We propose an algorithm to find the community structure in complex networks based on the combination of spectral analysis and modularity optimization. The clustering produced by our algorithm is as accurate as the best algorithms on the literature of modularity optimization; however, the main asset of the algorithm is its efficiency. The best match for our algorithm is Newman’s fast algorithm, which is the reference algorithm for clustering in large networks due to its efficiency. When both algorithms are compared, our algorithm outperforms the fast algorithm both in efficiency and accuracy of the clustering, in terms of modularity. Thus, the results suggest that the proposed algorithm is a good choice to analyze the community structure of medium and large networks in the range of tens and hundreds of thousand vertices.

This paper introduces a model of self-organization between communication and topology in social networks, with a feedback between different communication habits and the topology. To study this feedback, we let agents communicate to build a perception of a network and use this information to create strategic links. We observe a narrow distribution of links when the communication is low and a system with a broad distribution of links when the communication is high. We also analyze the outcome of chatting, cheating, and lying, as strategies to get better access to information in the network. Chatting, although only adopted by a few agents, gives a global gain in the system. Contrary, a global loss is inevitable in a system with too many liars.

Critical scaling and universality in the short-time dynamics for antiferromagnetic models on a three-dimensional stacked triangular lattice are investigated using Monte Carlo simulation. We have determined the critical point by searching for the best power law for the order parameter as a function of time and measured the critical exponents. Our results indicate that it is possible to distinguish weak first-order from second-order phase transitions and confirm that $XY$ antiferromagnetic systems undergo a (weak) first-order phase transition accompanied by pseudocritical scaling.

Strange nonchaotic attractors (SNAs) were previously thought to arise exclusively in quasiperiodic dynamical systems. A recent study has revealed, however, that such attractors can be induced by noise in nonquasiperiodic discrete-time maps or in periodically driven flows. In particular, in a periodic window of such a system where a periodic attractor coexists with a chaotic saddle (nonattracting chaotic invariant set), none of the Lyapunov exponents of the asymptotic attractor is positive. Small random noise is incapable of causing characteristic changes in the Lyapunov spectrum, but it can make the attractor geometrically strange by dynamically connecting the original periodic attractor with the chaotic saddle. Here we present a detailed study of noise-induced SNAs and the characterization of their properties. Numerical calculations reveal that the fractal dimensions of noise-induced SNAs typically assume fractional values, in contrast to SNAs in quasiperiodically driven systems whose dimensions are integers. An interesting finding is that the fluctuations of the finite-time Lyapunov exponents away from their asymptotic values obey an exponential distribution, the generality of which we are able to establish by a theoretical analysis using random matrices. We suggest a possible experimental test. We expect noise-induced SNAs to be general.

We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave packet in the high-energy diffraction regime, in which the particle’s de Broglie wavelength, while being small compared to the size of the scatterers, is large enough to prevent the formation of geometric shadow over distances of the order of the particle’s free flight path. The hard-disk or hard-sphere scattering system must be sufficiently dilute in order for this high-energy diffraction regime to be achievable. Apart from the overall exponential decay, the autocorrelation function exhibits a generally complicated sequence of relatively strong peaks corresponding to partial revivals of the wave packet. Both the exponential decay (or escape) rate and the revival peak structure are predominantly determined by the underlying classical dynamics. A relation between the escape rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the counterpart classical system, previously known for hard-disk billiards, is strengthened by generalization to three spatial dimensions. The results of the quantum mechanical calculation of the time-dependent autocorrelation function agree with predictions of the semiclassical periodic orbit theory.

We consider pulses of excitation in reaction-diffusion systems subjected to nonlocal coupling. This coupling represents long-range connections between the elements of the medium; the connection strength decays exponentially with the distance. Without coupling, pulses interact only repulsively and bound states with two or more pulses propagating at the same velocity are impossible. Upon switching on nonlocal coupling, pulses begin to interact attractively and form bound states. First we present numerical results on the emergence of bound states in the excitable Oregonator model for the photosensitive Belousov-Zhabotinsky reaction with nonlocal coupling. Then we show that the appearance of bound states is provided solely by the exponential decay of nonlocal coupling and thus can be found in a wide class of excitable systems, regardless of the particular kinetics. The theoretical explanation of the emergence of bound states is based on the bifurcation analysis of the profile equations that describe the spatial shape of pulses. The central object is a codimension-4 homoclinic orbit which exists for zero coupling strength. The emergence of bound states is described by the bifurcation to 2-homoclinic solutions from the codimension-4 homoclinic orbit upon switching on nonlocal coupling. We stress that the high codimension of the bifurcation to bound states is generic, provided that the coupling range is sufficiently large.

The effect of large scales on the statistics and dynamics of turbulent fluctuations is studied using data from high resolution direct numerical simulations. Three different kinds of forcing, and spatial resolutions ranging from ${256}^3$ to ${1024}^3$, are being used. The study is carried out by investigating the nonlinear triadic interactions in Fourier space, transfer functions, structure functions, and probability density functions. Our results show that the large scale flow plays an important role in the development and the statistical properties of the small scale turbulence. The role of helicity is also investigated. We discuss the link between these findings and intermittency, deviations from universality, and possible origins of the bottleneck effect. Finally, we briefly describe the consequences of our results for the subgrid modeling of turbulent flows.

We study the Kleinberg problem of navigation in small-world networks when the underlying lattice is a fractal consisting of $N\gg 1$ nodes. Our extensive numerical simulations confirm the prediction that the most efficient navigation is attained when the length $r$ of long-range links is taken from the distribution $P\left(\mathbf{r}\right)\sim r^{-\alpha }$, where $\alpha =d_{\mathrm{f}}$ is the fractal dimension of the underlying lattice. We find finite-size corrections to the exponent $\alpha$, proportional to $1∕(\ln N{)}^2$.

Recently it has been shown that there are three families of stochastic one-dimensional nonequilibrium lattice models for which the single-shock measures form an invariant subspace of the states of these models. Here, both the stationary states and dynamics of single-shocks on a one-dimensional lattice are studied. This is done for both an infinite lattice and a finite lattice with boundaries. It is seen that these models possess both static and dynamical phase transitions. The static phase transition is the well-known low-high density phase transition for the asymmetric simple exclusion process. The branching-coalescing random walk and asymmetric Kawasaki-Glauber process models also show the same phase transition. Double-shocks on a one-dimensional lattice are also investigated. It is shown that at the stationary state the contribution of double-shocks with higher width becomes small, and the main contribution comes from thin double-shocks.

Numerical self-consistent-field theory calculations by Tyler and Morse [Phys. Rev. Lett. 94, 208302 (2005)] predict a stable orthorhombic network phase with space group $Fddd$ in very weakly segregated diblock copolymer melts. Here, we examine the predicted stability of this phase within a simple Landau theory of weakly ordered crystals, and within a straightforward extension of Leibler’s theory of weakly segregated diblock copolymer melts. An $Fddd$ structure with a ratio of unit cell parameters $(a:b:c)=(1:2:2\sqrt{3})$ is found to compete very closely with the hexagonal $\left(H\right)$ and lamellar $\left(L\right)$ phases along the predicted $H\text{−}L$ phase boundary, and to be stable within a very narrow range of parameters around this metastable boundary.

A continuum Fokker-Planck model is considered for the RNA polymerase in the elongation phase, where the topology of a single free energy profile as a function of the translocation variable distinguishes the Brownian ratchet and power stroke mechanisms. The model yields a simple analytical stationary solution for arbitrary functional forms of the free energy. With the translocation potential of mean force estimated by the time-series data of the recent high-resolution single-molecule experiment [Abbondanzieri et al. Nature (London) 438, 460 (2005)], predictions of the model for the mechanical properties agree with experiments quantitatively with reasonable values of parameters. The evolution of the spatial distribution of translocation variable away from equilibrium with increasing nucleoside triphosphate concentration shows qualitatively different behavior in the two alternative scenarios, which could serve as an additional measurable signature of the underlying mechanism.

Fibroblasts are nonexcitable cells that are sometimes coupled with excitable cells (cardiomyocytes). Due to a higher resting potential, these cells may act as a current source or sink and therefore disturb the electrical activity of the surrounding excitable cells. The possible occurrence of spontaneous pacemaker activity resulting from these electrotonic interactions was investigated in a theoretical model of two coupled cells as well as in a multicellular fiber model based on the Courtemanche kinetics. The results indicate that repeated spontaneous activations can be observed after an alteration in the activation and recovery properties of the sodium current (changes in excitability properties), provided that the difference in the resting potential as well as the coupling between the excitable and nonexcitable cells is sufficiently high. This may constitute a mechanism of focal sources triggering arrhythmias such as atrial fibrillation.

We analyze a piecewise linear elastic model for the propagation of a crack in a stripe geometry under mode III conditions, in the absence of dissipation. The model is continuous in the propagation direction and discrete in the perpendicular direction. The velocity of the crack is a function of the value of the applied strain. We find analytically the value of the propagation velocity close to the Griffith threshold, and close to the strain of uniform breakdown. Contrary to the case of perfectly harmonic behavior up to the fracture point, in the piecewise linear elastic model the crack velocity is lower than the sound velocity, reaching this limiting value at the strain of uniform breakdown. We complement the analytical results with numerical simulations and find excellent agreement.

We demonstrate that the law of the rectilinear coexistence diameter in two-dimensional mixtures of nonspherical colloids and nonadsorbing polymers is violated. Upon approach to the critical point, the diameter shows logarithmic singular behavior governed by a term $t\ln t$, with $t$ the relative distance from the critical point. No sign of a term $t^{2\beta }$ could be detected, with $\beta$ the critical exponent of the order parameter, indicating a very weak or absent Yang-Yang anomaly. Our analysis thus reveals that nonspherical particle shape alone is not sufficient for the formation of a pronounced Yang-Yang anomaly in the critical behavior of fluids.

Within the mode-coupling theory (MCT) for glassy dynamics, the asymptotic low-frequency expansions for the dynamical susceptibilities at critical points are compared to the expansions for the dynamic moduli; this shows that the convergence properties of the two expansions can be quite different. In some parameter regions, the leading-order expansion formula for the modulus describes the solutions of the MCT equations of motion outside the transient regime successfully; at the same time, the leading- and next-to-leading-order expansion formulas for the susceptibility fail. In these cases, one can derive a Cole-Cole law for the susceptibilities; and this law accounts for the dynamics for frequencies below the band of microscopic excitations and above the high-frequency part of the $\alpha$ peak. It is shown that this scenario explains the optical-Kerr-effect data measured for salol and benzophenone (BZP). For BZP it is inferred that the depolarized light-scattering spectra exhibit a wing for the $\alpha$ peak within the Gigahertz band. This wing results from the crossover of the von Schweidler law part of the $\alpha$ peak to the high-frequency part of the Cole-Cole peak; and this crossover can be described quantitatively by the leading-order formulas of MCT for the modulus.

A molecular-statistical theory for the entire sequence of the chiral tilted smectic phases is derived. Uniaxial and biaxial subphases were found to be stable in different temperature ranges depending on the molecular parameters. The model of a chiral molecule possessing a strong transverse terminal dipole moment and a quadrupole moment located in the molecular core was used. Direct dispersion and electrostatic interactions (modulated by shape) between molecules located in the same or in the neighboring smectic layers are taken into account. An effective long-range interaction arises after the minimization of the free energy with respect to polarization vectors. If the molecular quadrupole moment is small, only uniaxial phases with different periodicities arise. Their periodicity may be tens and hundreds of layers $\left(\mathrm{Sm}\text{−}{C}^{*}\right)$, or approximately two layers $\left(\mathrm{Sm}\text{−}{C}_A^{*}\right)$, or several layers $\left(\mathrm{Sm}\text{−}{C}_{\alpha }^{*}\right)$. In the presence of the nonpolar biaxial ordering (in addition to polarization) there is a cap-shaped border in the phase diagram that separates $\mathrm{Sm}\text{−}{C}_A^{*}$, $\mathrm{Sm}\text{−}{C}^{*}$, and $\mathrm{Sm}\text{−}{C}_{\alpha }^{*}$. If the molecules are nonchiral, $\mathrm{Sm}\text{−}{C}_A$, $\mathrm{Sm}\text{−}C$, and the de Vries’s phases arise instead of the three phases mentioned above. If the molecular quadrupole moment is large, the left “arm” of the border breaks into two lines, and a sequence of biaxial subphases arises in the area between these two lines. Among these biaxial subphases, the one with periodicity of three smectic layers appears to be the broadest in the temperature range. In addition, the subphases with different periodicities were found to be stable in narrow temperature ranges. The long helical rotation in every biaxial subphase is calculated. It is found to change sign between the three-layer subphase and $\mathrm{Sm}\text{−}{C}^{*}$, and may diverge in the four-layer subphase if it arises. All calculations are done with help of (A)FLC Phase Diagram Plotter software developed by the first author and available at his web-page.

We present experimental visualizations of gas flow around solid blunt bodies by NMR imaging. NMR velocimetry is a model-free and tracer-free experimental means for quantitative and multi-dimensional flow visualization. Hyperpolarization of ${}^{129}\mathrm{Xe}$ provided sufficient NMR signal to overcome the low density of the dilute gas phase, and its long coherence time allows for true velocity vector mapping. In this study, the diverging gas flow around and wake patterns immediately behind a sphere could be vectorally visualized and quantified. In a similar experiment, the flow over an aerodynamic model airplane body revealed a less disrupted flow pattern.