Community structure plays a significant role in the analysis of social networks and similar graphs, yet this structure is little understood and not well captured by most models. We formally define a community to be a subgraph that is internally highly connected and has no deeper substructure. We use tools of combinatorics to show that any such community must contain a dense Erdős-Rényi (ER) subgraph. Based on mathematical arguments, we hypothesize that any graph with a heavy-tailed degree distribution and community structure must contain a scale-free collection of dense ER subgraphs. These theoretical observations corroborate well with empirical evidence. From this, we propose the Block Two-Level Erdős-Rényi (BTER) model, and demonstrate that it accurately captures the observable properties of many real-world social networks.

In this report we introduce the concept of common community structure in time-varying networks. We propose a novel optimization algorithm to rapidly detect common community structure in such networks. Both theoretical and numerical results show that the proposed method not only can resolve detailed common communities, but also can effectively identify the dynamical phenomena in time-varying networks.

We report on the observation of on-off intermittency in an optically injected dual-mode semiconductor laser. It is shown that quasi-single-mode chaotic dynamics of the injected mode are accompanied by intermittent and irregular bursts of the intensity of the uninjected mode. We define a threshold intensity of the uninjected mode to distinguish laminar and bursting states of the system. For small values of the threshold parameter we observe excellent agreement with the predictions of theory for the distribution of the laminar phase durations. For larger values of the threshold parameter, a gap appears in the distribution of laminar phase durations. Numerical simulations demonstrate that this gap is a consequence of the fact that in this case the on states of the system define large intensity spikes, which can belong either to the same or to distinct bursts away from the single-mode manifold.

Turing structures appear naturally and they are demonstrated under different spatial configurations such as stripes and spots as well as mixed states. The traditional tool to characterize these patterns is the Fourier transformation, which accounts for the spatial wavelength, but it fails to discriminate among different spatial configurations or mixed states. In this paper, we propose a parameter that clearly differentiates the different spatial configurations. As an application, we considered the transitions induced by an external forcing in a reaction-diffusion system although the results are straightforwardly extended to different problems with similar topologies. The method was also successfully tested on a temporally evolving pattern.

We investigate the influence of an additional torque on the motion of Brownian particles confined in a channel geometry with varying width. The particles are driven by random fluctuations modeled by an Ornstein-Uhlenbeck process with given correlation time ${\tau }_c$. The latter causes persistent motion and is implemented as (i) thermal noise in equilibrium and (ii) noisy propulsion in nonequilibrium. In the nonthermal process a directed transport emerges; its properties are studied in detail with respect to the correlation time, the torque, and the channel geometry. Eventually, the transport mechanism is traced back to a persistent sliding of particles along the even boundaries in contrast to scattered motion at uneven or rough ones.

We consider a minimal model of heterogeneous catalysis in which a molecule performs surface-mediated diffusion inside a confining domain whose boundary contains catalytic sites. We explicitly take into account the combination of surface and bulk diffusion, and we obtain exact results for the mean and variance of the territory covered on the boundary by the particle before its exit in the case of a two-dimensional spherical domain. Depending on the relative positions of the entrance and exit points, very different behaviors with respect to the mean adsorption time of the molecule on the surface are found. We also determine both exact lower and upper bounds and an approximate expression of the probability of reacting with catalytic sites before exiting the domain. These results provide a quantitative measure of the efficiency of an idealized catalyst.

In this study, we use two nonequilibrium molecular dynamics algorithms, boundary-driven shear and homogeneous shear, to explore the rheology and flow properties of a simple fluid undergoing steady simple shear. The two distinct algorithms are designed to elucidate the influences of nanoscale confinement. The results of rheological material functions, i.e., viscosity and normal pressure differences, show consistent Newtonian behaviors at low shear rates from both systems. The comparison validates that confinements of the order of 10 nm are not strong enough to deviate the simple fluid behaviors from the continuum hydrodynamics. The non-Newtonian phenomena of the simple fluid are further investigated by the homogeneous shear simulations with much higher shear rates. We observe the “string phase” at high shear rates by applying both profile-biased and profile-unbiased thermostats. Contrary to other findings where the string phase is found to be an artifact of the thermostats, we perform a thorough analysis of the fluid microstructures formed due to shear, which shows that it is possible to have a string phase and second shear thinning for dense simple fluids.

Using discrete molecular dynamics simulations we study the relation between the thermodynamic and diffusive behaviors of a primitive model of aqueous solutions of hydrophobic solutes consisting of hard spheres in the Jagla particles solvent, close to the liquid-liquid critical point of the solvent. We find that the fragile-to-strong dynamic transition in the diffusive behavior is always coupled to the low-density–high-density liquid transition. Above the liquid-liquid critical pressure, the diffusivity crossover occurs at the Widom line, the line along which the thermodynamic response functions show maxima. Below the liquid-liquid critical pressure, the diffusivity crossover occurs when the limit of mechanical stability lines are crossed, as indicated by the hysteresis observed when going from high to low temperature and vice versa. These findings show that the strong connection between dynamics and thermodynamics found in bulk water persists in hydrophobic solutions for concentrations from low to moderate, indicating that experiments measuring the relaxation time in aqueous solutions represent a viable route for solving the open questions in the field of supercooled water.

A combination of experiment and theory shows that dielectric elastomers exhibit complex interplay of nonlinear processes. Membranes of a dielectric elastomer are prepared in various states of prestretches by using rigid clamps and mechanical forces. Upon actuation by voltage, some membranes form wrinkles followed by snap-through instability, others form wrinkles without the snap-through instability, and still others fail by local instability without forming wrinkles. Membranes surviving these nonlinear processes are found to attain a constant dielectric strength, independent of the state of prestretches. Giant voltage-induced stretch of 3.6 is attained.

We analyze the structural behavior of a single polymer chain inside an attractive sphere. Our model is composed of a coarse-grained polymer and an attractive-sphere potential. By means of extensive multicanonical Monte Carlo simulations, it is shown that the system exhibits a rich phase diagram ranging from highly ordered compact to extended random coil structures and from desorbed to partially or even completely adsorbed conformations. These findings are identified with different structural observables.

We introduce a measure of activity of financial markets that provides a direct access to their level of endogeneity. This measure quantifies how much of price changes is due to endogenous feedback processes, as opposed to exogenous news. For this, we calibrate the self-excited conditional Poisson Hawkes model, which combines in a natural and parsimonious way exogenous influences with self-excited dynamics, to the E-mini S&P 500 futures contracts traded in the Chicago Mercantile Exchange from 1998 to 2010. We find that the level of endogeneity has increased significantly from 1998 to 2010, with only 70$\%$ in 1998 to less than 30$\%$ since 2007 of the price changes resulting from some revealed exogenous information. Analogous to nuclear plant safety measures concerned with avoiding “criticality,” our measure provides a direct quantification of the distance of the financial market from a critical state defined precisely as the limit of diverging trading activity in the absence of any external driving.

The method of surrogate data has been extensively applied to hypothesis testing of system linearity, when only one realization of the system, a time series, is known. Normally, surrogate data should preserve the linear stochastic structure and the amplitude distribution of the original series. Classical surrogate data methods (such as random permutation, amplitude adjusted Fourier transform, or iterative amplitude adjusted Fourier transform) are successful at preserving one or both of these features in stationary cases. However, they always produce stationary surrogates, hence existing nonstationarity could be interpreted as dynamic nonlinearity. Certain modifications have been proposed that additionally preserve some nonstationarity, at the expense of reproducing a great deal of nonlinearity. However, even those methods generally fail to preserve the trend (i.e., global nonstationarity in the mean) of the original series. This is the case of time series with unit roots in their autoregressive structure. Additionally, those methods, based on Fourier transform, either need first and last values in the original series to match, or they need to select a piece of the original series with matching ends. These conditions are often inapplicable and the resulting surrogates are adversely affected by the well-known artefact problem. In this study, we propose a simple technique that, applied within existing Fourier-transform-based methods, generates surrogate data that jointly preserve the aforementioned characteristics of the original series, including (even strong) trends. Moreover, our technique avoids the negative effects of end mismatch. Several artificial and real, stationary and nonstationary, linear and nonlinear time series are examined, in order to demonstrate the advantages of the methods. Corresponding surrogate data are produced with the classical and with the proposed methods, and the results are compared.

We measured the resonance spectra of two stadium-shaped dielectric microwave resonators and tested a semiclassical trace formula for chaotic dielectric resonators proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)]. We found good qualitative agreement between the experimental data and the predictions of the trace formula. Deviations could be attributed to missing resonances in the measured spectra in accordance with previous experiments [Phys. Rev. E 81, 066215 (2010)]. The investigation of the numerical length spectrum showed good qualitative and reasonable quantitative agreement with the trace formula. It demonstrated, however, the need for higher-order corrections of the trace formula. The application of a curvature correction to the Fresnel reflection coefficients entering the trace formula yielded better agreement, but deviations remained, indicating the necessity of further investigations.

We introduce a conditional pair distribution function (CPDF) which characterizes the probability density of finding an object (e.g., a particle in a fluid) to within a certain distance of each other, with each of these two having a nearest neighbor to a fixed but otherwise arbitrary distance. This function describes special four-body configurations, but also contains contributions due to the so-called mutual nearest neighbor (two-body) and shared neighbor (three-body) configurations. The CPDF is introduced to improve a Helmholtz free energy method based on space partitions. We derive exact expressions of the CPDF and various associated quantities for randomly distributed, noninteracting points at Euclidean spaces of one, two, and three dimensions. Results may be of interest in many diverse scientific fields, from fluid physics to social and biological sciences.

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature $T_0$ determined by the value of the asymmetry. In a narrow temperature range around $T_0$, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than $T_0$), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times is considered. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.

Random teleportation is a necessary evil for ranking and clustering directed networks based on random walks. Teleportation enables ergodic solutions, but the solutions must necessarily depend on the exact implementation and parametrization of the teleportation. For example, in the commonly used PageRank algorithm, the teleportation rate must trade off a heavily biased solution with a uniform solution. Here we show that teleportation to links rather than nodes enables a much smoother trade-off and effectively more robust results. We also show that, by not recording the teleportation steps of the random walker, we can further reduce the effect of teleportation with dramatic effects on clustering.

The power-off phase of pulsed low-pressure plasmas (the so-called afterglow) in noble gases is a rich field for both fundamental and application oriented research. The physics of these plasmas is complex and involves various processes: Initially, electrons cool rapidly to temperatures close to the gas temperature by evaporative cooling. At sufficiently high plasma densities the low kinetic electron energy strongly enhances three-body recombination into Rydberg states. Finally, subsequent collisional-radiative decay leads to emission of radiation and populates the metastable states of the atoms. The various steps are investigated experimentally and are compared to analytical models. This allows us to follow all steps throughout in a single experiment involving diagnostics of electron density, metastable density, and emission. Excellent agreement with the models is achieved. The mechanisms included are: (i) for electrons, balance between evaporative cooling and Coulomb collisions with ions leading to thermalization; (ii) consistent combination of re-ionization and microfield reduction of the ionization energy in the recombination rate; (iii) adiabatic balance of recombination and collisional and radiative de-excitation; and (iv) radiative population and diffusional and pooling collisional loss of metastable levels. Although the experiment is carried out in argon, the underlying physics is generally applicable for the afterglow of high-density low-pressure discharges in atomic gases.

We study electromagnetic forces and torques on a discrete spherical invisibility cloak under time-harmonic illumination. We consider the influence of material absorption and losses, and we show that while the impact of absorption on the optical force remains confined to frequencies near the absorption peak, its impact on the electromagnetic torque experienced by the cloak is spectrally broader and follows the spectrum of the absorption cross section of the cloak. We also investigate the mechanical shielding of a test particle within the cloak. We find that even an imperfect cloak can reduce the radiation pressure on the particle significantly; however, under certain conditions the force on the particle can be stronger than it would be in the absence of the cloak.

A numerical method to reduce the computing times of thin-film flows with moving contact lines is presented. The flows of a film and a droplet are calculated in a frame that moves with a nonconstant velocity $U\left(t\right)$. The criterion employed to define this velocity is to reduce the maximum height change in the flow’s most critical zone. The efficiency of the algorithm in reducing the CPU time is tested in gravity-driven flows, where the computing time is reduced by up to a factor of 13 depending on the parameters of the problem.

We consider bosons in a harmonic trap and investigate the fluctuations of the work performed by an adiabatic change of the trap curvature. Depending on the reservoir conditions such as temperature and chemical potential that provide the initial equilibrium state, the exponentiated work average (EWA) defined in the context of the Crooks relation and the Jarzynski equality may diverge if the trap becomes wider. We investigate how the probability distribution function (PDF) of the work signals this divergence. It is shown that at low temperatures the PDF is highly asymmetric with a steep fall-off at one side and an exponential tail at the other side. For high temperatures it is closer to a symmetric distribution approaching a Gaussian form. These properties of the work PDF are discussed in relation to the convergence of the EWA and to the existence of the hypothetical equilibrium state to which those thermodynamic potential changes refer that enter both the Crooks relation and the Jarzynski equality.