We analyze the global structure of the worldwide air transportation network, a critical infrastructure with an enormous impact on local, national, and international economies. We find that the worldwide air transportation network is a scale-free small-world network. In contrast to the prediction of scale-free network models, however, we find that the most connected cities are not necessarily the most central, resulting in anomalous values of the centrality. We demonstrate that these anomalies arise because of the multicommunity structure of the network. We identify the communities in the air transportation network and show that the community structure cannot be explained solely based on geographical constraints and that geopolitical considerations have to be taken into account. We identify each city's global role based on its pattern of intercommunity and intracommunity connections, which enables us to obtain scale-specific representations of the network.complex networks ͉ betweenness centrality ͉ critical infrastructures

We study a model in which particles interact with short-ranged attractive and long-ranged repulsive interactions, in an attempt to model the equilibrium cluster phase recently discovered in sterically stabilized colloidal systems in the presence of depletion interactions. At low packing fractions, particles form stable equilibrium clusters which act as building blocks of a cluster fluid. We study the possibility that cluster fluids generate a low-density disordered arrested phase, a gel, via a glass transition driven by the repulsive interaction. In this model the gel formation is formally described with the same physics of the glass formation.

We report calculations of the ground-state energies and geometries for clusters of different sizes (up to 80 particles), where individual particles interact simultaneously via a short-ranged attractive potential, modeled with a generalization of the Lennard-Jones potential, and a long-ranged repulsive Yukawa potential. We show that for specific choices of the parameters of the repulsive potential, the ground-state energy per particle has a minimum at a finite cluster size. For these values of the parameters in the thermodynamic limit, at low temperatures and small packing fractions, where clustering is favored and cluster-cluster interactions can be neglected, thermodynamically stable cluster phases can be formed. The analysis of the ground-state geometries shows that the spherical shape is marginally stable. In the majority of the studied cases, we find that above a certain size, ground-state clusters preferentially grow almost in one dimension.

We study the TIP5P water model proposed by Mahoney and Jorgensen, which is closer to real water than previously-proposed classical pairwise additive potentials. We simulate the model in a wide range of deeply supercooled states and find (i) the existence of a non-monotonic "noseshaped" temperature of maximum density line and a non-reentrant spinodal, (ii) the presence of a low temperature phase transition, (iii) the free evolution of bulk water to ice, and (iv) the timetemperature-transformation curves at different densities. PACS numbers:Much effort has been invested in exploring the overall phase diagram of water and the connection among its liquid, supercooled and glassy states [1,2,3], with particular interest in understanding the origin of the striking anomalies at low temperatures, such as the T -dependence of the isothermal compressibility K T , the constant pressure specific heat C P , and the thermal expansivity α P .The "stability limit conjecture" attributes the increase of the response functions upon supercooling to a continuous re-tracing spinodal line bounding the superheated, supercooled and stretched (negative pressure) metastable states [4]. This line at its minimum intersects the temperature of maximum density (TMD) curve tangentially. More recently, a different hypothesis has been developed, for which the spinodal does not re-enter into the positive pressure region, but rather the anomalies are attributed to a critical point below the homogeneous nucleation line [5]. The TMD line, which is negatively sloped at positive pressures, becomes positively sloped at sufficiently negative pressures and does not intersect the spinodal. A line of first order phase transitions -interpreted as the liquid state analog of the line separating low and high density amorphous glassy phases [3,5] -develops from this critical point.Simulations of supercooled metastable states are possible because the structural relaxation time at the temperatures of interest is several orders of magnitude shorter than the crystallization time. It is difficult, but not impossible [6], to observe crystallization in simulations of molecular models [7] because homogeneous nucleation rarely occurs on the time scales reachable by present day computers. Bulk water simulations have been crystallized by applying a homogeneous electric field [8] or placing liquid water in contact with pre-existing ice [9,10], but spontaneous crystallization of deeply supercooled model water has not been observed in simulations.In contrast, experimental measurements of metastable liquid states are strongly affected by homogeneous nucleation. The nucleation and growth of ice particles from aqueous solution has been extensively studied, and the "nose-shaped" time-temperature-transformation (TTT) curves have been measured [1,11,12]. The nonmonotonic relation between crystallization rate and supercooling depth results from the competition between the thermodynamic driving force for nucleation and the kinetics of growth [1]. Crystallization hinders direct experim...

We study thermodynamic and dynamic properties of a rigid model of the fragile glass-forming liquid orthoterphenyl. This model, introduced by Lewis and Wahnström in 1993, collapses each phenyl ring to a single interaction site; the intermolecular site-site interactions are described by the Lennard-Jones potential whose parameters have been selected to reproduce some bulk properties of the orthoterphenyl molecule. A system of N=343 molecules is considered in a wide range of densities and temperatures, reaching simulation times up to 1 micros. Such long trajectories allow us to equilibrate the system at temperatures below the mode coupling temperature T(c) at which the diffusion constant reaches values of order 10(-10) cm(2)/s and thereby to sample in a significant way the potential energy landscape in the entire temperature range. Working within the inherent structures thermodynamic formalism, we present results for the temperature and density dependence of the number, depth and shape of the basins of the potential energy surface. We evaluate the total entropy of the system by thermodynamic integration from the ideal-noninteracting-gas state and the vibrational entropy approximating the basin free energy with the free energy of 6N-3 harmonic oscillators. We evaluate the configurational part of the entropy as a difference between these two contributions. We study the connection between thermodynamical and dynamical properties of the system. We confirm that the temperature dependence of the configurational entropy and of the diffusion constant, as well as the inverse of the characteristic structural relaxation time, are strongly connected in supercooled states; we demonstrate that this connection is well represented by the Adam-Gibbs relation, stating a linear relation between logD and the quantity 1/TS(c). This relation is found to hold both above and below the critical temperature T(c)-as previously found in the case of silica-supporting the hypothesis that a connection exists between the number of basins and the connectivity properties of the potential energy surface.

We follow the dynamics of an ensemble of interacting self-propelled motorized particles in contact with an equilibrated thermal bath. We find that the fluctuation-dissipation relation allows for the definition of an effective temperature that is compatible with the results obtained using a tracer particle as a thermometer. The effective temperature takes a value which is higher than the temperature of the bath, and it is continuously controlled by the motor intensity.

The low-temperature thermal properties of dielectric crystals are governed by acoustic excitations with large wavelengths that are well described by plane waves. This is the Debye model, which rests on the assumption that the medium is an elastic continuum, holds true for acoustic wavelengths large on the microscopic scale fixed by the interatomic spacing, and gradually breaks down on approaching it. Glasses are characterized as well by universal low-temperature thermal properties that are, however, anomalous with respect to those of the corresponding crystalline phases. Related universal anomalies also appear in the low-frequency vibrational density of states and, despite a longstanding debate, remain poorly understood. By using molecular dynamics simulations of a model monatomic glass of extremely large size, we show that in glasses the structural disorder undermines the Debye model in a subtle way: The elastic continuum approximation for the acoustic excitations breaks down abruptly on the mesoscopic, medium-range-order length scale of Ϸ10 interatomic spacings, where it still works well for the corresponding crystalline systems. On this scale, the sound velocity shows a marked reduction with respect to the macroscopic value. This reduction turns out to be closely related to the universal excess over the Debye model prediction found in glasses at frequencies of Ϸ1 THz in the vibrational density of states or at temperatures of Ϸ10 K in the specific heat. disordered systems ͉ molecular dynamics ͉ vibrational properties G lasses are structurally disordered systems. As common experience shows, in the macroscopic limit they support sound waves as corresponding crystalline materials do. In fact, averaging on a large enough length scale, the details of the microscopic arrangement become essentially irrelevant. This holds true for sound waves with long wavelengths of at least several hundreds of nanometers, corresponding to wavenumbers q in the 10 Ϫ2 -nm Ϫ1 range, as those probed with light scattering techniques (1). On further increasing q, the effect of the structural disorder must appear at one point. The much larger q scale of few nm Ϫ1 is also well known because it can be accessed experimentally with inelastic X-ray (2) and neutron (3) scattering techniques, and numerically with molecular dynamics simulations (4-11). These studies typically probe the dynamic structure factor S(q, ), that is, the space and time Fourier transform of the density-density correlation function. These studies clearly indicate the existence in glasses of excitations that appear in those spectra as very broad peaks whose position as a function of q is characterized by a sinusoidal-like dispersion curve. Thus, these excitations strongly recall the acoustic modes in (poly-)crystalline systems up to roughly one half of the pseudo-Brillouin zone (12), i.e., down to distances corresponding to the interatomic spacing. For this reason, they are often dubbed as acoustic-like. However, as their broadening clearly indicates, they are far from being...

Glasses exhibit spatially inhomogeneous elastic properties, which can be investigated by measuring their elastic moduli at a local scale. Various methods to evaluate the local elastic modulus have been proposed in the literature. A first possibility is to measure the local stress-local strain curve and to obtain the local elastic modulus from the slope of the curve, or equivalently to use a local fluctuation formula. Another possible route is to assume an affine strain and to use the applied global strain instead of the local strain for the calculation of the local modulus. Most recently a third technique has been introduced, which is easy to be implemented and has the advantage of low computational cost. In this contribution, we compare these three approaches by using the same model glass and reveal the differences among them caused by the non-affine deformations.