We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals $i$ and $j$ is endowed with an infection rate ${\beta }_{ij}=\lambda w_{ij}$ proportional to the intensity of their contact $w_{ij}$, with a distribution $P\left(w_{ij}\right)$ taken from face-to-face experiments analyzed in Cattuto et al. [PLoS ONE 5, e11596 (2010)]. We find an extremely slow decay of the fraction of infected individuals, for a wide range of the control parameter $\lambda$. Using a distribution of width $a$ we identify two large regions in the $a-\lambda$ space with anomalous behaviors, which are reminiscent of rare region effects (Griffiths phases) found in models with quenched disorder. We show that the slow approach to extinction is caused by isolated small groups of highly interacting individuals, which keep epidemics alive for very long times. A mean-field approximation and a percolation approach capture with very good accuracy the absorbing-active transition line for weak (small $a$) and strong (large $a$) disorder, respectively.

The processes leading to change in languages are manifold. In order to reduce ambiguity in the transmission of information, agreement on a set of conventions for recurring problems is favored. In addition to that, speakers tend to use particular linguistic variants associated with the social groups they identify with. The influence of other groups propagating across the speech community as new variant forms sustains the competition between linguistic variants. With the utterance selection model, an evolutionary description of language change, Baxter et al. [Phys. Rev. E 73, 046118 (2006)] have provided a mathematical formulation of the interactions inside a group of speakers, exploring the mechanisms that lead to or inhibit the fixation of linguistic variants. In this paper, we take the utterance selection model one step further by describing a speech community consisting of multiple interacting groups. Tuning the interaction strength between groups allows us to gain deeper understanding about the way in which linguistic variants propagate and how their distribution depends on the group partitioning. Both for the group size and the number of groups we find scaling behaviors with two asymptotic regimes. If groups are strongly connected, the dynamics is that of the standard utterance selection model, whereas if their coupling is weak, the magnitude of the latter along with the system size governs the way consensus is reached. Furthermore, we find that a high influence of the interlocutor on a speaker's utterances can act as a counterweight to group segregation.

The attracting and repelling of spiral waves in a two-dimensional excitable medium in the presence of localized excitability inhomogeneities are studied. The choice of two effects depends on the comparison of excitabilities inside and outside the localized obstacle. We inspect the changes in attracting and repelling behaviors with respect to the size of the obstacle and the initial distance between the center of the spiral core and the obstacle. To understand the occurrence of these phenomena, we investigated the small $v$-value areas near the tip and the function of the wave velocity as the excitability parameter $\varepsilon$. Considering the attributes of the attractive obstacle, an eliminating scheme of spiral waves is proposed in which the attractive obstacle is rapidly moved at several fixed times. This method can avoid the high-amplitude and high-frequency stimulus in most conventional methods.

The coalescence and mixing of a sessile and an impacting liquid droplet on a solid surface are studied experimentally and numerically in terms of lateral separation and droplet speed. Two droplet generators are used to produce differently colored droplets. Two high-speed imaging systems are used to investigate the impact and coalescence of the droplets in color from a side view with a simultaneous gray-scale view from below. Millimeter-sized droplets were used with dynamical conditions, based on the Reynolds and Weber numbers, relevant to microfluidics and commercial inkjet printing. Experimental measurements of advancing and receding static contact angles are used to calibrate a contact angle hysteresis model within a lattice Boltzmann framework, which is shown to capture the observed dynamics qualitatively and the final droplet configuration quantitatively. Our results show that no detectable mixing occurs during impact and coalescence of similar-sized droplets, but when the sessile droplet is sufficiently larger than the impacting droplet vortex ring generation can be observed. Finally we show how a gradient of wettability on the substrate can potentially enhance mixing.

The kinetic theory of fully degenerate electrons in a weakly coupled plasma is considered. We derive an evolution equation for a generalized Fermi surface that also depends on the electron spin state. The equation allows for the study of weakly nonlinear modifications of the Fermi surface within perturbation theory. We apply the theory to Landau damping of ion-acoustic waves. The transition to the nonlinear stage and the nonlinear modification of the Fermi surface are investigated.

Propagation of dust acoustic waves (DAWs) with the effect of power law dust size distribution (DSD) in a magnetized dusty plasma with opposite polarity dust is studied. Using a reductive perturbation method, a Zakharov-Kuznetsov equation appropriate for describing three-dimensional DAWs is derived. The compressive and rarefactive solitons are possible in the present model. Due to the DSD effect, a soliton with a smaller amplitude and width and a larger velocity is observed. The stability criterion for obliquely propagating DAWs in such plasma using small-$k$ expansion method is investigated. The growth rate of instability is derived and analyzed under the effect of power law DSD. It is found that the growth rate of instability is strongly affected by the power law DSD. The relevance of these findings to space plasma phenomena is briefly discussed.

With an eye on dust particles immersed into an ionized gas, we study the effect of a negative charge on the scattering of light by a dielectric particle with a strong transverse optical phonon resonance in the dielectric constant. Surplus electrons alter the scattering behavior of the particle by their phonon-limited conductivity in the surface layer (negative electron affinity) or in the bulk of the particle (positive electron affinity). We identify a charge-dependent increase of the extinction efficiency for low frequencies, a shift of the extinction resonance above the transverse optical phonon frequency, and a rapid variation of the polarization angles over this resonance. These effects could be used for noninvasive optical measurements of the charge of the particle.

We report on a statistical analysis of the engagement in the electoral processes of all Brazilian cities by considering the number of party memberships and the number of candidates for mayor and councillor. By investigating the relationships between the number of party members and the population of voters, we have found that the functional forms of these relationships are well described by sublinear power laws (allometric scaling) surrounded by a multiplicative log-normal noise. We have observed that this pattern is quite similar to those we previously reported for the relationships between the number of candidates (mayor and councillor) and population of voters [Europhys. Lett. 96, 48001 (2011)], suggesting that similar universal laws may be ruling the engagement in the electoral processes. We also note that the power-law exponents display a clear hierarchy, where the more influential is the political position the smaller is the value of the exponent. We have also investigated the probability distributions of the number of candidates (mayor and councillor), party memberships, and voters. The results indicate that the most influential positions are characterized by distributions with very short tails, while less influential positions display an intermediate power-law decay before showing an exponential-like cutoff. We discuss the possibility that, in addition to the political power of the position, limitations in the number of available seats can also be connected with this changing of behavior. We further believe that our empirical findings point out to an under-representation effect, where the larger the city is, the larger are the obstacles for more individuals to become directly engaged in the electoral process.

We study the long-range spatial correlations in the nonequilibrium steady state of a randomly driven granular fluid with the emphasis on obtaining the explicit form of the static structure factors. The presence of immobile particles immersed in such a fluidized bed of fine particles leads to the confinement of the fluctuation spectrum of the hydrodynamic fields, which results in effective long-range interactions between the intruders. The analytical predictions are in agreement with the results of discrete element method simulations. By changing the shape and orientation of the intruders, we address how the effective force is affected by small changes in the boundary conditions.

We investigate the contact-line dynamics of two immiscible fluids in a narrow fluidic confinement comprising wettability-gradient surfaces, where the bulk fluid motion is actuated by an externally applied electric field. We assume that the channel walls bear spatially uniform surface potential. Our analysis, based on the diffuse interface formalism, reveals that the contact line undergoes stick-slip motion over the chemical patches and its velocity is a strong function of the interfacial electrokinetics. We also show that the tendency of the contact line of getting pinned to the selected patches can decrease or increase with its progression along the channel, depending on the ratio of the permittivities of the two fluids. Finally, we establish the functional dependency of the time taken by the contact line to move across the patches (capillary filling time) on the combined consequences of interfacial electrochemistry and wettability patterning.

We analyze numerically thermal fluctuations of the static overlap between equilibrium configurations in a glass-forming liquid approaching the glass transition. We find that the emergence of slow dynamics near the onset temperature correlates with the development of non-Gaussian probability distributions of overlap fluctuations, measured using both annealed and quenched definitions. Below a critical temperature, a thermodynamic field conjugate to the overlap induces a first-order phase transition, whose existence we numerically demonstrate in the annealed case. These results establish that the approach to the glass transition is accompanied by profound changes in the nature of thermodynamic fluctuations, deconstructing the view that glassy dynamics occurs with little structural evolution.

We test the recently introduced radiation model against the gravity model for the system composed of England and Wales, both for commuting patterns and for public transportation flows. The analysis is performed both at macroscopic scales, i.e., at the national scale, and at microscopic scales, i.e., at the city level. It is shown that the thermodynamic limit assumption for the original radiation model significantly underestimates the commuting flows for large cities. We then generalize the radiation model, introducing the correct normalization factor for finite systems. We show that even if the gravity model has a better overall performance the parameter-free radiation model gives competitive results, especially for large scales.

We introduce the simplest one-dimensional nonlinear model with parity-time ($\mathcal{PT}$) symmetry, which makes it possible to find exact analytical solutions for localized modes (“solitons”). The $\mathcal{PT}$-symmetric element is represented by a pointlike ($\delta$-functional) gain-loss dipole $\sim$${\delta }^{\prime }\left(x\right)$, combined with the usual attractive potential $\sim$$\delta \left(x\right)$. The nonlinearity is represented by self-focusing (SF) or self-defocusing (SDF) Kerr terms, both spatially uniform and localized. The system can be implemented in planar optical waveguides. For the sake of comparison, also introduced is a model with separated $\delta$-functional gain and loss, embedded into the linear medium and combined with the $\delta$-localized Kerr nonlinearity and attractive potential. Full analytical solutions for pinned modes are found in both models. The exact solutions are compared with numerical counterparts, which are obtained in the gain-loss-dipole model with the ${\delta }^{\prime }$ and $\delta$ functions replaced by their Lorentzian regularization. With the increase of the dipole's strength $\gamma$, the single-peak shape of the numerically found mode, supported by the uniform SF nonlinearity, transforms into a double peak. This transition coincides with the onset of the escape instability of the pinned soliton. In the case of the SDF uniform nonlinearity, the pinned modes are stable, keeping the single-peak shape.

Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva et al., Comput. Phys. Commun. 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.

We present an in-depth analysis of the sometimes understated role of the principle of energy conservation in linear irreversible thermodynamics. Our case study is that of a thermoelectric generator (TEG), which is a heat engine of choice in irreversible thermodynamics, owing to the coupling between the electrical and heat fluxes. We show why Onsager's reciprocal relations must be considered locally and how internal dissipative processes emerge from the extension of these relations to a global scale: The linear behavior of a heat engine at the local scale is associated with a dissipation process that must partake in the global energy balance. We discuss the consequences of internal dissipations on the so-called efficiency at maximum power, in the light of our comparative analyses of exoreversibility and endoreversibility on the one hand and of two classes of heat engines, autonomous and periodically driven, on the other hand. Finally, basing our analysis on energy conservation, we also discuss recent works which claim the possibility to overcome the traditional boundaries on efficiency imposed by finite-time thermodynamics in thermoelectric systems with broken time-reversal symmetry; this we do by introducing a “thermal” thermopower and an “electrical” thermopower which permits an analysis of the thermoelectric response of the TEG considering a possible dissymmetry between the electrical/thermal and the thermal/electrical couplings.

Large-scale simulations and analytical theory have been combined to obtain the nonequilibrium velocity distribution, $f\left(v\right)$, of randomly accelerated particles in suspension. The simulations are based on an event-driven algorithm, generalized to include friction. They reveal strongly anomalous but largely universal distributions, which are independent of volume fraction and collision processes, which suggests a one-particle model should capture all the essential features. We have formulated this one-particle model and solved it analytically in the limit of strong damping, where we find that $f\left(v\right)$ decays as $1/v$ for multiple decades, eventually crossing over to a Gaussian decay for the largest velocities. Many particle simulations and numerical solution of the one-particle model agree for all values of the damping.

Catching fish with a fishing net is typically done either by dragging a fishing net through quiescent water or by placing a stationary basket trap into a stream. We transfer these general concepts to micron-sized self-motile particles moving in a solvent at low Reynolds number and study their collective trapping behavior by means of computer simulations of a two-dimensional system of self-propelled rods. A chevron-shaped obstacle is dragged through the active suspension with a constant speed $v$ and acts as a trapping “net.” Three trapping states can be identified corresponding to no trapping, partial trapping, and complete trapping and their relative stability is studied as a function of the apex angle of the wedge, the swimmer density, and the drag speed $v$. When the net is dragged along the inner wedge, complete trapping is facilitated and a partially trapped state changes into a complete trapping state if the drag speed exceeds a certain value. Reversing the drag direction leads to a reentrant transition from no trapping to complete trapping and then back to no trapping upon increasing the drag speed along the outer wedge contour. The transition to complete trapping is marked by a templated self-assembly of rods forming polar smectic structures anchored onto the inner contour of the wedge. Our predictions can be verified in experiments of artificial or microbial swimmers confined in microfluidic trapping devices.

We reexamine previous observations of folding kinetics of compressed lipid monolayers in light of the accepted mechanical buckling mechanism recently proposed by L. Pocivavsek et al. [Science 320, 912 (2008)]. Using simple models, we set conservative limits on (a) the energy released in the mechanical buckling process and (b) the kinetic energy entailed by the observed folding motion. These limits imply a kinetic energy at least 30 times greater than the energy supplied by the buckling instability. We discuss possible extensions of the accepted picture that might resolve this discrepancy.

The field-induced director dynamics for a low molar mass nematic liquid crystal (LC) has been investigated theoretically based on the hydrodynamic theory including the director motion with appropriate boundary and initial conditions. Analysis of the numerical results for the turn-on process provides evidence for the appearance of the spatially periodic patterns in 4-$n$-pentyl-4${}^{\prime }$-cyanobiphenyl LC film, only in response to the suddenly applied strong electric field orthogonal to the magnetic field. It has been shown that at the values of the voltage of 200 V across the 194.7 $\mu$m LC film and the magnetic field of 7.05 T directed at the angle $\alpha =1.57(\sim 89.{99}^{\circ })$ between two fields, there is a threshold value of the amplitude of the thermal fluctuations of the director over the LC sample which provides the nonuniform rotation mode rather than the uniform one, whereas the lower values both of the amplitude and the angle $\alpha$ [$<1.565(\sim 88.{81}^{\circ }$)] dominate the uniform mode. During the turn-off process, the reorientation of the director to its equilibrium orientation is characterized by the complex destruction of the initially periodic structure to a monodomain state.

We demonstrate that crossed arrays of optical fibers support the double-discrete linear and nonlinear propagation of light beams, in which not only the transverse coordinate (the fiber's number) is discrete, but also the longitudinal (propagation) coordinate, i.e., the number of the fiber-crossing site, is effectively discrete too. In the linear limit, this transmission regime features double-discrete self-collimation. The nonlinear fishnet arrays with both focusing and defocusing nonlinearities give rise to double-discrete spatial solitons. Solitons bifurcating from two different branches of the linear dispersion relation feature strong interactions and form composite states. In the continuum limit, the model of the nonlinear fishnet reduces to a system of coupled-mode equations similar to those describing Bragg gratings, but without the cross-phase-modulation terms.