We analyze the formation of one-dimensional localized patterns in a nonlinear dissipative medium including a set of two narrow “hot spots” (HSs), which carry the linear gain, local potential, cubic self-interaction, and cubic loss, while the linear loss acts in the host medium. This system can be realized as a spatial-domain one in optics and also in Bose-Einstein condensates of quasiparticles in solid-state settings. Recently, exact solutions were found for localized modes pinned to the single HS represented by the δ function. The present paper reports analytical and numerical solutions for coexisting two- and multipeak modes, which may be symmetric or antisymmetric with respect to the underlying HS pair. Stability of the modes is explored through simulations of their perturbed evolution. The sign of the cubic nonlinearity plays a crucial role: in the case of the self-focusing, only the fundamental symmetric and antisymmetric modes, with two local peaks tacked to the HSs, and no additional peaks between them, may be stable. In this case, all the higher-order multipeak modes, being unstable, evolve into the fundamental ones. Stability regions for the fundamental modes are reported. A more interesting situation is found in the case of the self-defocusing cubic nonlinearity, with the HS pair giving rise to a multistability, with up to eight coexisting stable multipeak patterns, symmetric and antisymmetric ones. The system without the self-interaction, the nonlinearity being represented only by the local cubic loss, is investigated too. This case is similar to those with the self-focusing or defocusing nonlinearity, if the linear potential of the HS is, respectively, attractive or repulsive. An additional feature of the former setting is the coexistence of the stable fundamental modes with robust breathers.

The lattice Boltzmann methods (LBMs) have successfully been applied to microscale flows in the hydrodynamic regime, such as flows of liquids in porous media. However, the LBM in its standard formulation does not produce correct results beyond the hydrodynamic regime, i.e., for slip and transitional ones. Following the work of Shan and He [Phys. Rev. Lett. 80, 65 (1998)], we propose to extend the LBM to these regimes in which nonequilibrium effects are obvious and require us to include a larger number of distribution-function moments.

We analyze a theoretical model for energy and electron transfer in an artificial photosynthetic system. The photosystem consists of a molecular triad (i.e., with a donor, a photosensitive unit, and an acceptor) coupled to four accessory light-harvesting-antenna pigments. The resonant energy transfer from the antennas to the artificial reaction center (the molecular triad) is described here by the Förster mechanism. We consider two different kinds of arrangements of the accessory light-harvesting pigments around the reaction center. The first arrangement allows direct excitation transfer to the reaction center from all the surrounding pigments. The second configuration transmits energy via a cascade mechanism along a chain of light-harvesting chromophores, where only one chromophore is connected to the reaction center. We show that the artificial photosynthetic system using the cascade energy transfer absorbs photons in a broader wavelength range and converts their energy into electricity with a higher efficiency than the system based on direct couplings between all the antenna chromophores and the reaction center.

Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas, and wave-particle systems. These systems, adequately described by the Vlasov equation, present quasistationary states (QSS), i.e., long lasting intermediate stages of the dynamics that occur after a short significant evolution called “violent relaxation.” The nature of the relaxation, in the absence of collisions, is not yet fully understood. We demonstrate in this article the occurrence of stretching and folding behavior in numerical simulations of the Vlasov equation, providing a plausible relaxation mechanism that brings the system from its initial condition into the QSS regime. Area-preserving discrete-time maps with a mean-field coupling term are found to display a similar behavior in phase space as the Vlasov system.

Existence of a nonequilibrium tricritical point has been revealed in the Hamiltonian mean-field model by a nonequilibrium statistical mechanics. This statistical mechanics gives a distribution function containing unknown parameters, and the parameters are determined by solving simultaneous equations depending on a given initial state. Due to difficulty in solving these equations, pointwise numerical detection of the tricritical point has been unavoidable on a plane characterizing a family of initial states. In order to look into the tricritical point, we expand the simultaneous equations with respect to the order parameter and reduce them to one algebraic equation. The tricritical point is precisely identified by analyzing coefficients of the reduced equation. Reentrance to an ordered phase in a high-energy region is revisited around the obtained tricritical point.

The electrophoretic mobility of double-stranded DNA in polyacrylamide gel is investigated using an activated hopping model for the transport of a charged object within a heterogeneous medium. The model is premised upon a representation of the DNA path through the gel matrix as a series of traps with alternating large and small cross sections. Calculations of the trap dimensions from gel data show that the path imposes varying degrees of confinement upon migrating analytes, which retard their forward motion in a size-dependent manner. An expression derived for DNA mobility is shown to provide accurate predictions for the dynamics of linear DNA (67–622 bp) in gels of multiple concentrations. For star-branched DNA, the incorporation within the model of a length scale previously proposed to account for analyte architecture [Yuan et al., Anal. Chem. 78, 6179 (2006)] leads to mobility predictions that compare well with experimental results for a wide range of DNA shapes and molecular weights.

We present an experimental study of drainage in two-dimensional porous media exhibiting bimodal pore size distributions. The role of the pore size heterogeneity is investigated by measuring separately the desaturation curves of the two pore populations. The displaced wetting fluid remains trapped in small pores at low capillary numbers and is swept only above a critical capillary number proportional to the permeability of the big pores network. Based on this observation, we derive a simple criterion for phase trapping based on the balance of viscous to capillary forces. Numerical implementation of this theory in a pore network model quantitatively fits our experimental results. This combination of approaches demonstrates quantitatively the influence of geometrical heterogeneities on drainage in porous media.

An acoustic vortex in an inviscid fluid and its radiation torque on an axisymmetric absorbing object are analyzed beyond the paraxial approximation to clarify an analogy with an optical vortex. The angular momentum flux density tensor from the conservation of angular momentum is used as an efficient description of the transport of angular momentum. Analysis of a monochromatic nonparaxial acoustic vortex beam indicates that the local ratio of the axial (or radial) flux density of axial angular momentum to the axial (or radial) flux density of energy is exactly equal to the ratio of the beam's topological charge $l$ to the acoustic frequency $\omega$. The axial radiation torque exerted by the beam on an axisymmetric object centered on the beam's axis due to the transfer of angular momentum is proportional to the power absorbed by the object with a factor $l/\omega$, which can be understood as a result of phonon absorption from the beam. Depending on the vortex's helicity, the torque is parallel or antiparallel to the beam's axis.

For stationary time series, the cross-covariance and the cross-correlation as functions of time lag $n$ serve to quantify the similarity of two time series. The latter measure is also used to assess whether the cross-correlations are statistically significant. For nonstationary time series, the analogous measures are detrended cross-correlations analysis (DCCA) and the recently proposed detrended cross-correlation coefficient, ${\rho }_{\mathrm{DCCA}}(T,n)$, where $T$ is the total length of the time series and $n$ the window size. For ${\rho }_{\mathrm{DCCA}}(T,n)$, we numerically calculated the Cauchy inequality $-1\le {\rho }_{\mathrm{DCCA}}(T,n)\le 1$. Here we derive $-1\le {\rho }_{\mathrm{DCCA}}(T,n)\le 1$ for a standard variance-covariance approach and for a detrending approach. For overlapping windows, we find the range of ${\rho }_{\mathrm{DCCA}}$ within which the cross-correlations become statistically significant. For overlapping windows we numerically determine—and for nonoverlapping windows we derive—that the standard deviation of ${\rho }_{\mathrm{DCCA}}(T,n)$ tends with increasing $T$ to $1/T$. Using ${\rho }_{\mathrm{DCCA}}(T,n)$ we show that the Chinese financial market's tendency to follow the U.S. market is extremely weak. We also propose an additional statistical test that can be used to quantify the existence of cross-correlations between two power-law correlated time series.

Spatial segregation in the wall normal direction is investigated in suspensions containing a binary mixture of neo-Hookean capsules subjected to pressure driven flow in a planar slit. The two components of the binary mixture have unequal membrane rigidities. The problem is studied numerically using an accelerated implementation of the boundary integral method. The effect of a variety of parameters was investigated, including the capillary number, rigidity ratio between the two species, volume fraction, confinement ratio, and number fraction of the more floppy particle $X_f$ in the mixture. It was observed that in suspensions of pure species, the mean wall normal positions of the stiff and the floppy particles are comparable. In mixtures, however, the stiff particles were found to be increasingly displaced toward the walls with increasing $X_f$, while the floppy particles were found to increasingly accumulate near the centerline with decreasing $X_f$. This segregation behavior was universally observed independent of the parameters. The origin of this segregation is traced to the effect of the number fraction $X_f$ on the localization of the stiff and the floppy particles in the near wall region—the probability of escape of a stiff particle from the near wall region to the interior is greatly reduced with increasing $X_f$, while the exact opposite trend is observed for a floppy particle with decreasing $X_f$. Simple model studies on heterogeneous pair collisions involving a stiff and a floppy particle mechanistically explain the contrasting effect of $X_f$ on the near wall localization of the two species. The key observation in these studies is that the stiff particle experiences much larger cross-stream displacement in heterogeneous collisions than the floppy particle. A unified mechanism incorporating the wall-induced migration of deformable particles away from the wall and the particle fluxes associated with heterogeneous and homogeneous pair collisions is presented.

This paper presents a unified theory of phoretic phenomena in single-component fluids. Simple formulas are given for the phoretic velocities of small inert force-free non-Brownian particles migrating through otherwise quiescent single-component gases and liquids and animated by a gradient in the fluid's temperature (thermophoresis), pressure (barophoresis), density (pycnophoresis), or any combination thereof. The ansatz builds upon a recent paper [Phys. Rev. E 84, 046309 (2011)] concerned with slip of the fluid's mass velocity at solid surfaces—that is, with phenomena arising from violations of the classical no-slip fluid-mechanical boundary condition. Experimental and other data are cited in support of the phoretic model developed herein.

We report on the spontaneous emergence of computation from adaptive synchronization of networked dynamical systems. The fundamentals are nonlinear elements, interacting in a directed graph via a coupling that adapts itself to the synchronization level between two input signals. These units can emulate different Boolean logics, and perform any computational task in a Turing sense, each specific operation being associated with a given network's motif. The resilience of the computation against noise is proven, and the general applicability is demonstrated with regard to periodic and chaotic oscillators, and excitable systems mimicking neural dynamics.

Large deviation theory has emerged as the natural language with which to study transitions between dynamical phases, such as the glass transition. Here we use this approach to show that the entrainment of an oscillator to an external driving force can be described as a phase transition between two regions in a joint space-time representation. Specifically, we numerically obtain exact solutions of the large deviation function for a discrete, finite model of an oscillator under a periodically varying external force. We find that the first derivative of the expectation value of the current diverges in the limit of large system size. For weak forcing, perturbation theory allows us to relate the observed frequency of the oscillator to the spectrum of eigenvalues for the unforced system. We find that in the entrainment region where the oscillator exhibits the frequency of the driving force, there is a strong coupling between the ground state and excited states.

In order to identify the ingredients of thermal rectification, we analytically investigate the heat flow in the asymmetric classical and quantum self-consistent harmonic chains of oscillators. We confirm the absence of rectification in the classical version of the model, and, for the quantum analog, we show that the combination of a local heat flow proportional to the temperature gradient and a local thermal conductivity dependent on parameters asymmetrically distributed in the chain and on the local temperature lead to thermal rectification. Some of these ingredients are provided by the quantum nature of the specific model analyzed here, but they are not restricted to quantum phenomena and can also appear in anharmonic classical models. The comprehension of such mechanism is important for the advance of phononics, since thermal rectifiers are the basic components of several devices proposed to control the heat flow.

We report a detailed study, using state-of-the-art simulation and theoretical methods, of the effective (depletion) potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres, the size disparity being measured by the ratio of diameters $q\equiv {\sigma }_s/{\sigma }_b$. Small particles are treated grand canonically, their influence being parameterized in terms of their packing fraction in the reservoir ${\eta }_s^r$. Two Monte Carlo simulation schemes—the geometrical cluster algorithm, and staged particle insertion—are deployed to obtain accurate depletion potentials for a number of combinations of $q⩽0.1$ and ${\eta }_s^r$. After applying corrections for simulation finite-size effects, the depletion potentials are compared with the prediction of new density functional theory (DFT) calculations based on the insertion trick using the Rosenfeld functional and several subsequent modifications. While agreement between the DFT and simulation is generally good, significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods, namely, ${\eta }_s^r=0.35$. These discrepancies are, however, small compared to those between simulation and the much poorer predictions of the Derjaguin approximation at this ${\eta }_s^r$. The recently proposed morphometric approximation performs better than Derjaguin but is somewhat poorer than DFT for the size ratios and small-sphere packing fractions that we consider. The effective potentials from simulation, DFT, and the morphometric approximation were used to compute the second virial coefficient $B_2$ as a function of ${\eta }_s^r$. Comparison of the results enables an assessment of the extent to which DFT can be expected to correctly predict the propensity toward fluid-fluid phase separation in additive binary hard-sphere mixtures with $q⩽0.1$. In all, the new simulation results provide a fully quantitative benchmark for assessing the relative accuracy of theoretical approaches for calculating depletion potentials in highly size-asymmetric mixtures.

The Boltzmann equation subject to a general boundary condition is expanded in a power series with respect to a thermodynamic force disturbing a gaseous system. Recurrence relations between the terms of the expansion are obtained using the main properties of the collision integral and of the gas-surface interaction kernel. The reciprocal relation for nonlinear irreversible phenomena, i.e., a relation between the terms of different orders, is obtained. The relations can be used to estimate the range of applicability of linearized solutions and to predict nonlinear phenomena in gaseous systems.

The effect of the boundary friction coefficient on the rheological properties of the electrorheological (ER) fluids in quasistatic and dynamic states is investigated by computer simulation. The relation between the shear stress and the boundary friction coefficient in quasistatic and dynamic states is discussed qualitatively and quantitatively, and the trend matches the previously reported experimental results well. The flow curves of ER fluids, under different friction coefficients, are calculated, and it is found that the friction coefficient affects the flow curves. In two dimensions, the transitions in structure corresponding to the shear stress variations are presented to understand the mechanism of ER fluids.

We carry out Monte Carlo simulations and study the dependence of the behaviors of steps on impurities on a vicinal face. We assume that the impurities are immobile and the lifetime of them is much longer than that of adatoms. During growth, the impurities in front of a step prevent the step from advancing. If a wide terrace appears due to the fluctuations of step positions, the number of impurities on the terrace is more than other terraces. The step at the upper side of the wide terrace is slower than other steps, so that an equidistant train of steps becomes unstable. In our Monte Carlo simulations, with steps gathering and separating repeatedly, the bunches of steps are formed on the unstable surface.

The nonlinear dynamics of a nonisothermal thin liquid film on a horizontal cylindrical surface subjected to axial harmonic vibration is investigated in this paper. It is found that the capillary instability of an axisymmetric film on a still cylinder can be saturated via the Marangoni effect by heating the film at the gas side, similar to the saturation of the Rayleigh-Taylor instability in the planar case. If the capillary instability is not saturated by the Marangoni effect, the combined capillary-Marangoni instability can be saturated by the harmonic axial forcing provided that the forcing amplitude exceeds a certain critical value depending on the rest of parameters. The critical amplitude is demonstrated to increase with the Marangoni number when other parameters are fixed. The critical forcing amplitude at a given forcing frequency is shown to be well approximated by a piecewise linear function of the Marangoni number.