The soft-disk model previously developed and applied by Durian [D. J. Durian, Phys. Rev. Lett. 75, 4780 (1995)] is brought to bear on problems of foam rheology of longstanding and current interest, using two-dimensional systems. The questions at issue include the origin of the Herschel-Bulkley relation, normal stress effects (dilatancy), and localization in the presence of wall drag. We show that even a model that incorporates only linear viscous effects at the local level gives rise to nonlinear (power-law) dependence of the limit stress on strain rate. With wall drag, shear localization is found. Its nonexponential form and the variation of localization length with boundary velocity are well described by a continuum model in the spirit of Janiaud et al. [Phys. Rev. Lett. 97, 038302 (2006)]. Other results satisfactorily link localization to model parameters, and hence tie together continuum and local descriptions.

We consider a nematic liquid crystal constrained by two coaxial cylinders under the action of low-frequency axial or radial electric fields. Assuming an initially hybrid configuration, we find the equilibrium texture of the nematic subjected to weak anchoring boundary conditions on both cylindrical surfaces. We analyze the distinct textures of the nematic as a function of the strength of the interaction of the nematic with the sidewalls, the radii ratio of the cylinders, and the applied electric field. Also, for each radii ratio and strength of the nematic-surface interaction, we determine the critical field for which a complete alignment of the nematic liquid crystal occurs.

We demonstrate that flows of conducting fluid along a Möbius strip and related surfaces are hydromagnetic dynamos, i.e., they can produce an exponentially growing magnetic field from an infinitesimal seed. The critical magnetic Reynolds number in one of our models is as low as about 16. Together with other attractive features, this makes this flow an interesting candidate for a laboratory dynamo experiment.

We compare the different existing strategies of mutual nonlinear prediction regarding their ability to assess the coupling strength and directionality of the interactions in bivariate time series. Under the common framework of $k$-nearest neighbor local linear prediction, we test three approaches based on cross prediction, mixed prediction, and predictability improvement. The measures of interdependence provided by these approaches are first evaluated on short realizations of bivariate time series generated by coupled Henon models, investigating also the effects of noise. The usefulness of the three mutual nonlinear prediction schemes is then assessed in a common physiological application during known conditions of interaction—i.e., the analysis of the interdependence between heart rate and arterial pressure variability in healthy humans during supine resting and passive head-up tilting. Based on both simulation results and physiological interpretability of cardiovascular results, we conclude that cross prediction is valuable to quantify the coupling strength and predictability improvement to elicit directionality of the interactions in short and noisy bivariate time series.

Ion transport through a T-intersection of two silica nanochannels (a main channel, $5\text{−}\mu \mathrm{m}$ long and $30\text{−}\mathrm{nm}$ wide, and a subchannel, $5\text{−}\mu \mathrm{m}$ long and $15\text{−}\mathrm{nm}$ wide) with a surface charge distribution was investigated based on continuum dynamics calculations. The surface charge within $250\mathrm{nm}$ of the intersection in the main channel and the entire subchannel was positive and that in the main channel outside this intersection region was negative. This nanofluidic system is analogous to a $p\text{−}n\text{−}p$ transistor. The calculation results revealed that, by adjusting the electric potentials at the ends of the nanochannels, the ionic current could be (1) cut off, (2) regulated in the main channel, (3) diverged into the main and subchannels, (4) turned from the main channel to the subchannel, and (5) merged into the subchannel. A series connection of this nanofluidic system can therefore be used in biotechnological applications for electrophoretic separation and for sorting of ions and biomolecules.

Low-frequency properties of a plasma are examined within the average-atom approximation, which presumes that scattering of a conducting electron on each atom takes place independently of other atoms. The relaxation time $\tau$ distinguishes a high-frequency region $\omega \tau >1$, where the single-atom approximation is applicable explicitly, from extreme low frequencies $\omega \tau <1$, where, naively, the single-atom approximation is invalid. A proposed generalization of the formalism, which takes into account many-atom collisions, is found to be accurate in all frequency regions, from $\omega =0$ to $\omega \tau >1$, reproducing the Ziman formula in the static limit, results based on the Kubo-Greenwood formula for high frequencies and satisfying the conductivity sum rule precisely. The correspondence between physical processes leading to the conventional Ohm’s law and the infrared properties of QED is discussed. The suggested average-atom approach to frequency-dependent conductivity is illustrated by numerical calculations for an aluminum plasma in the temperature range $2–10\mathrm{eV}$.

Sound emission produced by the interaction of several vortices in a two-dimensional homogeneous system obeying the nonlinear Schrödinger (NLS) equation is considered. The radiation effect is explicitly computed in terms of assumed vortex motion. The results are applied to a simple test case of two corotating vortices. The prediction is compared to the result of numerical simulations of the NLS equation. The numerical data give support to the estimate of radiation.

Exact chirped soliton solutions of a generalized nonlinear Schrödinger equation with the cubic-quintic nonlinearities as well as the self-steeping were obtained using a variable parametric method. It was found that the formation of solutions is determined by the sign of a joint parameter solely. By performing numerical simulations, the chirped solutions are stable under perturbations.

We consider an irreversible autocatalytic conversion reaction $\mathrm{A}+\mathrm{B}\to 2\mathrm{A}$ under subdiffusion described by continuous-time random walks. The reactants’ transformations take place independently of their motion and are described by constant rates. The analog of this reaction in the case of normal diffusion is described by the Fisher-Kolmogorov-Petrovskii-Piskunov equation leading to the existence of a nonzero minimal front propagation velocity, which is really attained by the front in its stable motion. We show that for subdiffusion, this minimal propagation velocity is zero, which suggests propagation failure.

We investigate the unjamming response of disordered packings of frictional hard disks with the help of computer simulations. First, we generate jammed configurations of the disks and then force them to move again by local perturbations. We study the spatial distribution of the stress and displacement response and find long range effects of the perturbation in both cases. We record the penetration depth of the displacements and the critical force that is needed to make the system yield. These quantities are tested in two types of systems: in ideal homogeneous packings in zero gravity and in packings settled under gravity. The penetration depth and the critical force are sensitive to the interparticle friction coefficient. Qualitatively, the same nonmonotonic friction dependence is found both with and without gravity, however the location of the extrema are at different friction values. We discuss the role of the connectivity of the contact network and of the pressure gradient in the unjamming response.

The effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens fresh perspectives for rapidly rotating star seismology and also provides a potentially observable manifestation of wave chaos in a large-scale natural system.

The results of the theoretical studies on the leakage of the optical radiation through a truncated waveguide with a subwavelength-sized exit hole are reported. We develop a self-consistent approach for the description of the fields behavior by taking into account the transformation of the initial wave into all possible modes, which appear due to the influence of the exit aperture. Our approach allows us to evaluate the amplitude reflection coefficient for the initial evanescent wave and to establish its relationship with the impedance of an infinite waveguide and the impedance of the exit aperture coupling a truncated waveguide with a free space. We determine the complex flow through the exit hole and the transmission coefficient to the far-field zone and express them through the reflection coefficient. Special attention in the work is paid to the evaluation of specific dependencies of the reflection and transmission coefficients on the ratio of the aperture radius to the light wavelength, on the dielectric constants of the waveguide core and the surrounding matter, and on the type of the waveguide mode. It is demonstrated that in the case of a metallic matter at the exit of a waveguide there is a strong resonance enhancement in the amplitude of the reflected wave and in the resulting amplitude of the tangential component of the electric field.

Synchronization thresholds of an array of nondiagonally coupled oscillators are investigated. We present experimental results which show the existence of ragged synchronizability, i.e., the existence of multiple disconnected synchronization regions in the coupling parameter space. This phenomenon has been observed in an electronic implementation of an array of nondiagonally coupled van der Pol’s oscillators. Numerical simulations show good agreement with the experimental observations.

With Monte Carlo simulations, we study the dynamic relaxation at perfect and imperfect surfaces of the three-dimensional Ising model with an ordered initial state. The time evolution of the surface magnetization, the line magnetization of the defect line, and the corresponding susceptibilities and second cumulants is carefully examined. Universal dynamic scaling forms including a dynamic crossover scaling form are identified at the ordinary, special, and surface phase transitions. The critical exponents ${\beta }_1$ of the surface magnetization and ${\beta }_2$ of the line magnetization are extracted. The impact of the defect line on the universality classes is investigated.

In directional solidification, as the solidification velocity increases, the growth direction of cells or dendrites rotates from the direction of the thermal gradient to that of a preferred cristalline orientation. Meanwhile, their morphology varies with important implications for microsegregation. Here, we experimentally document the growth directions of these microstructures in a succinonitrile alloy in the whole accessible range of directions, velocities, and spacings. For this, we use a thin sample made of a single crystal on which the direction of the thermal gradient can be changed. This allows a fine monitoring of the misorientation angle between thermal gradient and preferred crystalline orientation. Data analysis shows evidence of an internal symmetry which traces back to a scale invariance of growth directions with respect to a Péclet number. This enables the identification of the relationship between growth directions and relevant variables, in fair agreement with experiment. Noticeable variations of growth directions with misorientation angles are evidenced and linked to a single parameter.

Based on a signaling process of complex networks, a method for identification of community structure is proposed. For a network with $n$ nodes, every node is assumed to be a system which can send, receive, and record signals. Each node is taken as the initial signal source to excite the whole network one time. Then the source node is associated with an $n$-dimensional vector which records the effects of the signaling process. By this process, the topological relationship of nodes on the network could be transferred into a geometrical structure of vectors in $n$-dimensional Euclidean space. Then the best partition of groups is determined by $F$ statistics and the final community structure is given by the $K$-means clustering method. This method can detect community structure both in unweighted and weighted networks. It has been applied to ad hoc networks and some real networks such as the Zachary karate club network and football team network. The results indicate that the algorithm based on the signaling process works well.

The dynamic behavior of spiral-shaped excitation patterns with oscillatory dispersion is investigated under the influence of externally applied direct current or alternating current. For these two types of electric field, wave-grouping phenomena are generally observed. For the direct current field, the spiral wave drifts approximately along a straight line and wave groupings appear in certain ranges of spatial polar angles when the strength of the external field is larger than a threshold. In terms of the Doppler effect induced by the drift of the spiral tip and the oscillatory dispersion, we propose a theory model to predict the spatial distribution of wave grouping and the critical strength of the current. In contrast, for the alternating current field, the spiral wave may stay stationary and wave grouping may appear in the whole space with a different manner. This finding indicates that movement of the spiral tip is not necessary for the appearance of wave grouping.

We seek a route to the equilibrium where all the agents cooperate in the iterated prisoner’s dilemma game on a two-dimensional plane, focusing on the role of tit-for-tat strategy. When a time horizon, within which a strategy can recall the past, is one time step, an equilibrium can be achieved as cooperating strategies dominate the whole population via proliferation of tit-for-tat. Extending the time horizon, we filter out poor strategies by simplified replicator dynamics and observe a similar evolutionary pattern to reach the cooperating equilibrium. In particular, the rise of a modified tit-for-tat strategy plays a central role, which implies how a robust strategy is adopted when provided with an enhanced memory capacity.

We analyze the conditions for the existence of current reversals in overdamped deterministic tilting ratchets under symmetric forcing. To this end, we use and extend the formalism recently introduced in R. Salgado-García, M. Aldana, and G. Martínez-Mekler [Phys. Rev. Lett. 96, 134101 (2006)] to transform the equations of motion of the ratchet into discrete circle maps. For a periodic dichotomous forcing we show that the phenomenon of current reversal is not uncommon and exists for a nonzero measure set of the parameter space. Additionally, we show numerically that, for a wide class of ratchet potentials, current reversals also occur when the discontinuous dichotomous forcing is replaced by symmetric continuous driving forces. The likelihood of the occurrence of current reversals is a consequence of the structural stability under small perturbations of the associated circle map with rational rotation number.