Self-assembly of minimum-energy configurations of a two-dimensional system consisting of charged particles confined in a quadratic trap and interacting through competing repulsive and attractive interparticle forces is studied by means of molecular dynamics simulation. It is shown that complex configurations, including concentric shells separated by bandlike voids, connected shells with multiple regularly arranged voids, as well as small clusters of particles organized into crystal- or liquidlike structures, can exist. With increase of the particle number, a larger variety of structural patterns becomes possible. The results here are useful for a better understanding of pattern formation in two-dimensional systems, as well as in the design of specific structures for technological applications.

We propose a method for computing the temperature dependence of the heat capacity in complex molecular systems. The proposed scheme is based on the use of the Langevin equation with low-frequency color noise. We obtain the temperature dependence of the correlation time of random noises, which enables us to model the partial thermalization of high-frequency vibrations. This purely quantum effect is responsible for the decreasing behavior of the specific heat $c\left(T\right)$ in the low-temperature regime. By applying the method to carbon nanotubes and polyethylene molecules, we show that the consideration of the color noise in the Langevin equation allows us to reproduce the temperature evolution of the specific heat with a good accuracy.

Contrary to the main conclusion of Embs et al. [Phys. Rev. E 73, 036302 (2006)], we demonstrate with amplitude correction factors that the predictions of the magnetization model proposed by Shliomis [Sov. Phys. JETP 34, 1291 (1972)] are well consistent with the experimental data for weakly nonequilibrium states and that the model proposed by Shliomis [Phys. Rev. E 64, 063501 (2001)] is valid even far from equilibrium. A model on the basis of the weak-field magnetization equation of Müller and Liu [Phys. Res. E 64, 061405 (2001)] with a “structure” modification is also shown to reproduce a wide range of experimental data. Our statement is confirmed by a more exact insight into the hydrodynamic problem of rotating ferrofluids.

In the preceding comment the authors present a theoretical analysis of experimental transverse magnetization data of a ferrofluid in a cylinder that is rotating in a magnetic field [Embs et al., Phys. Rev. E 73, 036302 (2006)]. This analysis of Weng and Chen is based on theoretically unfounded assumptions that imply unphysical properties of the velocity and vorticity fields of the rotating fluid, leading to wrong predictions for the magnetization. We show where the errors occurred. We uphold our main conclusion that the investigated single-relaxation-time models do not reproduce well the experimental results.

We present a detailed numerical study of dynamical heterogeneities in the aging regime of a simple binary Lennard-Jones glass former. For most waiting times $t_w$ and final times $t$, both the dynamical susceptibility ${\chi }_4(t,t_w)$ and the dynamical correlation length ${\xi }_4(t,t_w)$ can be approximated as products of two factors: (i) a waiting-time-dependent scale that grows as a power of $t_w$, and (ii) a scaling function dependent on $t,t_w$ only through the value of the intermediate scattering function $C(t,t_w)$. We find that ${\chi }_4(t,t_w)$ is determined only in part by the correlation volume.

The ferromagnetic-paramagnetic phase transition of the two-dimensional frustrated Ising model on a hyperbolic lattice is investigated by use of the corner transfer matrix renormalization group method. The model contains a ferromagnetic nearest-neighbor interaction $J_1$ and a competing antiferromagnetic interaction $J_2$. A mean-field-like second-order phase transition is observed when the ratio $\kappa =J_2∕J_1$ is less than 0.203. In the region $0.203<\kappa <1∕4$, the spontaneous magnetization is discontinuous at the transition temperature. Such tricritical behavior suggests that the phase transitions on hyperbolic lattices need not always be mean-field-like.

We measured the capillary wave spectra on the surface of ionic liquids using dynamic light scattering techniques. Empirical dispersion relations deduced from the time domain analysis clearly reveal the transition from oscillating to overdamped behavior with changing temperature and the wave vector. In particular, not only slow but also fast modes were observed in the overdamped regime. The empirical dispersion relations coincide with the theoretical dispersion relations deduced from the linearized Navier-Stokes equation when experimentally determined density, viscosity, and surface tension are assigned to the latter.

The height-height correlation function for a fluctuating interface between two coexisting bulk phases is derived by means of general equilibrium properties of the corresponding density-density correlation function. A wavelength-dependent surface tension $\gamma \left(\mathbf{q}\right)$ can be defined and expressed in terms of the direct correlation function $c(\mathbf{r},{\mathbf{r}}^{\prime })$, the equilibrium density profile ${\rho }_0\left(\mathbf{r}\right)$, and an operator which relates density to surface configurations. Neither the concept of an effective interface Hamiltonian nor the difference in pressure is needed to determine the general structure of the height-height correlations or $\gamma \left(\mathbf{q}\right)$, respectively. This result generalizes the Mecke-Dietrich surface tension ${\gamma }_{\mathsf{MD}}\left(q\right)$ [Phys. Rev. E 59, 6766 (1999)] and modifies recently published criticism concerning ${\gamma }_{\mathsf{MD}}\left(q\right)$ [Tarazona, Checa, and Chacón, Phys. Rev. Lett. 99, 196101 (2007)].

A position-dependent stochastic diffusion model of gating in ion channels is developed by considering the spatial variation of the diffusion coefficient between the closed and open states. It is assumed that a sensor which regulates the opening of the ion channel experiences Brownian motion in a closed region $R_c$ and a transition region $R_m$, where the dynamics is described by probability densities $p_c(x,t)$ and $p_m(x,t)$ which satisfy interacting Fokker-Planck equations with diffusion coefficient $D_c\left(x\right)=D_c\exp \left({\gamma }_{c}x\right)$ and $D_m\left(x\right)=D_m\exp (-{\gamma }_{m}x)$. The analytical solution of the coupled equations may be approximated by the lowest frequency relaxation, a short time after the application of a depolarizing voltage clamp, when $D_m⪡D_c$ or the diffusion parameter ${\gamma }_m$ is sufficiently large. Thus, an empirical rate equation that describes gating transitions may be derived from a stochastic diffusion model if there is a large diffusion (or potential) barrier between open and closed states.

Although most sodium ion channels clustered in nodes of Ranvier provide the physiological basis for saltatory conduction, sodium ion channels cannot be excluded from internodal regions completely. The density of internodal sodium ion channels is of the order of $10∕\mu {\mathrm{m}}^2$. The function of internodal sodium ion channels has been neglected for a long time; however, experimental and theoretical results show that internodal sodium ion channels play an important role in action potential propagation. In this paper, based on the compartment model, we investigate the function of internodal sodium ion channels. We find that internodal sodium ion channels can promote action potential propagation, enlarge the maximal internodal distance guaranteeing stable action potential propagation, and increase the propagation speed of action potentials. In this paper, we find an optimal conductance of internodal sodium ion channels $(4–5\mathrm{mS}∕{\mathrm{cm}}^2)$, which accords with the active internodal sodium ion conductance in a real myelinated axon. With the optimal conductance, the average sodium ion channel conductance of the axon is minimal, and the metabolic energy consumption due to ion channels is also minimal.

The theory of linear mode conversion near evanescent layers is generalized for non-one-dimensionally inhomogeneous gyrotropic media. Effects are found that cannot be described within the standard one-dimensional paradigm of wave tunneling through the evanescent region when the mode coupling region assumes essentially two-dimensional topology.

The duration of transient fronts in a bistable reaction-diffusion equation in a bounded domain is considered. The speed of the front decreases exponentially with the length of the domain, and the duration increases exponentially with the domain length. The duration of the fronts generated from random initial conditions is distributed in a power-law form up to a cutoff time. The cutoff time then increases exponentially with the domain length so that the power-law distribution dominates for large domains. Further, external noise of intermediate strength increases the mean duration of the fronts. The increases in the duration with the domain length become almost linear, however, in the presence of asymmetry in the cubic nonlinearity.

It is demonstrated that a standard coupled-mode theory can successfully describe weakly nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this theory are in reasonable agreement with numerical simulations of the exact equations of motion for ideal planar potential free-surface flows, even for strongly nonlinear waves. In numerical experiments, self-localized groups of nearly standing water waves can exist up to hundreds of wave periods. Generalizations of the model to the three-dimensional case are also derived.

We propose an optical transformation to bend electromagnetic waves by designing proper inhomogeneous and anisotropic materials, which are hereinafter referred to as metamaterials (MTMs). When the waveguide bends are filled with MTMs, the incident waves will pass through the bends without any reflections (for full-parameter MTMs) or with very small reflections (for simplified-parameter MTMs). When MTMs are placed in air, the incident waves will be bent to any designed directions. We also discuss the wave bending using layered homogeneous uniaxial MTMs, which can be easily realized using artificial structures.

Optimal energy amplification via autoresonance in dissipative systems subjected to separatrix crossings is discussed through the universal model of a damped driven pendulum. Analytical expressions of the autoresonance responses and forces as well as the associated adiabatic invariants for the phase space regions separated by the underlying separatrix are derived from the energy-based theory of autoresonance. Additionally, applications to a single Josephson junction, topological solitons in Frenkel-Kontorova chains, as well as to the three-wave problem in dissipative media are discussed in detail from the autoresonance analysis.

For noisy self-sustained oscillators, both reliability, the stability of a response to a noisy driving, and coherence, understood in the sense of constancy of oscillation frequency, are important characteristics. Although both characteristics and techniques for controlling them have received great attention from researchers, owing to their importance for neurons, lasers, clocks, electric generators, etc., these characteristics were previously considered separately. In this paper, a strong quantitative relation between coherence and reliability is revealed for a limit cycle oscillator subject to a weak noisy driving and a linear delayed feedback, a convection control tool. The analytical findings are verified and enriched with a numerical simulation for the Van der Pol–Duffing oscillator.

It is found that a micrometer-sized droplet in an aqueous solution of binary polymers [water/polyethylene-glycol (PEG)/dextran] disappears upon irradiation with a focused yttrium-aluminum-garnet laser. The interface of the dextran-rich droplet broadens and disappears, and it reappears upon turning the laser off, whereas the PEG-rich droplet shrinks and disappears. These phenomena are discussed in terms of the free energy by considering the laser-induced dielectric potential.

We study the persistent random walk of photons on a one-dimensional lattice of random asymmetric transmittances. Each site is characterized by its intensity transmittance $t$ $(t^{\prime }\ne t)$ for photons moving to the right (left) direction. Transmittances at different sites are assumed independent, distributed according to a given probability density $\mathcal{F}(t,t^{\prime })$. We use the effective medium approximation and identify two classes of $\mathcal{F}(t,t^{\prime })$ which lead to the normal diffusion of photons. Monte Carlo simulations confirm our predictions. We mention that the metamaterial introduced by Fedetov et al. [Nano Lett. 7, 1996 (2007)] can be used to realize a lattice of random asymmetric transmittances.

We study zero-temperature quantum spin chains, which are characterized by a nonvanishing current. For the $XX$ model starting from the initial state ∣⋯↑↑↑↓↓↓⋯⟩ we derive an exact expression for the variance of the total spin current. We show that asymptotically the variance exhibits an anomalously slow logarithmic growth; we also extract the subleading constant term. We then argue that the logarithmic growth remains valid for the $XXZ$ model in the critical region.

Multiparticle dynamics in one-dimensional asymmetric exclusion processes with disorder is investigated theoretically by computational and analytical methods. It is argued that the general phase diagram consists of three nonequilibrium phases that are determined by the dynamic behavior at the entrance, at the exit and at the slowest defect bond in the bulk of the system. Specifically, we consider dynamics of asymmetric exclusion process with two identical defect bonds as a function of distance between them. Two approximate theoretical methods that treat the system as a sequence of segments with exact description of dynamics inside the segments and neglect correlations between them, are presented. In addition, a numerical iterative procedure for calculating dynamic properties of asymmetric exclusion systems is developed. Our theoretical predictions are compared with extensive Monte Carlo computer simulations. It is shown that correlations play an important role in the particle dynamics. When two defect bonds are far away from each other the strongest correlations are found at these bonds. However, bringing defect bonds closer leads to the shift of correlations to the region between them. Our analysis indicates that it is possible to develop a successful theoretical description of asymmetric exclusion processes with disorder by properly taking into account the correlations.