Considering the simultaneous propagation of multicomponent fields in an isotropic medium, an $N$-coupled nonlinear Schrödinger system with the self-phase modulation, cross-phase modulation, and energy exchange terms is investigated in this paper. First, via symbolic computation, the Painlevé singularity structure analysis shows that such a system admits the Painlevé property. Then, with the Ablowitz-Kaup-Newell-Segur scheme, the linear eigenvalue problem (Lax pair) associated with this model is constructed in the frame of the block matrices. With the Hirota bilinear method, the bright one- and two-soliton solutions of this system are presented. In addition, the bright multisoliton solutions of the system for $N=2$ are straightforwardly derived by the linear superposition of soliton solutions of two independent scalar nonlinear Schrödinger equations. Furthermore, through the analysis for the soliton solutions, the corresponding propagation behavior and applications for soliton pulses in nonlinear optical fibers are considered. Finally, three significant conserved quantities, i.e., energy, momentum, and Hamiltonian, are also given.

This paper presents a simulation model of concentrated colloidal nanoparticulate flows to investigate self-organization of the nanoparticles and rheology of the colloid. The motion of solid nanoparticles is treated by an off-lattice Newtonian dynamics. The flow of solvent is treated by an on-lattice fluctuating Navier-Stokes equation. A fictitious domain method is employed to couple the motion of nanoparticles with the flow of solvent. The surface of nanoparticles is expressed by discontinuous solid-liquid boundary to calculate accurately contact interaction and Derjaguin-Landau-Verwey-Overbeek interaction between the nanoparticles. At the same time, the surface is expressed by continuous solid-liquid boundary to calculate efficiently hydrodynamic interaction between the nanoparticles and the solvent. Unlike other simulation models that focus on the hydrodynamic interaction, the present model includes all crucial interactions, such as contact force and torque, van der Waals force, electrostatic force, hydrodynamic force, and torque including thermal fluctuation of the solvent that causes translational and rotational Brownian motions of the nanoparticles. Especially the present model contains the frictional force that plays a significant role on nanoparticles in contact with one another. A fascinating novelty of the present model is that computational cost is constant regardless of the concentration of nanoparticles. The capability of the present simulation model is demonstrated by two-dimensional simulations of concentrated colloidal nanoparticles in simple shear flows between flat plates. The self-organization of concentrated colloidal nanoparticles and the viscosity of colloid are investigated in a wide range of Péclet numbers.

Cooperative behaviors near the disorder-induced critical point in a random-field Ising model are numerically investigated by analyzing time-dependent magnetization in ordering processes from a special initial condition. We find that the intensity of fluctuations of time-dependent magnetization, $\chi \left(t\right)$, attains a maximum value at a time $t=\tau$ in a normal phase and that $\chi \left(\tau \right)$ and $\tau$ exhibit divergences near the disorder-induced critical point. Furthermore, spin configurations around the time $\tau$ are characterized by a length scale, which also exhibits a divergence near the critical point. We estimate the critical exponents that characterize these power-law divergences by using a finite-size scaling method.

We study numerically phase separation in a binary fluid subject to an applied shear flow in two dimensions, with full hydrodynamics. To do so, we introduce a mixed finite-differencing and spectral simulation technique, with a transformation to render trivial the implementation of Lees-Edwards sheared periodic boundary conditions. For systems with inertia, we reproduce the nonequilibrium steady states reported in a recent lattice Boltzmann study. The domain coarsening that would occur in zero shear is arrested by the applied shear flow, which restores a finite-domain-size set by the inverse shear rate. For inertialess systems, in contrast, we find no evidence of nonequilibrium steady states free of finite-size effects: Coarsening persists indefinitely until the typical domain size attains the system size, as in zero shear. We present an analytical argument that supports this observation and that furthermore provides a possible explanation for a hitherto puzzling property of the nonequilibrium steady states with inertia.

This paper aims at understanding coevolutionary dynamics of cooperative behaviors and network structures of interactions. We constructed an evolutionary model in which each individual not only has a strategy for prisoner’s dilemma to play with its neighboring members on the network, but also has a strategy for changing its neighboring structure of the network. By conducting evolutionary experiments with various settings of the payoff matrix, we found that the coevolutionary cycles of cooperative behaviors of individuals and their network structures repeatedly occurred when both the temptation to defect and the cost for playing a game were moderate.

A mechanical model was developed to study the indentation of an atomic force microscopic (AFM) tip on a cell with adhesion mediated by receptor-ligand binding. The effects of indentation rate, indentation depth, indenter size, and the mechanical properties of cells on the adhesion force were investigated. It was found that the presence of adhesion between the cell and AFM tip may affect both the loading curve and unloading curve, which may in turn change the extracted elastic modulus values using the conventional indentation models. It was found that an increase in the receptor-ligand reaction rate may lead to a transition from a decrease of the maximum adhesion force with the indentation rate to an increase of the maximum adhesion force with the indentation rate. It was also found that factors such as indenter size, indentation depth, and cell mechanical properties influence the maximum adhesion force, and their corresponding underlying mechanisms were discussed.

We show that both the maximum energy gain and the accelerated beam quality can be efficiently controlled by the plasma-density profile. Choosing a proper density gradient one can uplift the dephasing limitation and keep the phase synchronism between the bunch of relativistic particles and the plasma wave over extended distances. Putting electrons into the $n$th wake period behind the driving laser pulse, the maximum energy gain is increased by the factor, which is proportional to $n$, over that in the case of uniform plasma. Layered plasma is suggested to keep the resonant condition for laser-wakefield excitation. The acceleration is limited then by laser depletion rather than by dephasing. Further, we show that the natural energy spread of the particle bunch acquired at the acceleration stage can be effectively removed by a matched deceleration stage, where a larger plasma density is used.

We propose a method for extracting general features from multivariate data using a network of phase oscillators subject to an analogue of the Kuramoto model for collective synchronization. In this method, the natural frequencies of the oscillators are extended to vector quantities to which multivariate data are assigned. The common frequency vectors of the groups of partially synchronized oscillators are interpreted to be the template vectors representing the general features of the data set. We show that the proposed method becomes equivalent to the self-organizing map algorithm devised by Kohonen when the governing equations are linearized about their solutions of partial synchronization. As a case study to test the utility of our method, we applied it to care-needs-certification data in the Japanese public long-term care insurance program, and found major general patterns in the health status of the elderly needing nursing care.

Uncovering the directionality of coupling is a significant step in understanding drive-response relationships in complex systems. In this paper, we discuss a nonparametric method for detecting the directionality of coupling based on the estimation of information theoretic functionals. We consider several different methods for estimating conditional mutual information. The behavior of each estimator with respect to its free parameter is shown using a linear model where an analytical estimate of conditional mutual information is available. Numerical experiments in detecting coupling directionality are performed using chaotic oscillators, where the influence of the phase extraction method and relative frequency ratio is investigated.

The motion of small, spherical particles of finite size in fluid flows at low Reynolds numbers is described by the strongly nonlinear Maxey-Riley equations. Due to the Stokes drag, the particle motion is dissipative, giving rise to the possibility of attractors in phase space. We investigate the case of an infinite cellular flow field with time-periodic forcing. The dynamics of this system are studied in a part of the parameter space. We focus particularly on the size of the particles, whose variations are most important in active physical processes, for example, for aggregation and fragmentation of particles. Depending on their size the particles will settle on different attractors in phase space in the long-term limit, corresponding to periodic, quasiperiodic, or chaotic motion. One of the invariant sets that can be observed in a large part of this parameter region is a quasiperiodic motion in the form of a torus. We identify some of the bifurcations that these tori undergo, as particle size and mass ratio relative to the fluid are varied. In this way we provide a physical example for sub- and supercritical pitchfork bifurcations of tori.

A lattice Boltzmann model has been developed to simulate heat transfer in supercritical fluids. A supercritical viscous fluid layer between two plates heated from the bottom has been studied. It is demonstrated that the model can be used to study heat transfer near the critical point where the so-called piston effect speeds up the transfer of heat and results in homogeneous heating in the bulk of the layer. We have also studied the onset of convection in a Rayleigh-Bénard configuration. It is shown that our model can well predict qualitatively the onset of convection near the critical point, where there is a crossover between the Rayleigh and Schwarzschild criteria.

We present an analysis of the transverse-velocity fluctuations in an isothermal liquid layer with a uniform shear rate between two parallel horizontal boundaries as a function of the wave number and the Reynolds number. The results were obtained by solving a stochastic version of the Orr-Sommerfeld equation subject to no-slip boundary conditions in a second-order Galerkin approximation. We find that the spatial Fourier transform of the transverse-velocity fluctuations exhibits a maximum as a function of the (horizontal) wave number $q_{\parallel }$. This maximum is associated with a crossover from a $q_{\parallel }^{-4}$ dependence for larger $q_{\parallel }$ to a $q_{\parallel }^2$ dependence for small $q_{\parallel }$. The $q_{\parallel }^{-4}$ dependence at larger wave numbers is independent of the boundary conditions, but the small-$q_{\parallel }$ behavior is strongly affected by the boundary conditions. The nonequilibrium enhancement of the intensity of the transverse-velocity fluctuations remains finite for all values of the Reynolds number, but increases approximately with the square of the Reynolds number. The relation between our results and those obtained by previous authors in the absence of boundary conditions is elucidated.

We propose an asymmetric negotiation strategy to investigate the influence of high-degree agents on the agreement dynamics in a structured language game, the naming game. We introduce a model parameter, which governs the frequency of high-degree agents acting as speakers in communication. It is found that there exists an optimal value of the parameter that induces the fastest convergence to a global consensus on naming an object for both scale-free and small-world naming games. This phenomenon indicates that, although a strong influence of high-degree agents favors consensus achievement, very strong influences inhibit the convergence process, making it even slower than in the absence of influence of high-degree agents. Investigation of the total memory used by agents implies that there is some trade-off between the convergence speed and the required total memory. Other quantities, including the evolution of the number of different names and the relationship between agents’ memories and their degrees, are also studied. The results are helpful for better understanding of the dynamics of the naming game with asymmetric negotiation strategy.

Two neutrally buoyant intruder particles in a granular bed fluidized by vertical, sinusoidal vibration are known to interact with each other over a range of about five intruder diameters. Using molecular dynamics simulations, we investigate in detail the spatial and temporal nature of this interaction. We show that the force of attraction between intruders can be calculated from the local density and kinetic energy using a simple equation of state. Moreover, the interaction can be changed from attractive to repulsive by reducing the coefficient of restitution between the intruders and host particles, one of the key results of this work.

The aging of a charged colloidal system has been studied by small-angle x-ray scattering, in the exchanged momentum range $Q=0.03–5{\mathrm{nm}}^{-1}$, and by dynamic light scattering, at different clay concentrations $(C_w=0.6–2.8\%)$. The static structure factor $S\left(Q\right)$ has been determined as a function of both aging time and concentration. This is the direct experimental evidence of the existence and evolution with aging time of two different arrested states in a single system simply obtained only by changing its volume fraction: an inhomogeneous state is reached at low concentrations, while a homogeneous one is found at high concentrations.

A two-dimensional model within the $\stackrel{̿}{Q}$-tensor description of liquid crystals is used to describe the inhomogeneous order reconstruction in a nematic cell driven by tony modulation in the anchoring conditions. Homogeneous and inhomogeneous reconstruction are contrasted: the former is defectless, the latter is defect mediated. While the transition thresholds are comparable in both cases and in good agreement with experimental data, the biaxial wall breaking is considerably slower in the inhomogeneous transition than in the homogeneous one. The shape of the signal given by the electric current flowing through the cell allows us to distinguish the actual path followed by the transition.

An attempt to find a probability-amplitude-based Hamiltonian representation of the symmetrical version of integrable semidiscrete multicomponent nonlinear Schrödinger systems is made. Thus the on-cell locality of the general point transformation in combination with the model multicomponentness is shown to contradict the concept of canonical Hamiltonian representation in terms of probability amplitudes. Nevertheless, the above concept can be realized in a slightly adjusted semidiscrete multicomponent nonlinear Schrödinger system that preserves some physically valuable solutions of the original (either symmetric or asymmetric) integrable model. The advantages of the adjusted Hamiltonian model for the analysis of real physical systems are formulated. Examples of longitudinal and lateral soliton dynamics on multichain tubular lattices subjected to uniform electric and magnetic fields are given.

We study the stability and synchronization of predator-prey populations subjected to noise. The system is described by patches of local populations coupled by migration and predation over a neighborhood. When a single patch is considered, random perturbations tend to destabilize the populations, leading to extinction. If the number of patches is small, stabilization in the presence of noise is maintained at the expense of synchronization. As the number of patches increases, both the stability and the synchrony among patches increase. However, a residual asynchrony, large compared with the noise amplitude, seems to persist even in the limit of an infinite number of patches. Therefore, the mechanism of stabilization by asynchrony recently proposed by Abta et al. [Phys. Rev. Lett. 98, 098104 (2007)], combining noise, diffusion, and nonlinearities, seems to be more general than first proposed.

We study entanglement in a system comprising two coupled quartic oscillators. It is shown that the entanglement, as measured by the von Neumann entropy, increases with the classical chaos parameter for generic chaotic eigenstates. We consider certain isolated periodic orbits whose bifurcation sequence affects a class of strongly scarred quantum eigenstates, called the channel localized states. For these states, the entanglement is a local minima in the vicinity of a pitchfork bifurcation but is a local maxima near an antipitchfork bifurcation. We place these results in the context of the close connections that may exist between entanglement measures and conventional measures of localization. We also point to an interesting near degeneracy that arises in the spectrum of reduced density matrices of certain states as an interplay between localization and symmetry.