The nonlinear optical coupler with a negative-index metamaterial (NIM) channel is different from a conventional one, mainly in that the former has an effective feedback mechanism due to the opposite directionality of the phase velocities in the two channels. In this paper, we study modulation instability (MI) in this new kind of couplers, trying to identify the different MI properties from those in conventional couplers. It is found that MI in the nonlinear optical coupler with a NIM channel is significantly influenced by the ratio of the forward- to backward-propagating wave’s power and the nonlinear parameters. And the threshold condition for the ratio and input power can exist only in the normal dispersion regime where the ratio is positive. In addition, it is shown that MI occurs only for finite values of input power when the NIM channel is self-defocusing nonlinear material and another channel is self-focusing nonlinear material in the anomalous dispersion regime. Further, increasing input power may suppress the MI, quite different from the MI in the conventional couplers. For the conventional one, the increase of input power generally promotes the occurrence of MI. These findings suggest that the controllability of NIMs provides more ways to manipulate MI and soliton in couplers with NIM channels.

In the present study we propose a lattice Boltzmann equation (LBE) model derived from density gradient expansions of the discrete BBGKY evolution equations. The model is based on the mechanical approach of the gradient theory of interfaces. The basic input is the radial distribution function, which is related exclusively to the molecular interaction potential, rather than semiempirical equations of state used in previous LBE models. This function can be provided from independent molecular simulations or from approximate theories. Evidently the accuracy of the interaction potential, and thus the radial distribution function, reflects on the accuracy of the thermodynamic properties and consistency of the derived LBE model. We have applied the proposed model to obtain equilibrium bulk and interfacial properties of a Lennard-Jones fluid at different temperatures, $T$, close to critical, $T_c$. The results demonstrate that the LBE model is in excellent agreement with gradient theory as well as with independent literature results based on different molecular simulation approaches. Hence the proposed LBE model can recover accurately bulk and interfacial thermodynamics for a Lennard Jones fluid at $T/T_c>0.9$.

We present a time-saving simulator within the framework of the density functional theory to calculate the transport properties of electrons through nanostructures suspended between semi-infinite electrodes. By introducing the Fourier transform and preconditioning conjugate-gradient algorithms into the simulator, a highly efficient performance can be achieved in determining scattering wave functions and electron-transport properties of nanostructures suspended between semi-infinite jellium electrodes. To demonstrate the performance of the present algorithms, we study the conductance of metallic nanowires and the origin of the oscillatory behavior in the conductance of an Ir nanowire. It is confirmed that the $s\text{−}{d}_{z^2}$ channel of the Ir nanowire exhibits the transmission oscillation with a period of two-atom length, which is also dominant in the experimentally obtained conductance trace.

The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by analytic constructions, the importance of an efficient numerical method for conducting de novo (from-scratch) searches for dense packings becomes crucial. In this paper, we use the divide and concur framework to develop a general search method for the solution of periodic constraint problems, and we apply it to the discovery of dense periodic packings. An important feature of the method is the integration of the unit-cell parameters with the other packing variables in the definition of the configuration space. The method we present led to previously reported improvements in the densest-known tetrahedron packing. Here, we use the method to reproduce the densest-known lattice sphere packings and the best-known lattice kissing arrangements in up to 14 and 11 dimensions, respectively, providing numerical evidence for their optimality. For nonspherical particles, we report a dense packing of regular four-dimensional simplices with density $\varphi =128/219\approx 0.5845$ and with a similar structure to the densest-known tetrahedron packing.

The wave-number $k$ dependent current-correlation function is considered for a harmonic oscillator model. An explicit analytic expression for the Laplace transformed correlation function is derived. It is compared with numerical solutions and results obtained by the recurrence relation method. Several limiting cases such as the long-wavelength limit $k\to 0$ and the deep inelastic limit $k\to \infty$ are discussed in detail. In particular, we show that the deep inelastic limit allows for an explicit summation of the continued fraction. An approximation scheme for the recurrants at intermediate values of $k$ is also considered.

We show here for the one-dimensional spin-1/2 axial-next-to-nearest-neighbor Ising model in an external magnetic field that the linear density of Yang-Lee zeros may diverge with critical exponent $\sigma =-2/3$ at the Yang-Lee edge singularity. The necessary condition for this unusual behavior is the triple degeneracy of the transfer-matrix eigenvalues. If this condition is absent we have the usual value $\sigma =-1/2$. Analogous results have been found in the literature in the spin-1 Blume-Emery-Griffths model and in the three-state Potts model in a magnetic field with two complex components. Our results support the universality of $\sigma =-2/3$ which might be a one-dimensional footprint of a tricritical version of the Yang-Lee edge singularity possibly present also in higher-dimensional spin models.

Efficiency at maximum power is studied for two simple engines (three- and five-state systems). This quantity is found to be sensitive to the variable with respect to which the maximization is implemented. It can be wildly different from the well-known Curzon-Ahlborn bound (one minus the square root of the temperature ratio), or can be even closer than previously realized. It is shown that when the power is optimized with respect to a maximum number of variables the Curzon-Ahlborn bound is a lower bound, accurate at high temperatures, but a rather poor estimate when the cold reservoir temperature approaches zero (at which point the Carnot limit is achieved).

Calcium is a crucial component in a plethora of cellular processes involved in cell birth, life, and death. Intercellular calcium waves that can spread through multiple cells provide one form of cellular communication mechanism between various parts of cell tissues. Here we introduce a simple, yet biophysically realistic model for the propagation of intercellular calcium waves based on the fire-diffuse-fire type model for calcium dynamics. Calcium release sites are considered to be discretely distributed along individual linear cells that are connected by gap junctions and a solution of this model can be found in terms of the Green’s function for this system. We develop the “sum-over-trips” formalism that takes into account the boundary conditions at gap junctions providing a generalization of the original sum-over-trips approach for constructing the response function for branched neural dendrites. We obtain the exact solution of the Green’s function in the Laplace (frequency) domain for an infinite array of cells and show that this Green’s function can be well approximated by its truncated version. This allows us to obtain an analytical traveling wave solution for an intercellular calcium wave and analyze the speed of solitary wave propagation as a function of physiologically important system parameters. Periodic and irregular traveling waves can be also sustained by the proposed model.

Recent advances in high-frequency financial trading have made light propagation delays between geographically separated exchanges relevant. Here we show that there exist optimal locations from which to coordinate the statistical arbitrage of pairs of spacelike separated securities, and calculate a representative map of such locations on Earth. Furthermore, trading local securities along chains of such intermediate locations results in a novel econophysical effect, in which the relativistic propagation of tradable information is effectively slowed or stopped by arbitrage.

We present a mechanism to avoid congestion in complex networks based on a local knowledge of traffic conditions and the ability of routers to self-coordinate their dynamical behavior. In particular, routers make use of local information about traffic conditions to either reject or accept information packets from their neighbors. We show that when nodes are only aware of their own congestion state they self-organize into a hierarchical configuration that delays remarkably the onset of congestion although leading to a sharp first-order-like congestion transition. We also consider the case when nodes are aware of the congestion state of their neighbors. In this case, we show that empathy between nodes is strongly beneficial to the overall performance of the system and it is possible to achieve larger values for the critical load together with a smooth, second-order-like, transition. Finally, we show how local empathy minimize the impact of congestion as much as global minimization. Therefore, here we present an outstanding example of how local dynamical rules can optimize the system’s functioning up to the levels reached using global knowledge.

We introduce a general framework, applicable to a broad class of random walks on networks, that quantifies the response of the mean first-passage time to a target node to a local perturbation of the network, both in the context of attacks (damaged link) or strategies of transport enhancement (added link). This approach enables to determine explicitly the dependence of this response on geometric parameters (such as the network size and the localization of the perturbation) and on the intensity of the perturbation. In particular, it is showed that the relative variation of the mean first-passage time is independent of the network size, and remains significant in the large size limit. Furthermore, in the case of noncompact exploration of the network, it is found that a targeted perturbation keeps a substantial impact on transport properties for any localization of the damaged link.

Experimental results for passive tracer dispersion in the turbulent surface layer under stable conditions are presented. In this case, the dispersion of tracer particles is determined by the interplay of three mechanisms: relative dispersion (celebrated Richardson’s mechanism), shear dispersion (particle separation due to variation of the mean velocity field) and specific surface-layer dispersion (induced by the gradient of the energy dissipation rate in the turbulent surface layer). The latter mechanism results in the rather slow (ballistic) law for the mean squared particle separation. Based on a simplified Langevin equation for particle separation we found that the ballistic regime always dominates at large times. This conclusion is supported by our extensive atmospheric observations. Exit-time statistics are derived from the experimental data set and show a reasonable match with the simple dimensional asymptotes for different mechanisms of tracer dispersion, as well as predictions of the multifractal model and experimental data from other sources.

Soft x-ray lasers pumped in the grazing incidence geometry show strongly reduced energetic needs but hardly changed conversion efficiency between the pump energy and the output short-wavelength radiation. Numerical analysis presented in the paper concerns with performance of a Ni-like Ag soft-x-ray laser pumped by a triple-pulse structure in the grazing incidence geometry as a function of the puming conditions. It was found that a weak precursor preceding the main preforming and heating pulses by a few nanoseconds is crucial for the energy deposition. Its presence enables in different arrangements a reasonable reduction in the pump energy and relaxation of the steep density gradients as well as a control over partition of the deposited energy. As a consequence, it was concluded that a well energetically balanced three- or multipulse composition seems to be a reasonable way to achieve performance improvement.

We investigate the long-time behavior of a wave packet initially localized at a single site $n_0$ in translationally invariant harmonic and anharmonic chains with random interactions. In the harmonic case, the energy profile $\overline{⟨e_n\left(t\right)⟩}$ averaged on time and disorder decays for large $\left|n-n_0\right|$ as a power law $\overline{⟨e_n\left(t\right)⟩}\approx C{\left|n-n_0\right|}^{-\eta }$, where $\eta =5/2$ and 3/2 for initial displacement and momentum excitations, respectively. The prefactor $C$ depends on the probability distribution of the harmonic coupling constants and diverges in the limit of weak disorder. As a consequence, the moments $⟨m_{\nu }\left(t\right)⟩$ of the energy distribution averaged with respect to disorder diverge in time as $t^{\beta \left(\nu \right)}$ for $\nu \ge 2$, where $\beta =\nu +1-\eta$ for $\nu >\eta -1$. Molecular-dynamics simulations yield good agreement with these theoretical predictions. Therefore, in this system, the second moment of the wave packet diverges as a function of time despite the wave packet is not spreading. Thus, this only criterion, often considered earlier as proving the spreading of a wave packet, cannot be considered as sufficient in any model. The anharmonic case is investigated numerically. It is found for intermediate disorder that the tail of the energy profile becomes very close to those of the harmonic case. For weak and strong disorders, our results suggest that the crossover to the harmonic behavior occurs at much larger $\left|n-n_0\right|$ and larger time.

We study the transmission of a tightly focused beam through a thick slab of three-dimensional disordered medium in the Anderson localized regime. We show that the transverse profile of the transmitted beam exhibits clear signatures of Anderson localization and that its mean square width provides a direct measure of the localization length. For a short incident pulse, the width is independent of absorption.

We analyze, experimentally and numerically, the steady states, obtained by tapping, of a two-dimensional granular layer. Contrary to the usual assumption, we show that the reversible (steady state branch) of the density-acceleration curve is nonmonotonous. Accordingly, steady states with the same mean volume can be reached by tapping the system with very different intensities. Simulations of dissipative frictional disks show that equal volume steady states have different values of the force moment tensor. Additionally, we find that steady states of equal stress can be obtained by changing the duration of the taps; however, these states present distinct mean volumes. These results confirm previous speculations that the volume and the force moment tensor are both needed to describe univocally equilibrium states in static granular assemblies.

Recently, Murali et al. [Phys. Rev. Lett. 102, 104101 (2009)] showed that some noisy nonlinear dynamics could be exploited to design nonlinear logic gate based on stochastic resonance (SR). In the paper, inspired by the Murali et al.’s articles, we consider the logical stochastic resonance (LSR) phenomenon in a bistable system by cycling various combinations of two logic inputs, in the presence of exponentially correlated noise. The effect of the colored noise on the LSR is evaluated by the success probability of obtained desired logic output. The two major results are presented. First, it shows that the LSR effect can be obtained by changing noise intensity. The logic output is obtained most reliably at an intermediate noise band. There is still a plateau on performance curve of the success probability versus noise intensity. As correlation time increases, the optimal noise band shifts to higher level and peak performance is degraded from 100% accuracy. Due to the influence of the colored noise, the plateau is a bit low and not completely flat. On the other hand, the performance measure can evolve nonmonotonically as correlation time increases, and a SR-like effect is obtained as a result of correlation time. It shows that actually some finite correlation time is better than delta correlation time at certain noise intensities. The study might provide an example where LSR phenomenon can exist robustly in the presence of colored noise.

The aging dynamics of poly(2-chlorostyrene) (P2CS) ultrathin films with thicknesses less than 10 nm were investigated using dielectric relaxation spectroscopy. The imaginary part of the dielectric susceptibility ${ϵ}^{″}$ for P2CS ultrathin films with a thickness of 3.7 nm increased with an increase in isothermal aging time, while this was not the case for P2CS thin films thicker than 9.0 nm. This anomalous increase in ${ϵ}^{″}$ for the ultrathin films is strongly correlated with the presence of a mobile liquidlike layer within the thin films.

Recent live observations of motors in long-range microtubule (MT) dependent transport in the fungus Ustilago maydis have reported bidirectional motion of dynein and an accumulation of the motors at the polymerization-active (the plus-end) of the microtubule. Quantitative data derived from in vivo observation of dynein has enabled us to develop an accurate, quantitatively-valid asymmetric simple exclusion process (ASEP) model that describes the coordinated motion of anterograde and retrograde motors sharing a single oriented microtubule. We give approximate expressions for the size and distribution of the accumulation, and discuss queueing properties for motors entering this accumulation. We show for this ASEP model, that the mean accumulation can be modeled as an $M/M/\infty$ queue that is Poisson distributed with mean $F_{arr}/p_d$, where $F_{arr}$ is the flux of motors that arrives at the tip and $p_d$ is the rate at which individual motors change direction from anterograde to retrograde motion. Deviations from this can in principle be used to gain information about other processes at work in the accumulation. Furthermore, our work is a significant step toward a mathematical description of the complex interactions of motors in cellular long-range transport of organelles.

We study the drift of spiral waves in a simple model of heterogeneous excitable medium, having gradients in the distribution of ion-channel expression or cellular coupling. We report the anomalous drift of spiral waves toward regions having shorter period or stronger coupling, in reaction-diffusion models of excitable media. Such anomalous drift can promote the onset of complex spatiotemporal patterns, e.g., those responsible for life-threatening arrhythmias in the heart.