We focus on the majority model in a topology consisting of two coupled fully connected networks, thereby mimicking the existence of communities in social networks. We show that a transition takes place at a value of the interconnectivity parameter. Above this value, only symmetric solutions prevail, where both communities agree with each other and reach consensus. Below this value, in contrast, the communities can reach opposite opinions and an asymmetric state is attained. The importance of the interface between the subnetworks is shown.

Liquid-crystalline (LC) phase behavior and photoinduction of optical anisotropy in the ionic self-assembly complex 4-(4-diethylaminophenylazo) benzenesulfonate-dimethyldidodecylammonium $\left(\mathrm{EO}\text{−}{\mathrm{C}}_{12}\mathrm{D}\right)$ has been investigated by polarized light microscopy, differential scanning calorimetry (DSC), x-ray scattering, null-ellipsometry, and UV-visible absorbance techniques. The complex exists in a bilayer smectic-$A$ $\left({\mathrm{sm}A}_2\right)$ LC phase at elevated temperatures $(65–160°\mathrm{C})$ and in a rectangular columnar $\left({\mathrm{Col}}_{\mathrm{r}}\right)$ LC phase in the temperature range of $-5–65°\mathrm{C}$. Hysteresis in the transition from the smectic to the columnar LC phase was observed. Detailed experimental investigations of the phase behavior, film-forming properties, and induction of optical anisotropy were performed. High values of photoinduced anisotropy (dichroic ratio of approximately 50) were detected when thin films of the complex were irradiated with linearly polarized light (${\mathrm{Ar}}^{+}$ laser, $\lambda =488\mathrm{nm}$). It was shown that the azobenzene units align perpendicular to the polarization of the exciting light causing an alignment of the columns parallel to the light electric field vector. On the basis of all experimental results a model of the photoinduced alignment of the photochromic complex is proposed in which photoalignment of the material is connected to the reorientation of domains.

Heat capacity and dielectric measurements have been made on a liquid crystal compound exhibiting de Vries type of smectic-$A^{*}$ $\left(\mathrm{Sm}\text{−}{A}^{*}\right)$ phase. Heat capacity shows a significant anomaly which is almost symmetric for above and below the $\mathrm{Sm}\text{−}{A}^{*}\text{−}\mathrm{Sm}\text{−}{C}^{*}$ transition temperature. The transition was found to be very weakly first order. The critical exponent $\gamma$ determined from the dielectric data lies $1.8\pm 0.2$. The present heat capacity data as well as former data for another compound of de Vries type have been analyzed in detail. It was found that the heat capacity data for both compounds are fitted well with a logarithmic divergence except in the immediate vicinity of the transition. These results agree with an expectation that de Vries $\mathrm{Sm}\text{−}{A}^{*}\text{−}\mathrm{Sm}\text{−}{C}^{*}$ transition can exhibit quasi-two-dimensional Ising critical behavior.

We consider a $A_m{B}_n$ diblock copolymer, whose links are capable of forming local reversible bonds with each other. We assume that the resulting structure of the bonds is RNA like—i.e., topologically isomorphic to a tree. We show that, depending on the relative strengths of $A$-$A$, $A$-$B$, and $B$-$B$ contacts, such a polymer can be in one of two different states. Namely, if a self-association is preferable (i.e., $A$-$A$ and $B$-$B$ bonds are comparatively stronger than $A$-$B$ contacts), then the polymer forms a typical randomly branched cloverleaf structure with the so-called roughness exponent $\gamma =1∕2$. On the contrary, if alternating association is preferable (i.e., $A$-$B$ bonds are stronger than $A$-$A$ and $B$-$B$ contacts), then the polymer tends to form a generally linear necklace structure with $\gamma =1$. The transition between cloverleaf and necklace states is studied in detail, and it is shown that it is a second-order phase transition.

Based on the wormlike chain model, a coarse-grained description of the nonlinear dynamics of a weakly bending semiflexible polymer is developed. By means of a multiple-scale perturbation analysis, a length-scale separation inherent to the weakly bending limit is exploited to reveal the deterministic nature of the spatio temporal relaxation of the backbone tension and to deduce the corresponding coarse-grained equation of motion. From this partial integro-differential equation, some detailed analytical predictions for the nonlinear response of a weakly bending polymer are derived in an accompanying paper [O. Hallatschek et al., following paper, Phys. Rev. E 75, 031906 (2007)].

In part I [O. Hallatschek et al., preceding paper, Phys. Rev. E 75, 031905 (2007)] of this contribution, a systematic coarse-grained description of the dynamics of a weakly bending semiflexible polymer was developed. Here, we discuss analytical solutions of the established deterministic partial integro-differential equation for the spatiotemporal relaxation of the backbone tension. For prototypal experimental situations, such as the sudden application or release of a strong external pulling force, it is demonstrated that the tensile dynamics reflects the self-affine conformational fluctuation spectrum in a variety of intermediate asymptotic power laws. Detailed and explicit analytical predictions for the tension propagation and relaxation and corresponding results for common observables, such as the end-to-end distance, are obtained.

The partial coalescence of a droplet onto a planar liquid-liquid interface is investigated experimentally by tuning the viscosities of both liquids. The problem mainly depends on four dimensionless parameters: The Bond number (gravity vs surface tension), the Ohnesorge numbers (viscosity in both fluids vs surface tension), and the density relative difference. The ratio between the daughter droplet size and the mother droplet size is investigated as a function of these dimensionless numbers. Global quantities such as the available surface energy of the droplet have been measured during the coalescence. The capillary waves propagation and damping are studied in detail. The relation between these waves and the partial coalescence is discussed. Additional viscous mechanisms are proposed in order to explain the asymmetric role played by both viscosities.

Production of a monoenergetic electron bunch in a self-injected laser-wakefield accelerator is investigated with a tomographic method which resolves the electron injection and acceleration processes. It is found that all the electrons in the monoenergetic electron bunch are injected at the same location in the plasma column and then accelerated with an acceleration gradient exceeding $2\mathrm{GeV}∕\mathrm{cm}$. The injection position shifts with the position of pump-pulse focus, and no significant deceleration is observed for the monoenergetic electron bunch after it reaches the maximum energy. The results are consistent with the model of transverse wave breaking and beam loading for the injection of monoenergetic electrons. The tomographic method adds a crucial dimension to the whole array of existing diagnostics for laser beams, plasma waves, and electron beams. With this method the details of the underlying physical processes in laser-plasma interactions can be resolved and compared directly to particle-in-cell simulations.

In this work, we assess theoretically the physical response of metamaterial composite structures that emulate the behavior of negative-permittivity materials in certain relevant setups. The metamaterials under analysis consist of metallic parallel-plate implants embedded in a dielectric host in a two-dimensional geometry. Simple design rules and formulas are presented, fully considering the effect and consequences of excitation of higher-order diffraction modes at the metamaterial-dielectric interface. Following the ideas of transparency and cloaking developed by us [Alù and Engheta, Phys. Rev. E 72, 016623 (2005)], we demonstrate, analytically and numerically, that it is possible in this way to design metamaterial cloaks that significantly reduce the total scattering cross section of a given two-dimensional dielectric obstacle in some frequency band. This effect, which may be realized in a feasible way, may find interesting applications in electromagnetic cloaking, total scattering cross section reduction, and noninvasive probing.

A mesoscopic numerical tool has been developed in this study for predictions of the effective thermal conductivities for microscale random porous media. To solve the energy transport equation with complex multiphase porous geometries, a lattice Boltzmann algorithm has been introduced to tackle the conjugate heat transfer among different phases. With boundary conditions correctly chosen, the algorithm has been initially validated by comparison with theoretical solutions for simpler cases and with the existing experimental data. Furthermore, to reflect the stochastic phase distribution characteristics of most porous media, a random internal morphology and structure generation-growth method, termed the quartet structure generation set (QSGS), has been proposed based on the stochastic cluster growth theory for generating more realistic microstructures of porous media. Thus by using the present lattice Boltzmann algorithm along with the structure generating tool QSGS, we can predict the effective thermal conductivities of porous media with multiphase structure and stochastic complex geometries, without resorting to any empirical parameters determined case by case. The methodology has been applied in this contribution to several two- and three-phase systems, and the results agree well with published experimental data, thus demonstrating that the present method is rigorous, general, and robust. Besides conventional porous media, the present approach is applicable in dealing with other multiphase mixtures, alloys, and multicomponent composites as well.

We use large-scale molecular dynamics simulations to study freely evolving granular gases with dimensionality $d=2,3$. The system dissipates kinetic energy (or cools) due to inelastic collisions between granular particles. The density and velocity fields are approximately homogeneous at early times, and the system is said to be in a homogeneous cooling state (HCS). However, fluctuations in the density and velocity fields grow, and the system evolves into an inhomogeneous cooling state (ICS). We study the nature of velocity distributions in both the HCS and ICS. We also investigate the aging property of the velocity autocorrelation function.

We have experimentally observed uphill solitary waves in the surface flow on a granular material. A heap is constructed by injecting sand between two vertical glass plates separated by a distance much larger than the average grain size, with an open boundary. As the heap reaches the open boundary, solitary fluctuations appear on the flowing layer and move “up the hill” (i.e., against the direction of the flow). We explain the phenomenon in the context of stop-and-go traffic models.

A phenomenon is presented, which changes the shape of gas bubbles in liquid crystals and also creates long gas tubes. The system consists of air bubbles which are injected into a nematic liquid crystal host. The shape of these air bubbles changes from spherical to ellipsoidal by initiating freezing of the sample. Furthermore, long gas tubes are formed from the air which was formerly dissolved in the liquid crystal. The gas tubes are created by the progression of the crystalline-liquid interface. Their length can reach up to 40 times their diameter. The diameter of the tubes depends on the pressure applied to the system, as well as on the interface velocity.

The conformation of a polymer on a curved surface is high on the agenda for polymer science. We assume that the free energy of the system is the sum of bending energy of the polymer and the electrostatic attraction between the polymer and surface. As is also assumed, the polymer is very stiff with an invariant length for each segment so that we can neglect its tensile energy and view its length as a constant. Based on the principle of minimization of free energy, we apply a variation method with a locally undetermined Lagrange multiplier to obtain a set of equations for the polymer conformation in terms of local geometrical quantities. We have obtained some numerical solutions for the conformations of the polymer chain on cylindrical and ellipsoidal surfaces. With some boundary conditions, we find that the free energy profiles of polymer chains behave differently and depend on the geometry of the surface for both cases. In the former case, the free energy of each segment distributes within a narrower range and its value per unit length oscillates almost periodically in the azimuthal angle. However, in the latter case the free energy distributes in a wider range with larger value at both ends and smaller value in the middle of the chain. The structure of a polymer wrapping around an ellipsoidal surface is apt to dewrap a polymer from the endpoints. The dependence of threshold lengths for a polymer on the initially anchored positions is also investigated. With initial conditions, the threshold wrapping length is found to increase with the electrostatic attraction strength for the ellipsoidal surface case. When a polymer wraps around a sphere surface, the threshold length increases monotonically with the radius without the self-intersection configuration for a polymer. We also discuss potential applications of the present theory to DNA/protein complex and further researches on DNA on the curved surface.

We investigate the bifurcation properties and pattern selection in Rayleigh-Bénard convecting binary mixtures for parameter combinations that are typical for colloidal fluids using the Galerkin method. In such fluids the typical Lewis numbers and separation ratios differ by orders of magnitude from the values found in molecular mixtures like alcohol/water. We study stationary rolls, square and crossroll patterns for positive separation ratios, and traveling waves for negative separation ratios. Results are compared to those for molecular mixtures.

The bifurcation behaviors of a parametrically excited solitary wave are investigated via Faraday’s water tank experiment. It is observed that, as the driving frequency $f_d$ is decreased or/and the driving amplitude $A_d$ is increased, the standing (but vertically oscillatory) solitary wave becomes modulationally unstable, leading to the temporal modulation of the vertical oscillation and the emergence of very low subharomic components on the frequency spectrum. Further lowering $f_d$ or/and increasing $A_d$ will cause the modulational oscillation unstable and then, the peak of the solitary wave becomes rocking along the trough in the longitudinal direction. These bifurcations also give rise to the emission of continuous waves resulting in complex wave patterns and complicated fluctuations, especially for the quite low $f_d$ and large $A_d$. A possible route from solitary waves to chaos via bifurcations and mode competitions is therefore suggested on the basis of these observations.

It is shown that the Weyl fractional derivative can quantize an open system. A fractional kicked rotor is studied in the framework of the fractional Schrödinger equation. The system is described by the non-Hermitian Hamiltonian by virtue of the Weyl fractional derivative. Violation of space symmetry leads to acceleration of the orbital momentum. Quantum localization saturates this acceleration, such that the average value of the orbital momentum can be a direct current and the system behaves like a ratchet. The classical counterpart is a nonlinear kicked rotor with absorbing boundary conditions.

Aging in an attraction-driven colloidal glass is studied by computer simulations. The system is equilibrated without attraction and instantaneously “quenched,” at constant colloid volume fraction, to one of two states beyond the glass transition; one is close to the transition, and the other one deep in the glass. The evolution of structural properties shows that bonds form in the system, increasing the local density, creating density deficits (holes) elsewhere. This process slows down with the time elapsed since the quench. As a consequence of bond formation, there is a slowing down of the dynamics, as measured by the mean-squared displacement and the density, bond, and environment correlation functions. The density correlations can be time rescaled to collapse their long time (structural) decay. The time scale for structural relaxation shows for both quenches a superlinear dependence on waiting time; it grows faster than the bond lifetime, showing the collective origin of the transition. At long waiting times and high attraction strength, we observe arrested dynamics for more than three decades in time, although individual bonds are not permanent on this time scale. The localization length decreases as the state moves deeper in the glass; the nonergodicity parameter oscillates in phase with the structure factor. Our main results are obtained for systems with a barrier in the pair potential that inhibits phase separation. However, when this barrier is removed for the case of a deep quench, we find changes in the static structure but almost none in the dynamics. Hence our results for the aging behavior remain relevant to experiments in which the glass transition competes with phase separation.

Recently it was found that fluid smectic phases of bent core liquid crystals formed freestanding fibers of extremely high slenderness ratios. Studies of these fibers showed that their structure was composed of concentric cylindrical smectic layers. For this configuration to be stable there must be an energy term that desires bending of the smectic layers. We show that an energy term that deals with the divergence of the dipolar direction can encourage layer bending if the layer chirality value is allowed to vary. The energy term associated with holding the layer chirality is closely related to layer compressions and electrical self-interactions. For our model, we assumed a simple smectic-C geometry with constant molecular tilt and cone angle defined by the director with respect to the layer normal, but allowed a constant variation of the polar direction about the director. Applying this simplified model to a free energy which accounts for director distortions, divergence of the polar direction, biaxial layer strain, surface tension, and electrical self-interactions, we were able to show consistency between the stable fiber radius and other properties predicted in our model to results from experimental studies.