We consider finite-size effects on heat transfer between thermal reservoirs mediated by a quantum system, where the number of modes in each reservoir is finite. Our approach is based on the generalized quantum Langevin equation and the thermal reservoirs are described as ensembles of oscillators within the Drude-Ullersma model. A general expression for the heat current between the thermal reservoirs in the long-time quasistatic regime, when an observation time is of the order of ${\Delta }^{-1}$ and $\Delta$ is the mode spacing constant of a thermal reservoir, is obtained. The resulting equations that govern the long-time relaxation for the mode temperatures and the average temperatures of the reservoirs are derived and approximate analytical solutions are found. The obtained time dependencies of the temperatures and the resulting heat current reveal peculiarities at $t=2\pi m/\Delta$ with non-negative integers $m$ and the heat current vanishes nonmonotonically when $t\to \infty$. The validity of Fourier's law for a chain of finite-size macroscopic subsystems is considered. As is shown, for characteristic times of the order of ${\Delta }^{-1}$ the temperatures of subsystems' modes deviate from each other and the validity of Fourier's law cannot be established. In a case when deviations of initial temperatures of the subsystems from their average value are small, $t\to \infty$ asymptotic values for the mode temperatures do not depend on a mode's number and are the same as if Fourier's law were valid for all times.

We address the problem of orientational order in frustrated interaction systems as a function of the relative range of the competing interactions. We study a spin model Hamiltonian with short-range ferromagnetic interaction competing with an antiferromagnetic component that decays as a power law of the distance between spins, $1/r^{\alpha }$. These systems may develop a nematic phase between the isotropic disordered and stripe phases. We evaluate the nematic order parameter using a self-consistent mean-field calculation. Our main result indicates that the nematic phase exists, at mean-field level, provided $0<\alpha <4$. We analytically compute the nematic critical temperature and show that it increases with the range of the interaction, reaching its maximum near $\alpha \sim 0.5$. We also compute a coarse-grained effective Hamiltonian for long wavelength fluctuations. For $0<\alpha <4$ the inverse susceptibility develops a set of continuous minima at wave vectors $|\vec{k}|=k_0\left(\alpha \right)$ which dictate the long-distance physics of the system. For $\alpha \to 4$, $k_0\to 0$, making the competition between interactions ineffective for greater values of $\alpha$.

The Monte Carlo simulation method in the grand canonical ensemble is used to study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles with negative nonadditivity and the weaker interaction between the pairs of unlike than between the pairs of like particles. We have determined the evolution of the phase diagram topology when the parameters describing the interaction between unlike particles vary. It has been found that such systems may exhibit reentrant miscibility in the liquid and the solid phases.

We study the statistical properties of the impedance matrix (related to the scattering matrix) describing the input-output properties of waves in cavities in which ray trajectories that are regular and chaotic coexist (i.e., “mixed” systems). The impedance can be written as a summation over eigenmodes where the eigenmodes can typically be classified as either regular or chaotic. By appropriate characterizations of regular and chaotic contributions, we obtain statistical predictions for the impedance. We then test these predictions by comparison with numerical calculations for a specific cavity shape, obtaining good agreement.

The chiralities of spiral waves usually refer to their rotation directions (the turning orientations of the spiral temporal movements as time elapses) and their curl directions (the winding orientations of the spiral spatial geometrical structures themselves). Traditionally, they are the same as each other. Namely, they are both clockwise or both counterclockwise. Moreover, the chiralities are determined by the topological charges of spiral waves, and thus they are conserved quantities. After the inwardly propagating spirals were experimentally observed, the relationship between the chiralities and the one between the chiralities and the topological charges are no longer preserved. The chiralities thus become more complex than ever before. As a result, there is now a desire to further study them. In this paper, the chiralities and their transition properties for all kinds of spiral waves are systemically studied in the framework of the complex Ginzburg-Landau equation, and the general relationships both between the chiralities and between the chiralities and the topological charges are obtained. The investigation of some other models, such as the FitzHugh-Nagumo model, the nonuniform Oregonator model, the modified standard model, etc., is also discussed for comparison.

A microfluidic method is presented to measure the elastic membrane properties of a population of microcapsules with diameter of order 60 $\mu$m. The technique consists of flowing a suspension of capsules enclosed by a polymerized ovalbumin membrane through a square-section microfluidic channel with cross dimension comparable with the capsule mean diameter. The deformed profile and the velocity of a given capsule are recorded. A full mechanical model of the motion and deformation of an initially spherical capsule flowing inside a square-section channel is designed for different flow strengths, confinement ratios, and membrane constitutive laws. The experimental deformed profiles are analyzed with the numerical model. This allows us to find the ratio between the viscous and elastic forces and thus the shear elastic modulus of the membrane. We show that the ovalbumin membrane tends to have a strain-softening behavior under the conditions studied here.

Raman-seed pulse amplification in a one-dimensional backscattering geometry is investigated with the help of numerical simulations and analytical estimates. The significant dependence of the initial amplification on the pulse form is revisited on the basis of a three-wave interaction as well as a kinetic Vlasov model. It is shown how the short duration of the input seed pulse influences its subsequent behavior, depending on plasma density and pump strength. The evolution during a “start-up period,” which has been observed earlier, can be explained analytically. In the nonlinear (pump depletion) regime, the pulse generated in the start-up period will be further amplified and may evolve into a self-similar $\pi$-pulse solution. The Vlasov code predicts algebraic growth in time of the seed amplitude, similar to the findings based on self-similar solutions of the three-wave-interaction model. An initially very narrow pulse is shown to grow more slowly than an initially broad one.

We report here results on the study of the totally asymmetric simple exclusion process, defined on an open network, consisting of head and tail simple-chain segments with a double-chain section inserted in between. Results of numerical simulations for relatively short chains reveal an interesting feature of the network. When the current through the system takes its maximum value, a simple translation of the double-chain section forward or backward along the network leads to a sharp change in the shape of the density profiles in the parallel chains, thus affecting the total number of particles in that part of the network. In the symmetric case of equal injection and ejection rates $\alpha =\beta >1/2$ and equal lengths of the head and tail sections, the density profiles in the two parallel chains are almost linear, characteristic of the coexistence line (shock phase). Upon moving the section forward (backward), their shape changes to the one typical for the high- (low-) density phases of a simple chain. The total bulk density of particles in a section with a large number of parallel chains is evaluated too. The observed effect might have interesting implications for the traffic flow control as well as for biological transport processes in living cells. An explanation of this phenomenon is offered in terms of a finite-size dependence of the effective injection and ejection rates at the ends of the double-chain section.

We apply the method of transitionless quantum driving for time-dependent quantum systems to spin systems. For a given Hamiltonian, the driving Hamiltonian is constructed so that the adiabatic states of the original system obey the Schrödinger equation. For several typical systems such as the $XY$ spin chain and the Lipkin-Meshkov-Glick model, the driving Hamiltonian is constructed explicitly. We discuss possible interesting situations when the driving Hamiltonian becomes time independent and when the driving Hamiltonian is equivalent to the original one. For many-body systems, a crucial problem occurs at the quantum phase transition point where the energy gap between the ground and first excited states becomes zero. We discuss how the defect can be circumvented in the present method.

Discovering overlapping community structures is a crucial step to understanding the structure and dynamics of many networks. In this paper we develop a symmetric binary matrix factorization model to identify overlapping communities. Our model allows us not only to assign community memberships explicitly to nodes, but also to distinguish outliers from overlapping nodes. In addition, we propose a modified partition density to evaluate the quality of community structures. We use this to determine the most appropriate number of communities. We evaluate our methods using both synthetic benchmarks and real-world networks, demonstrating the effectiveness of our approach.

Neural cryptography, a type of public key exchange protocol, is widely considered as an effective method for sharing a common secret key between two neural networks on public channels. How to design neural cryptography remains a great challenge. In this paper, in order to provide an approach to solve this challenge, a generalized network architecture and a significant heuristic rule are designed. The proposed generic framework is named as tree state classification machine (TSCM), which extends and unifies the existing structures, i.e., tree parity machine (TPM) and tree committee machine (TCM). Furthermore, we carefully study and find that the heuristic rule can improve the security of TSCM-based neural cryptography. Therefore, TSCM and the heuristic rule can guide us to designing a great deal of effective neural cryptography candidates, in which it is possible to achieve the more secure instances. Significantly, in the light of TSCM and the heuristic rule, we further expound that our designed neural cryptography outperforms TPM (the most secure model at present) on security. Finally, a series of numerical simulation experiments are provided to verify validity and applicability of our results.

The problem of finding an optimal back-to-front airplane boarding policy is explored, using a mathematical model that is related to the $1+1$ polynuclear growth model with concave boundary conditions and to causal sets in gravity. We study all airplane configurations and boarding group sizes. Optimal boarding policies for various airplane configurations are presented. Detailed calculations are provided along with simulations that support the main conclusions of the theory. We show that the effectiveness of back-to-front policies undergoes a phase transition when passing from lightly congested airplanes to heavily congested airplanes. The phase transition also affects the nature of the optimal or near-optimal policies. Under what we consider to be realistic conditions, optimal back-to-front policies lead to a modest $8–12\%$ improvement in boarding time over random (no policy) boarding, using two boarding groups. Having more than two groups is not effective.

In this paper, we identify that the different regimes encountered in a vertical capillary filling or a capillary-rise problem are determined entirely by two dimensionless parameters: Ohnesorge number (Oh) and Bond number (Bo). The initial universal inertial regime, which has been analyzed in our recent paper [Das et al., Phys. Rev. E 86, 067301 (2012)], is followed by any one of three possible regimes, dictated by the ratio Oh/Bo. For $\text{Oh}/\text{Bo}\gg 1$, the viscous effects dominate the gravitational effects, and one encounters the classical Washburn regime. For the other limit, i.e., $\text{Oh}/\text{Bo}\ll 1$, the viscous effects are insignificant and there is no Washburn regime. On the contrary, the inertial regime transits to the oscillatory regime with the filling length $\ell$ oscillating about the Jurin height ($\sim 1/\text{Bo}$), which is the maximum height attained by a liquid column in vertical capillary filling, with the viscous effects ($\sim \text{Oh}$) dictating the nature of the oscillations. For $\text{Oh}/\text{Bo}\sim 1$, we get a behavior intermediate of these two extreme regimes. Finally, we identify the correct force picture that drives the oscillatory regime and in the process achieve quantitative match with the experimental results, that was precluded in the previous studies.

We report an experimental investigation of pair dispersions in turbulent thermal convection with initial separation $r_0$ ranging from sub-Kolmogorov scale to scales in the inertial range. In the dissipative range of scales we observed the exponential growth of the separation between a pair of particles predicted by Batchelor and obtained a Batchelor constant $0.23\pm 0.07$. For large $r_0$, it is found that, for almost all time ranges, both the mean-square separation and distance neighbor function exhibit the forms predicted by Batchelor, whereas the two quantities agree with Richardson's predictions for small $r_0$. Moreover, the measured value of the Richardson constant $g=0.10\pm 0.07$, which is smaller than those found in other turbulence systems. We also demonstrate the crossover of the mean-square separation from the exponential to the Batchelor regimes in both temporal and spatial scales.

A numerical study of decaying stably stratified flows is performed. Relatively high stratification (Froude number $\approx {10}^{-2}$–10${}^{-1}$) and moderate Reynolds (Re) numbers ($\mathrm{Re}\approx$ 3–$6\times {10}^3$) are considered and a particular emphasis is placed on the role of helicity (velocity-vorticity correlations), which is not an invariant of the nondissipative equations. The problem is tackled by integrating the Boussinesq equations in a periodic cubical domain using different initial conditions: a nonhelical Taylor-Green (TG) flow, a fully helical Beltrami [Arnold-Beltrami-Childress (ABC)] flow, and random flows with a tunable helicity. We show that for stratified ABC flows helicity undergoes a substantially slower decay than for unstratified ABC flows. This fact is likely associated to the combined effect of stratification and large-scale coherent structures. Indeed, when the latter are missing, as in random flows, helicity is rapidly destroyed by the onset of gravitational waves. A type of large-scale dissipative “cyclostrophic” balance can be invoked to explain this behavior. No production of helicity is observed, contrary to the case of rotating and stratified flows. When helicity survives in the system, it strongly affects the temporal energy decay and the energy distribution among Fourier modes. We discover in fact that the decay rate of energy for stratified helical flows is much slower than for stratified nonhelical flows and can be considered with a phenomenological model in a way similar to what is done for unstratified rotating flows. We also show that helicity, when strong, has a measurable effect on the Fourier spectra, in particular at scales larger than the buoyancy scale, for which it displays a rather flat scaling associated with vertical shear, as observed in the planetary boundary layer.

In the present paper, we apply the implicit-correction method to the immersed-boundary thermal lattice Boltzmann method (IB-TLBM) for the natural convection between two concentric horizontal cylinders and in a square enclosure containing a circular cylinder. The Chapman-Enskog multiscale expansion proves the existence of an extra term in the temperature equation from the source term of the kinetic equation. In order to eliminate the extra term, we redefine the temperature and the source term in the lattice Boltzmann equation. When the relaxation time is less than unity, the new definition of the temperature and source term enhances the accuracy of the thermal lattice Boltzmann method. The implicit-correction method is required in order to calculate the thermal interaction between a fluid and a rigid solid using the redefined temperature. Simulation of the heat conduction between two concentric cylinders indicates that the error at each boundary point of the proposed IB-TLBM is reduced by the increment of the number of Lagrangian points constituting the boundaries. We derive the theoretical relation between a temperature slip at the boundary and the relaxation time and demonstrate that the IB-TLBM requires a small relaxation time in order to avoid temperature distortion around the immersed boundary. The streamline, isotherms, and average Nusselt number calculated by the proposed method agree well with those of previous numerical studies involving natural convection. The proposed IB-TLBM improves the accuracy of the boundary conditions for the temperature and velocity using an adequate discrete area for each of the Lagrangian nodes and reduces the penetration of the streamline on the surface of the body.

Simple models of irreversible dynamical processes such as bootstrap percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing nontypical trajectories, which can be crucial for the understanding of out-of-equilibrium phenomena, is still considered to be intractable in most cases. Here we introduce an efficient method to find and analyze optimized trajectories of cascade processes. We show that for a wide class of irreversible dynamical rules, this problem can be solved efficiently on large-scale systems.

The radical-pair mechanism is one of two distinct mechanisms used to explain the navigation of birds in geomagnetic fields, however little research has been done to explore the role of quantum entanglement in this mechanism. In this paper we study the lifetime of radical-pair entanglement corresponding to the magnitude and direction of magnetic fields to show that the entanglement lasts long enough in birds to be used for navigation. We also find that the birds appear to not be able to orient themselves directly based on radical-pair entanglement due to a lack of orientation sensitivity of the entanglement in the geomagnetic field. To explore the entanglement mechanism further, we propose a model in which the hyperfine interactions are replaced by local magnetic fields of similar strength. The entanglement of the radical pair in this model lasts longer and displays an angular sensitivity in weak magnetic fields, both of which are not present in previous models.

We study the kicked rotator in the classically fully chaotic regime using Izrailev's $N$-dimensional model for various $N\le 4000$, which in the limit $N\to \infty$ tends to the quantized kicked rotator. We do treat not only the case $K=5$, as studied previously, but also many different values of the classical kick parameter $5\le K\le 35$ and many different values of the quantum parameter $k\in [5,60]$. We describe the features of dynamical localization of chaotic eigenstates as a paradigm for other both time-periodic and time-independent (autonomous) fully chaotic or/and mixed-type Hamilton systems. We generalize the scaling variable $\Lambda =l_{\infty }/N$ to the case of anomalous diffusion in the classical phase space by deriving the localization length $l_{\infty }$ for the case of generalized classical diffusion. We greatly improve the accuracy and statistical significance of the numerical calculations, giving rise to the following conclusions: (1) The level-spacing distribution of the eigenphases (or quasienergies) is very well described by the Brody distribution, systematically better than by other proposed models, for various Brody exponents ${\beta }_{\mathrm{BR}}$. (2) We study the eigenfunctions of the Floquet operator and characterize their localization properties using the information entropy measure, which after normalization is given by ${\beta }_{\mathrm{loc}}$ in the interval $[0,1]$. The level repulsion parameters ${\beta }_{\mathrm{BR}}$ and ${\beta }_{\mathrm{loc}}$ are almost linearly related, close to the identity line. (3) We show the existence of a scaling law between ${\beta }_{\mathrm{loc}}$ and the relative localization length $\Lambda$, now including the regimes of anomalous diffusion. The above findings are important also for chaotic eigenstates in time-independent systems [Batistić and Robnik, J. Phys. A: Math. Gen. 43, 215101 (2010); arXiv:1302.7174 (2013)], where the Brody distribution is confirmed to a very high degree of precision for dynamically localized chaotic eigenstates, even in the mixed-type systems (after separation of regular and chaotic eigenstates).