q from this Gamma distribution. The corresponding q-exponential curves reproduce with a very good accuracy the pdfs of returns and velocity differences

• [1] S. Rizzo, A. Rapisarda, cond-mat/0406684;
• [2] C. Beck, Phys. Rev. Lett. 87 (2001) 180601; C. Beck, Physica A 306 (2002) 189; C. Beck, G.S. Lewis and H.L. Swinney, Phys. Rev. E 63 (2001) 035303
• [3] C. Beck C., E.G.D. Cohen, Physica A 322 (2003) 267.

Three stories outside Boltzmann-Gibbs statistics: Mori's q transitions, glassy dynamics, and superstatistical random walks

A. Robledo
Instituto de Física, UNAM, Mexico

First, we analyze the trajectories inside the Feigenbaum attractor and obtain the atypical weak sensitivity to initial conditions and loss of information associated to their dynamics. We identify the Mori singularities in its Lyapunov spectrum with the appearance of a special value for the entropic index q of the Tsallis statistics. Second, the dynamics of iterates at the noise-perturbed transition to chaos in unimodal maps is shown to exhibit the characteristic elements of the glass transition, e.g. two-step relaxation and aging. The properties of the bifurcation gap induced by the noise, including a relationship between relaxation time and entropy, are seen to be comparable to those of a supercooled liquid above a glass transition temperature. And third, the fields of applicability of the Boltzmann-Gibbs, the Tsallis, and the 'Super' statistics are determined by considering Weierstrass random walks and their analog renewal processes together with their corresponding central limit theorems.

Plank distribution by Beck-Cohen superstattistics

A. M. C. Souza1 and C. Tsallis2
1 Departamento de Fisica, Universidade Federal de Sergipe, 49100-000,Sao Cristovao-SE, Brazil
2 Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil.

We consider a phenomenological approach along the lines of nonextensive statistical mechanics to introduce a generalization of Planck quantization. The Beck-Cohen superstatistics associated with this distribution is obtained. We show that the probability density function of the acceleration of particles in turbulence flows are in agreement with the approach introduced here.

Influence of Noise Induced Effects and Periodical Driving on Temporal Characteristic of Josephson Junctions

A. L. Pankratov (1) and B. Spagnolo(2)
(1)Institute for Physics of Microstructures of Russian Academy of Russia, Nizhny Novgorod, Russia
(2)Dipartimento di Fisica e Tecnologie Relative and INFM, Viale delle Scienze, Pad. 18, I-90128 Palermo, Italy

We report an analytical and numerical analysis of influence of fluctuations and periodic driving on temporal characteristic of the Josephson junction. We consider two cases: (a) dichotomous driving and (b) sinusoidal driving. For case (a) the analytical expression of standard deviation of switching time is obtained for arbitrary noise intensity and works well in the range of frequencies of practical interest. For the case of sinusoidal driving the resonant activation effect was observed in the considered system: mean switching time has a minimum as a function of driving frequency. The frequency range where the noise enhanced stability phenomenon is observed and must be avoided is given. The consequences of these noise induced effects on the optimization of timing errors in overdamped Josephson junctions is discussed.

Mathematical structure behind Tsallis statistics

H. Suyari
Department of Information and Image Sciences, Faculty of Engineering, Chiba University, Japan

We present the conclusive mathematical structure behind Tsallis statistics:
(i) law of error in Tsallis statistics [4],
(ii) q-Stirling's formula in Tsallis statistics [5],
(iii) the one-to-one correspondence between the q-multinomial coefficient and Tsallis entropy [6],
(iv) symmetry behind Tsallis statistics [6],
(v) the numerical computations revealing the existence of the central limit theorem in Tsallis statistics [6],
(vi) Pascal's triangle in Tsallis statistics and its properties [6].
In particular, the fifth result (v) provides us with a mathematical representation of the ubiquitous existences of power-law behaviors in nature.

References:
[1] H. Suyari, Nonextensive entropies derived from form invariance of pseudoadditivity, Phys.Rev.E., vol. 65,
066118 (2002).
[2] H. Suyari, On the most concise set of axioms and the uniqueness theorem for Tsallis entropy, J.Phys.A:Math.Gen., vol.35, pp.10731-10738 (2002).
[3] H. Suyari, Generalization of Shannon-Khinchin axioms to nonextensive systems and the uniqueness theorem
for the nonextensive entropy, to appear in IEEE Trans. Inform. Theory.
[4] H. Suyari and M. Tsukada, Law of error in Tsallis statistics, cond-mat/0401540.
[5] H. Suyari, q-Stirling's formula in Tsallis statistics, cond-mat/0401541.
[6] H. Suyari, Mathematical structure derived from the q-multinomial coefficient in Tsallis statistics, cond-
mat/0401546.

Localization and delocalization of knots in polymers.

A. L. Stella
INFM-Dipartimento di Fisica e Sezione INFN, Padova- Italy.

The the concept of knot length is a mathematical and theoretical challenge. The ubiquity of topological entanglement in systems with long macromolecular chains makes this concept extremely relevant for molecular biology, micromanipulation experiments, protein folding etc. We give statistical definitions of the length, l, of a loose prime knot tied into a long, fluctuating ring macromolecule. Monte Carlo results for the equilibrium, good solvent regime show that < l > ~ Nt, where N is the ring length and t ~ 0.75 is independent of the knot topology. In the collapsed regime below the theta temperature, length determinations based on the entropic competition of different knots within the same ring show delocalization (t~1). This delocalization appears to imply an extension of the 4/3 power law valid for ideal knots to the case of fluctuating knotted rings. Applications of our results and methods to the search of knotted proteins, will be discussed.

Metastability and out of equilibrium dynamics of ultrathin magnetic films

F. A. Tamarit
Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Córdoba, Argentina

The two dimensional Ising model with competing short range ferromagnetic interactions and long range antiferro-magnetic interactions is perhaps the most simple one containing the minimal microscopic ingredients necessary for an appropriate description of the macroscopic properties of ultrathin films and quasi--two--dimensional magnetic materials. Despite such relative simplicity, the frustration generates complex behaviors that have eluded, up to now, a complete understanding of its general properties. In this talk, we review recent advances in the comprehension of both equilibrium and non-equilibrium properties of the model. This includes a detailed description of several known properties of the thermodynamical phase diagram, as well as the existence of several types of metastable states and their influence on the low temperature dynamics.

Aging, Scaling and Sensitivity to Initial Conditions Properties of Coherent-noise Models

U. Tirnakli1, S. Abe2
1Department of Physics,Faculty of Science, Ege University, 35100 Izmir, Turkey
2Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan

In recent years, there has been an increasing interest in extended dynamical systems which display scale-free behavior. A variety of these systems could be enumerated such as earthquakes, sandpiles, extinctions in Biology, networks, etc. Up to now, there is no unique and unified theory for the systems exhibiting scale-free behavior. One of the candidates to be a possible origin of such behavior in extended systems is the notion of self-organized criticality (SOC). One of the most important common features of the models which exhibit SOC is
that they are all under the influence of a small driving force which acts locally. On the other hand, there exist other simple and robust mechanisms producing scale-free behavior in the absence of criticality or even in the absence of interactions among elements of the system. One of the most important models of this kind is the coherent noise model of Newman. Newman model (NM) is introduced to model large-scale evolution and extinction, and is based on the notion of external stress imposed coherently on all agents of the system. Since this model does not have any interaction among agents, it does not exhibit criticality, but nevertheless, shows a power-law distribution of avalanche sizes. One of the key features of NM -or coherent noise models in general- (at least, from our point of view) is the existence of aftershocks, which is usually not present in SOC models.
In this work, we numerically analyze the aging and scaling properties of NM and compare our results with the recent findings of a completely different model system Moreover, we study the sensitivity to initial conditions of the model using damage spreading technique.

Nonequivalent microcanonical states as nonequilibrium canonical states

H. Touchette
Queen Mary College, University of London, UK

I will discuss in this talk the nature of nonequivalent microcanonical states, i.e., states which are seen at equilibrium in the microcanonical ensemble but not in the canonical ensemble. I will show that such nonequivalent microcanonical states realize in effect two kinds of nonequilibrium critical `points' of the canonical ensemble, namely: (i) metastable (spinodal) saddle-points or (ii) unstable critical points depending on the sign (positive or negative, respectively) of their associated microcanonical heat capacity. This result settles a conjecture put forward recently by Antoni, Ruffo and Torcini [Phys. Rev. E, 66, 025103, 2002] and by Ellis, Touchette and Turkington [Physica A 335, 518, 2004].

On the dynamical foundation of nonextensive statistical mechanics

C. Tsallis
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil

Ubiquitous artificial and natural systems exist which are not adequately tractable within Boltzmann-Gibbs (BG) statistical mechanics frame. A vast class of such systems appears to be appropriately handled within a generalization of the BG theory named nonextensive statistical mechanics. After a brief introduction of the formalism, we shall focus on the present status of its dynamical foundations.

Bibliography: "Nonextensive Entropy - Interdisciplinary Applications", M. Gell-Mann and C. Tsallis (Oxford University Press, New York, 2004), and http://tsallis.cat.cbpf.br/biblio.htm

The architecture of complex weighted networks

A. Vespignani
Laboratoire de Physique Theorique, Universite de Paris-Sud ORSAY, France

Along with a complex topological structure, real networks display a large heterogeneity in the capacity and intensity of the connections. These features, however, have mainly not been considered in past studies where links are usually represented as binary states, i.e. either present or absent. Here, we study the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively. In both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network. We define new appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices. This information allows us to characterize for the first time the correlations among weighted quantities and the underlying topological structure of the network. We also propose a model for the growth of weighted networks that couples the establishment of new edges and vertices and the weights' dynamical evolution. The model is based on a simple weight-driven dynamics and generates networks exhibiting the statistical properties observed in several real-world systems.

Complexity in collective behaviour

T. Vicsek(*)
Eotvos University, Budapest, Hungary

The interpretation of collective human behaviour represents a great challenge for sciences. Here we discuss an emerging approach to this problem based on the quantitative methods of statistical physics. We demonstrate that in cases when the interactions between the members of a group are relatively well defined (e.g, pedestrian traffic, network formation, synchronization, panic, etc) the corresponding models reproduce relevant aspects of the observed phenomena. In particular, people moving in the same environment typically develop specific patterns of collective motion including the formation of lanes, flocking or jamming at bottlenecks. We simulate such phenomena assuming realistic interactions between particles representing humans. The two specific cases to be discussed in more detail are waves produced by crowds at large sporting events and the main features of escape panic under various conditions. Our models allow the prediction of the main features of crowd behaviour even in cases when experimental methods are obviously not applicable and, thus, are expected to be useful
in assessing the level of security in situations involving large groups of excited people.

(*) The above results have been obtained in collaboration with A-L.Barabasi, A. Czirok, I. Farkas, Z. Neda and D. Helbing

Complexity at an elementary level

A. Zichichi
CERN, Dipartimento di Fisica, Università di Bologna and INFN