We reconsider the collisional dynamics of bright solitons in the coupled nonlinear Schrödinger equation. We observe that apart from the intensity redistribution in the interaction of bright solitons, one also witnesses a rotation of the trajectories of bright solitons. The angle of rotation can be varied by suitably manipulating the self-phase-modulation (SPM) or cross-phase-modulation (XPM) parameters. The rotation of the trajectories of the bright solitons arises due to the excess energy that is injected into the dynamical system through SPM or XPM. This extra energy contributes not only to the rotation of the trajectories, but also to the realignment of intensity distribution between the two modes. We also notice that the angular separation between the bright solitons can also be maneuvered suitably. The above results, which exclude quantum superposition for the field vectors, may have wider ramifications in nonlinear optics, Bose-Einstein condensates, and left- and right-handed metamaterials.

An adaptive feedback technique for stabilizing a priori unknown saddle steady states of dynamical systems is described. The method is based on an unstable low-pass filter combined with a stable low-pass filter. The cutoff frequencies of both filters can be set relatively high. This allows considerable increase in the rate of convergence to the steady state. We demonstrate numerically and experimentally that the technique is robust to the influence of unknown external forces, which change the position of the steady state in the phase space. Experiments have been performed using electrical circuits imitating the damped Duffing-Holmes and chaotic Lindberg systems.

The carnivorous aquatic waterwheel plant (Aldrovanda vesiculosa L.) and the closely related terrestrial Venus flytrap (Dionaea muscipula Sol. ex J. Ellis) both feature elaborate snap-traps, which shut after reception of an external mechanical stimulus by prey animals. Although Aldrovanda is usually considered a miniature aquatic Dionaea, the shutting mechanisms of the two plants differ quite markedly. The fast shutting of Aldrovanda is indeed based on a simple swelling or shrinking mechanism, while the movement of Dionaea's traps is accelerated by the snap-buckling of the lobes. The purpose of this Brief Report is to describe several key improvements to the elastic models that have recently been introduced to elucidate these movements [Poppinga and Joyeux, Phys. Rev. E 84, 041928 (2011)]. In particular, a precise mechanism for the action of the motor cells of Aldrovanda is proposed, the facts that the opening of the leaves of Dionaea is an irreversible mechanism based on growth and that the strain field is anisotropic and much smaller on the inner than on the outer surface of the leaves during shutting are taken properly into account, and a more accurate formula for calculating mean curvatures is used. The improvements brought to the model are described in detail and the physical consequences of these improvements are discussed.

Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed in general. We investigate the effect of the absence of DBC on the convergence toward equilibrium. Surprisingly, it is shown that the DBC violation always makes the relaxation faster. Our result implies the existence of a kind of thermodynamic inequality that connects the nonequilibrium process relaxing toward steady state with the relaxation process which has the same probability distribution as its equilibrium state.

We measure all nonzero elements of the three-dimensional diffusion tensor $\mathbf{D}$ for clusters of colloidal spheres to a precision of 1% or better using digital holographic microscopy. We study both dimers and triangular trimers of spheres, for which no analytical calculations of the diffusion tensor exist. We observe anisotropic rotational and translational diffusion arising from the asymmetries of the clusters. In the case of the three-particle triangular cluster, we also detect a small but statistically significant difference in the rotational diffusion about the two in-plane axes. We attribute this difference to weak breaking of threefold rotational symmetry due to a small amount of particle polydispersity. Our experimental measurements agree well with numerical calculations and show how diffusion constants can be measured under conditions relevant to colloidal self-assembly, where theoretical and even numerical prediction is difficult.

The Brownian motion of a charged harmonic oscillator in the presence of additional force fields, such as a constant magnetic field and arbitrary time-dependent electric and mechanical forces, is studied in a rotational reference frame under uniform motion. By assuming an isotropic surrounding medium (a scalar friction constant), we solve explicitly the Smoluchowski equation associated with the Langevin equation for the charged harmonic oscillator and calculate the mean square displacements along and orthogonal to the rotation axis.

We introduce a stochastic model of binary opinion dynamics in which the opinions are determined by the size of the neighboring domains. The exit probability here shows a step function behavior, indicating the existence of a separatrix distinguishing two different regions of basin of attraction. This behavior, in one dimension, is in contrast to other well known opinion dynamics models where no such behavior has been observed so far. The coarsening study of the model also yields novel exponent values. A lower value of persistence exponent is obtained in the present model, which involves stochastic dynamics, when compared to that in a similar type of model with deterministic dynamics. This apparently counterintuitive result is justified using further analysis. Based on these results, it is concluded that the proposed model belongs to a unique dynamical class.

We consider anomalous diffusion of a particle moving in a tilted periodic potential in the presence of Lévy noise and nonlinear friction. Using Monte Carlo simulations, we have found some interesting characteristics of diffusion in such a nonlinear system: when the noise intensity is weak and the external force is close to the critical value at which local minima of the potential just vanish, the nonmonotonic behavior of the effective diffusion index and the superballistic diffusion are observed. This is due to the bimodal nature of the velocity distribution, and thus the test particles exist in either a running state or a long-tailed behind state in the spatial coordinate; the latter is disintegrated into small pieces of the probability peaks. We provide a relation between the group diffusion coefficient and the phase diffusion coefficient. It is shown that the distance between the above two-state centers increasing with time plays the definitive role in the superballistic group diffusion.

We generalize fluctuating hydrodynamics to study the effect of fractional time derivatives on the light-scattering spectrum of a suspension in a viscoelastic solvent under an external density gradient. Viscoelasticity introduces additional memory effects into the fluctuating hydrodynamic equations, causing the time scales associated with the mesoscopic variables and those of the microscopic events to be no longer well separated. This situation is taken into account by introducing Caputo's fractional time derivative into the description. The structure factor of the suspension is calculated, and we find that its nonequilibrium correction is an odd function of the frequency. It exhibits a shift towards negative frequencies proportional to the magnitude of the imposed gradient. We consider solvents that are described by Maxwell's or power-law rheological equations of state. The fractional structure factor is compared with the nonfractional one, and it is found that the ratio of the former to the latter may be positive and up to two orders of magnitude for both types of viscoelasticity. This prediction of our model calculation suggests that this relative change might be measurable.

Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average packing fractions $0.634\le \varphi \le 0.829$ for small to large sphere radius ratios $\alpha$ restricted to $\alpha \ge 0.100$. Surprisingly, this range of average packing fractions is obtained for packings containing a subset of spheres (called the backbone) that are exactly strictly jammed, exactly isostatic, and also generated from random initial conditions. Additionally, the average packing fractions of these packings at certain $\alpha$ and small sphere relative number concentrations $x$ approach those of the corresponding densest known ordered packings. These findings suggest for entropic reasons that these high-density disordered packings should be good glass formers and that they may be easy to prepare experimentally. We also identify an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded). The backbone packing fraction is about $0.624$ over the majority of the $\alpha$-$x$ plane, even when large numbers of small spheres are present in the backbone. Over the (relatively small) area of the $\alpha$-$x$ plane where the backbone is not roughly constant, we find that backbone packing fractions range from about $0.606$ to $0.829$, with the volume of rattler spheres comprising between $1.6\%$ and $26.9\%$ of total sphere volume. To generate isostatic strictly jammed packings, we use an implementation of the Torquato-Jiao sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)], which is an efficient producer of inherent structures (mechanically stable configurations at the local maxima in the density landscape). The identification and explicit construction of binary packings with such high packing fractions could have important practical implications for granular composites where density is critical both to material properties and fabrication cost, including for solid propellants, concrete, and ceramics. The densities and structures of jammed binary packings at various $\alpha$ and $x$ are also relevant to the formation of a glass phase in multicomponent metallic systems.

In spite of numerous theoretical and experimental reports of excitability in lasers with injected signal based on the locking-unlocking transition, the response of the system to controlled external perturbations (which is at the basis of the definition of excitable systems) has not been experimentally studied yet. In the following, we analyze the response of an injection-locked semiconductor laser to different external perturbations. We demonstrate the existence of a perturbation threshold beyond which the response of the system is independent of the strength of the stimulation and, thus, demonstrate its excitable character. We show that optically perturbing such an excitable system via the control of the phase of the injection beam can be useful for optical pulse generation.

This paper deals with the long wave instability of an electroconductor fluid film, flowing down an inclined plane at small to moderate Reynolds numbers, under the action of electromagnetic fields. A coherent second order long wave model and two simplified versions of it, referred to as first and second reduced models (FRM and SRM), are proposed to describe the nonlinear behavior of the flow. The modeling procedure consists of a combination of the lubrication theory and the weighted residual approach using an appropriate projection basis. A suitable choice of weighting functions allows a significant reduction of the dimension of the problem. The full model is naturally unique, i.e., independent of the particular form of the trial functions. The linear stability of the problem is investigated, and the influence of electromagnetic field on the flow stability is analyzed. Two cases are considered: the applied magnetic field is either normal or parallel to the fluid flow direction, while the electric field is transversal. The numerical solution of the Orr-Sommerfeld (OS) eigenvalue problem and those of the depth averaging model are used to assess the accuracy of the reduced models. It is found that the current models have the advantage of the Benney-like model, which is known to asymptote the exact solution near criticality. Moreover, far from the instability threshold, the current reduced models continue to follow the OS solution up to moderate Reynolds numbers, while the averaging model diverges rapidly. The model SRM gives better results than FRM beyond sufficiently high Reynolds numbers.

The anisotropic structure of fluidized suspensions is governed by their microstructures which are in turn determined by the dynamics of particle pair interactions. Here, we present a numerical simulation of particle interaction in linearly stratified fluids. It is shown that unlike homogeneous fluids, stratification results in the attraction of particles settling abreast. The attraction between the particles is characterized by the combined effects of buoyancy, inertia, and diffusion. The interaction of the particles settling in tandem can be fundamentally altered due to the presence of the background density gradients and the drafting-kissing-tumbling behavior in a homogeneous fluid can be replaced by drafting-kissing-separation or drafting-separation phenomenon depending on the strength of the stratification. In the case of weak stratification, drafting-kissing-tumbling occurs, however, a prolonged kissing time is observed and the rate of change of the orientation of particles is reduced. It is shown that the formation of the buoyancy-induced vortical structures and the generation of stratified jets behind the particles are the fundamental mechanisms in governing the dynamics of the particle pair interaction in stratified fluids.

Universal scaling laws form one of the central issues in physics. A nonstandard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems. Recently, we found that a statistical quantity related to fluctuations follows a nonstandard scaling law with respect to the system size in a synchronized state of globally coupled nonidentical phase oscillators [I. Nishikawa et al., Chaos 22, 013133 (2012)]. However, it is still unclear how widely this nonstandard scaling law is observed. In the present paper, we discuss the conditions required for the unusual scaling law in globally coupled oscillator systems and validate the conditions by numerical simulations of several different models.

Extending the recent work on models with spatially nonuniform nonlinearities, we study bright solitons generated by the nonpolynomial self-defocusing (SDF) nonlinearity in the framework of the one-dimensional (1D) Muñoz-Mateo–Delgado (MM-D) equation (the 1D reduction of the Gross-Pitaevskii equation with the SDF nonlinearity), with the local strength of the nonlinearity growing at $\left|x\right|\to \infty$ faster than $\left|x\right|$. We produce numerical solutions and analytical ones, obtained by means of the Thomas-Fermi approximation, for nodeless ground states and for excited modes with one, two, three and four nodes, in two versions of the model, with steep (exponential) and mild (algebraic) nonlinear-modulation profiles. In both cases, the ground states and the single-node ones are completely stable, while the stability of the higher-order modes depends on their norm (in the case of the algebraic modulation, they are fully unstable). Unstable states spontaneously evolve into their stable lower-order counterparts.

Elimination of seemingly unnecessary variables in Markovian models may cause a difference in the value of irreversible entropy production between the original and reduced dynamics. We show that such difference, which we call the hidden entropy production, obeys an integral fluctuation theorem if all variables are time-reversal invariant, or if the density function is symmetric with respect to the change of sign of the time-reversal antisymmetric variables. The theorem has wide applicability, since the proposed condition is mostly satisfied in the case where the hidden fast variables are equilibrated. The main consequence of this theorem is that the entropy production decreases by the coarse-graining procedure. By contrast, in the case where a stochastic process is obtained by coarse-graining a deterministic and reversible dynamics, the entropy production may increase, implying that the integral fluctuation theorem should not hold for such reductions. We reveal, with an explicit example, that the nonequilibrated time-reversal antisymmetric variables play a crucial role in distinguishing these two cases, thus guaranteeing the consistency of the presented theorem.

The general possible form of mean-field parametrization in a running frame in terms of current, energy, and density functionals is examined under the restrictions of Galilean invariance. It is found that only two density-dependent parameters remain which are usually condensed in a position-dependent effective mass and the self-energy formed by current and mass. The position-dependent mass induces a position-dependent local current, which is identified for different nonlinear frames. In a second step the response to an external perturbation and relaxation towards a local equilibrium is investigated. The response function is found to be universal in the sense that the actual parametrization of the local equilibrium does not matter and is eliminated from the theory due to the conservation laws. The explicit form of the response with respect to density, momentum, and energy is derived. The compressibility sum rule as well as the sum rule by first- and third-order frequency moments are proved analytically to be fulfilled simultaneously. The results are presented for Bose or Fermi systems in one, two, and three dimensions.

In this paper we present a general model for the dynamic behavior of multiphase systems in which the bulk phases and interfaces have a complex microstructure (for example, immiscible polymer blends with added compatibilizers, or polymer stabilized emulsions with thickening agents dispersed in the continuous phase). The model is developed in the context of the GENERIC framework (general equation for the nonequilibrium reversible irreversible coupling). We incorporate scalar and tensorial structural variables in the set of independent bulk and surface excess variables, and these structural variables allow us to link the highly nonlinear rheological response typically observed in complex multiphase systems, directly to the time evolution of the microstructure of the bulk phases and phase interfaces. We present a general form of the Poisson and dissipative brackets for the chosen set of bulk and surface excess variables, and show that to satisfy the entropy degeneracy property, we need to add several contributions to the moving interface normal transfer term, involving the tensorial bulk and interfacial structural variables. We present the full set of balance equations, constitutive equations, and boundary conditions for the calculation of the time evolution of the bulk and interfacial variables, and this general set of equations can be used to develop specific models for a wide range of complex multiphase systems.

In this paper we use the GENERIC (general equation for nonequilibrium reversible-irreversible coupling) nonequilibrium thermodynamics framework to derive constitutive equations for the surface extra stress tensor of an interface stabilized by a two-dimensional suspension of anisotropic colloidal particles. The dependence of the surface stress tensor on the microstructure of the interface is incorporated through a dependence on a single tensorial structural variable, characterizing the average orientation of the particles. The constitutive equation for the stress tensor is combined with a time-evolution equation describing the changes in the orientation tensor as a result of the applied deformation field. We examine the predictions of the model in in-plane steady shear flow, in-plane oscillatory shear flow, and oscillatory dilatational flow. The model is able to predict the experimentally observed shear thinning behavior in surface shear flow, and also the experimentally observed emergence of even harmonics in the frequency spectrum of the surface stress in oscillatory dilatational flow. Our results show that the highly nonlinear stress-deformation behavior of interfaces with a complex microstructure can be modeled well using simple structural models like the one presented here.

In this paper, we investigate the enhancement mechanism of the mechanical properties for hard-soft block copolymers by using molecular dynamics simulations at various temperatures. A coarse-grained approach is adopted to study sufficiently generic models. Our numerical experiments demonstrate that the nonbond potential plays a more significant role in mechanical properties compared to the bond potential. This finding serves as a cornerstone to understand the hard-soft materials. To explore the effect of hard segments, four copolymers with different concentrations and energy factors that describe the interaction between hard beads are conducted. Simulation results show that the mechanical performances of the system with large attractive force and small concentration of hard segments could be improved dramatically in conjunction with a moderate increment of the glass transition temperature. In particular, the energy factor shows a substantial influence in determining the microphase separation as well as the morphology of hard domains. These observations are believed to provide design guidelines for polymeric materials in engineering practice.