In this reply to the Comment by Li-Shi Luo, we discuss the results of the lattice Bhatnagar-Gross-Krook (LBGK) model for high-Knudsen-number (Kn) flow and heat transfer, in the range of $\mathrm{Kn}⩽1$. We present various studies employing the LBGK model for high-Kn flow and heat transfer simulations. It is concluded that, with the use of the LBGK model in the thermal lattice Boltzmann method for $\mathrm{Kn}⩾0.8$, some approximations appear in the negative pressure deviation from the linear distribution along the channel. But for $\mathrm{Kn}<0.8$, the velocity and temperature profiles, compressibility effects, Knudsen layer capturing, and Knudsen paradox phenomenon can be predicted by the LBGK model. We also reject Li-Shi Luo’s claim about the nonconvergence of our numerical scheme by presenting a velocity profile across the channel corresponding to three different high-resolution meshes.

We obtain the quantum Langevin equation (QLE) of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a quantum heat bath through momentum variables. The bath is modeled as a collection of independent quantum harmonic oscillators. The QLE involves a random force which does not depend on the magnetic field, and a quantum-generalized classical Lorentz force. These features are also present in the QLE for the case of particle-bath coupling through coordinate variables. However, significant differences are also observed. For example, the mean force in the QLE is characterized by a memory function that depends explicitly on the magnetic field. The random force has a modified form with correlation and commutator different from those in the case of coordinate-coordinate coupling. Moreover, the coupling constants, in addition to appearing in the random force and in the mean force, also renormalize the inertial term and the harmonic potential term in the QLE.

We investigate the three-dimensional lattice $XY$ model with nearest neighbor interaction. The vector order parameter of this system lies on the vertices of a cubic lattice, which is embedded in a system with a film geometry. The orientations of the vectors are fixed at the two opposite sides of the film. The angle between the vectors at the two boundaries is $\alpha$ where $0\le \alpha \le \pi$. We make use of the mean field approximation to study the mean length and orientation of the vector order parameter throughout the film—and the Casimir force it generates—as a function of the temperature $T$, the angle $\alpha$, and the thickness $L$ of the system. Among the results of that calculation are a Casimir force that depends in a continuous way on both the parameter $\alpha$ and the temperature and that can be attractive or repulsive. In particular, by varying $\alpha$ and/or $T$ one controls both the sign and the magnitude of the Casimir force in a reversible way. Furthermore, for the case $\alpha =\pi$, we discover an additional phase transition occurring only in the finite system associated with the variation of the orientations of the vectors.

Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E 83, 011201 (2011)]. It is demonstrated here that the RFA technique yields the exact solution of the Percus-Yevick (PY) closure to the Ornstein-Zernike (OZ) equation for binary mixtures at arbitrary odd dimensions. The proof relies mainly on the Fourier transforms ${\widehat{c}}_{ij}\left(k\right)$ of the direct correlation functions defined by the OZ relation. From the analysis of the poles of ${\widehat{c}}_{ij}\left(k\right)$ we show that the direct correlation functions evaluated by the RFA method vanish outside the hard core, as required by the PY theory.

Using a quantitative phase-field model, a systematic investigation of cellular growth in directional solidification is carried out with emphasis on the selection of cellular tip undercooling, tip radius, and cellular spacing. Previous analytical models of cellular growth are evaluated according to the phase-field simulation results. The results show that cellular tip undercooling and tip radius not only depend on the pulling velocity and thermal gradient, but also depend on the cellular interaction related to the cellular spacing. The cellular interaction results in a finite stable range of cellular spacing. The lower limit is determined by the submerging mechanism while the upper limit comes from the tip splitting instability corresponding to the absence of the cellular growth solution, both of which can be obtained from phase-field simulation. Further discussions on the phase-field results also present an analytical method to predict the lower limit. Phase-field simulations on cell elimination between cells with equal spacing validate the finite range of cellular spacing and give deep insight into the cellular doublon and oscillatory instability between cell elimination and tip splitting.

Monte Carlo simulations based on an integration scheme for free energy differences is used to compute critical Casimir forces for three-dimensional Ising films with various boundary fields. We study the scaling behavior of the critical Casimir force, including the scaling variable related to the boundary fields. Finite size corrections to scaling are taken into account. We pay special attention to that range of surface field strengths within which the force changes from repulsive to attractive upon increasing the temperature. Our data are compared with other results available in the literature.

The helical flexoelectro-optic effect shows interesting in-plane electro-optic switching behavior due to flexoelectric coupling with applied electric fields. Previous understanding of the behavior has been generally based on an analytic approach that makes certain assumptions about the uniformity of the helical structure and the induced tilt angle under field application. Here we remove these assumptions and develop a perturbative approximation to describe the structure in more detail. We also use a numerical method to investigate the behavior in regimes where the perturbative approach is inappropriate. The impact of variation in elastic constants and dielectric anisotropy is investigated. We find that dielectric behavior in particular can lead to substantial differences between the tilt angle obtained here and those obtained using previous analytic models.

The glass transition dynamics of stacked thin films of polystyrene and poly(2-chlorostyrene) were investigated using differential scanning calorimetry and dielectric relaxation spectroscopy. The glass transition temperature $T_g$ of as-stacked thin polystyrene films has a strong depression from that of the bulk samples. However, after annealing at high temperatures above $T_g$, the stacked thin films exhibit glass transition at a temperature almost equal to the $T_g$ of the bulk system. The $\alpha$-process dynamics of stacked thin films of poly(2-chlorostyrene) show a time evolution from single-thin-film-like dynamics to bulk-like dynamics during the isothermal annealing process. The relaxation rate of the $\alpha$ process becomes smaller with increase in the annealing time. The time scale for the evolution of the $\alpha$ dynamics during the annealing process is very long compared with that for the reptation dynamics. At the same time, the temperature dependence of the relaxation time for the $\alpha$ process changes from Arrhenius-like to Vogel-Fulcher-Tammann dependence with increase of the annealing time. The fragility index increases and the distribution of the $\alpha$-relaxation times becomes smaller with increase in the annealing time for isothermal annealing. The observed change in the $\alpha$ process is discussed with respect to the interfacial interaction between the thin layers of stacked thin polymer films.

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. Traditionally, Aldrovanda is considered as a miniature, aquatic Dionaea, an assumption which was already established by Charles Darwin. However, videos of snapping traps from both species suggest completely different closure mechanisms. Indeed, the well-described snapping mechanism in Dionaea comprises abrupt curvature inversion of the two trap lobes, while the closing movement in Aldrovanda involves deformation of the trap midrib but not of the lobes, which do not change curvature. In this paper, we present detailed mechanical models for these plants, which are based on the theory of thin solid membranes and explain this difference by showing that the fast snapping of Aldrovanda is due to kinematic amplification of the bending deformation of the midrib, while that of Dionaea unambiguously relies on the buckling instability that affects the two lobes.

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems. This synergy between structural properties (symmetries) and convergence properties (contraction) is illustrated in the contexts of network motifs arising, for example, in genetic networks, from invariance to environmental symmetries, and from imposing different patterns of synchrony in a network.

The packing fraction of geometric random packings of discretely sized particles is addressed in the present paper. In an earlier paper [Brouwers, Phys. Rev. E 74, 031309 (2006); Brouwers, Phys. Rev. E 74, 069901(E) (2006)], analytical solutions were presented for the packing fraction of polydisperse geometric packings for discretely sized particles with infinitely large size ratio and the packing of continuously sized particles. Here the packing of discretely sized particles with finite size ratio $u$ is analyzed and compared with empirical data concerning five ternary geometric random close packings of spheres with a size ratio of 2, yielding good agreement.

We study the daily trading volume volatility of 17 197 stocks in the US stock markets during the period 1989–2008 and analyze the time return intervals $\tau$ between volume volatilities above a given threshold $q$. For different thresholds $q$, the probability density function $P_q\left(\tau \right)$ scales with mean interval $\langle \tau \rangle$ as $P_q\left(\tau \right)={\langle \tau \rangle }^{-1}f(\tau /\langle \tau \rangle )$, and the tails of the scaling function can be well approximated by a power law $f\left(x\right)\sim x^{-\gamma }$. We also study the relation between the form of the distribution function $P_q\left(\tau \right)$ and several financial factors: stock lifetime, market capitalization, volume, and trading value. We find a systematic tendency of $P_q\left(\tau \right)$ associated with these factors, suggesting a multiscaling feature in the volume return intervals. We analyze the conditional probability $P_q\left(\tau \right|{\tau }_0)$ for $\tau$ following a certain interval ${\tau }_0$, and find that $P_q\left(\tau \right|{\tau }_0)$ depends on ${\tau }_0$ such that immediately following a short (long) return interval a second short (long) return interval tends to occur. We also find indications that there is a long-term correlation in the daily volume volatility. We compare our results to those found earlier for price volatility.

In this work, higher-order moving average polynomials are defined by straightforward generalization of the standard moving average. The self-similarity of the polynomials is analyzed for fractional Brownian series and quantified in terms of the Hurst exponent $H$ by using the detrending moving average method. We prove that the exponent $H$ of the fractional Brownian series and of the detrending moving average variance asymptotically agree for the first-order polynomial. Such asymptotic values are compared with the results obtained by the simulations. The higher-order polynomials correspond to trend estimates at shorter time scales as the degree of the polynomial increases. Importantly, the increase of polynomial degree does not require to change the moving average window. Thus trends at different time scales can be obtained on data sets with the same size. These polynomials could be interesting for those applications relying on trend estimates over different time horizons (financial markets) or on filtering at different frequencies (image analysis).

We investigate the interaction between reaction-diffusion systems coupled by diffusion. The photosensitive CDIMA (chorine dioxide–iodine–malonic acid) reaction allows us to study experimentally the mutual influence of two layers of Turing patterns coupled via a diffusive interaction. By illuminating each of the layers with different intensities of homogeneous external light, the chemical conditions in each layer can be shifted, allowing us to study the result of diffusive interaction between Turing patterns with different spatial configurations. Our experiments suggest a complex scenario for the interaction between different patterns, strongly dependent on the spatial characteristics of the interacting patterns. Numerical simulations are also reported in full agreement with experimental observations.

We develop a theory of collective phase description for globally coupled noisy excitable elements exhibiting macroscopic oscillations. Collective phase equations describing macroscopic rhythms of the system are derived from Langevin-type equations of globally coupled active rotators via a nonlinear Fokker-Planck equation. The theory is an extension of the conventional phase reduction method for ordinary limit cycles to limit-cycle solutions in infinite-dimensional dynamical systems, such as the time-periodic solutions to nonlinear Fokker-Planck equations representing macroscopic rhythms. We demonstrate that the type of the collective phase sensitivity function near the onset of collective oscillations crucially depends on the type of the bifurcation, namely, it is type I for the saddle-node bifurcation and type II for the Hopf bifurcation.

We introduce a general mechanism for amplitude death in coupled synchronizable dynamical systems. It is known that when two systems are coupled directly, they can synchronize under suitable conditions. When an indirect feedback coupling through an environment or an external system is introduced in them, it is found to induce a tendency for antisynchronization. We show that, for sufficient strengths, these two competing effects can lead to amplitude death. We provide a general stability analysis that gives the threshold values for onset of amplitude death. We study in detail the nature of the transition to death in several specific cases and find that the transitions can be of two types—continuous and discontinuous. By choosing a variety of dynamics, for example, periodic, chaotic, hyperchaotic, and time-delay systems, we illustrate that this mechanism is quite general and works for different types of direct coupling, such as diffusive, replacement, and synaptic couplings, and for different damped dynamics of the environment.

We examine the stability of liquids with spherical interfaces evaporating from funnels constructed of different materials. A linear stability analysis predicts stable evaporation for funnels constructed of insulating materials and introduces a stability parameter for funnels constructed of conducting materials. The stability parameter is free of fitting variables since we use the statistical rate theory expression for the evaporation flux. The theoretical predictions are found to be consistent with experimental observations for ${\text{H}}_2\text{O}$ evaporating from a funnel constructed of poly(methyl methacrylate) and for ${\text{H}}_2\text{O}$ and ${\text{D}}_2\text{O}$ evaporating from a funnel constructed of stainless steel.

A well-known no-energy-gain theorem states that an electron cannot gain energy when being overrun by a plane (transverse) laser pulse of finite length. The theorem is based on symmetries which are broken when radiation reaction (RR) is included. It is shown here that an electron, e.g., being initially at rest, will gain a positive velocity component in the laser propagation direction after being overrun by an intense laser pulse (of finite duration and with intensity of order $5\times {10}^{22}$ W/cm${}^2$ or larger). The velocity increment is due to RR effects. The latter are incorporated in the Landau-Lifshitz form. Both linear as well as circular polarization of the laser pulse are considered. It is demonstrated that the velocity gain is proportional to the pulse length and the square of the peak amplitude of the laser pulse. The results of numerical simulations are supported by analytical estimates.

Starting from a cluster variational method, and inspired by the correctness of the paramagnetic ansatz [at high temperatures in general, and at any temperature in the two-dimensional (2D) Edwards-Anderson (EA) model] we propose a message-passing algorithm—the dual algorithm—to estimate the marginal probabilities of spin glasses on finite-dimensional lattices. We use the EA models in 2D and 3D as benchmarks. The dual algorithm improves the Bethe approximation, and we show that in a wide range of temperatures (compared to the Bethe critical temperature) our algorithm compares very well with Monte Carlo simulations, with the double-loop algorithm, and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover, it is usually 100 times faster than other provably convergent methods, as the double-loop algorithm. In 2D and 3D the quality of the inference deteriorates only where the correlation length becomes very large, i.e., at low temperatures in 2D and close to the critical temperature in 3D.

The general problem of two-phase transport in phase-field models is analyzed: the flux of a conserved quantity is driven by the gradient of a potential through a medium that consists of domains of two distinct phases which are separated by diffuse interfaces. It is shown that the finite thickness of the interfaces induces two effects that are not present in the analogous sharp-interface problem: a surface excess current and a potential jump at the interfaces. It is shown that both effects can be eliminated simultaneously only if the coefficient of proportionality between flux and potential gradient (mobility) is allowed to become a tensor in the interfaces. This opens the possibility for precise and efficient simulations of transport problems with finite interface thickness.