We have studied the glass transition temperature ($T_g$) and molecular mobility of polystyrene (PS) thin films near the interface between the polymer thin film and substrate with bilayer thin films consisting of surface hydrogenated PS (h-PS) and bottom deuterated PS (d-PS) using neutron reflectivity. With decreasing the thickness of the bottom d-PS layer, $T_g$ near the interface between the polymer thin film and substrate increased compared to bulk $T_g$ and a drastic increase of $T_g$ was observed for the bottom d-PS layer <155 Å thick. The orientation of polymer chains at the interface is supposed to be related to the increase of $T_g$ near the interface between the polymer and substrate. The polymer chain mobility decreased with thickness even for the bottom d-PS layer with no discernible change of $T_g$. It is considered that the numerous contacts between polymer chains and substrate are related to the decrease of mobility near the interface between the polymer thin film and substrate.

We investigate the dynamics of an ecological system made up of one predator feeding on two different prey species. In a large range of parameter space, the system displays oscillating solutions. We show that, in the regime in which the two preys coexist, the better fit prey consistently peaks first. Further, we classify the possible oscillations of the network by a symbolic dynamics method. Our findings show that the symbolic orbits of an ecological system contain information about which of two preys is the better fit, and when one is bound to extinction.

Phase-disorder-induced resonance has been recently uncovered in an ensemble of coupled excitable neurons with weak external signal, where each neuron takes a constant initial signal phase [Phys. Rev. E 82, 010902(R) (2010)]. However, it is unclear how the initial phase disorder influences the behavior of a single or isolated neuron, which constitutes the ensemble. In order to answer this question, we here consider the case of a single neuron with phase noise originated from the time-varying initial signal phase, in contrast to the constant initial phase in each neuron studied in the above referenced paper. Interestingly, we find that the phase noise can induce resonance even in the single neuronal system with subthreshold signal. Moreover, we reveal that, with the presence of phase noise, the neuron also shows another resonance behavior by varying the period of the external signal. An analysis is conducted to uncover the mechanisms behind these resonance phenomena.

An “infection,” understood here in a very broad sense, can be propagated through the network of social contacts among individuals. These social contacts include both “close” contacts and “casual” encounters among individuals in transport, leisure, shopping, etc. Knowing the first through the study of the social networks is not a difficult task, but having a clear picture of the network of casual contacts is a very hard problem in a society of increasing mobility. Here we assume, on the basis of several pieces of empirical evidence, that the casual contacts between two individuals are a function of their social distance in the network of close contacts. Then, we assume that we know the network of close contacts and infer the casual encounters by means of nonrandom long-range (LR) interactions determined by the social proximity of the two individuals. This approach is then implemented in a susceptible-infected-susceptible (SIS) model accounting for the spread of infections in complex networks. A parameter called “conductance” controls the feasibility of those casual encounters. In a zero conductance network only contagion through close contacts is allowed. As the conductance increases the probability of having casual encounters also increases. We show here that as the conductance parameter increases, the rate of propagation increases dramatically and the infection is less likely to die out. This increment is particularly marked in networks with scale-free degree distributions, where infections easily become epidemics. Our model provides a general framework for studying epidemic spreading in networks with arbitrary topology with and without casual contacts accounted for by means of LR interactions.

We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the dynamics in the limit of a large number of oscillators and use it to quantify the degree of cluster synchrony, cluster asymmetry, and switching. We use a variation of the recent dimensionality-reduction technique of Ott and Antonsen [Chaos 18, 037113 (2008)] and find an analytic description of the degree of cluster synchrony valid on a globally attracting manifold. Shaped by this manifold, there is an infinite family of steady-state distributions of oscillators, resulting in a high degree of multistability in the cluster asymmetry. We also show how through external forcing the degree of asymmetry can be controlled, and suggest that systems displaying cluster synchrony can be used to encode and store data.

This paper deals with theoretical studies on the $2p-3d$ absorption in iron, nickel, and copper plasmas related to LULI2000 (Laboratoire pour l'Utilisation des Lasers Intenses, 2000J facility) measurements in which target temperatures were of the order of 20 eV and plasma densities were in the range 0.004–0.01 ${\mathrm{g}/\mathrm{cm}}^3$. The radiatively heated targets were close to local thermodynamic equilibrium (LTE). The structure of $2p-3d$ transitions has been studied with the help of the statistical superconfiguration opacity code sco and with the fine-structure atomic physics codes hullac and fac. A new mixed version of the sco code allowing one to treat part of the configurations by detailed calculation based on the Cowan’s code rcg has been also used in these comparisons. Special attention was paid to comparisons between theory and experiment concerning the term features which cannot be reproduced by sco. The differences in the spin-orbit splitting and the statistical (thermal) broadening of the $2p-3d$ transitions have been investigated as a function of the atomic number $Z$. It appears that at the conditions of the experiment the role of the term and configuration broadening was different in the three analyzed elements, this broadening being sensitive to the atomic number. Some effects of the temperature gradients and possible non-LTE effects have been studied with the help of the radiative-collisional code scric. The sensitivity of the $2p-3d$ structures with respect to temperature and density in medium-$Z$ plasmas may be helpful for diagnostics of LTE plasmas especially in future experiments on the $\Delta n=0$ absorption in medium-$Z$ plasmas for astrophysical applications.

Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can generate particular three-dimensional shapes from thin elastic sheets by mere imposition of a two-dimensional pattern of locally isotropic growth. Not every shape is possible. Several types of obstruction can arise, some of which depend on the sheet thickness. We provide some examples using the axisymmetric form of the problem, which is analytically tractable.

The Lagrange-mesh method is a very accurate procedure for computing eigenvalues and eigenfunctions of a two-body quantum equation written in the configuration space. Using a Gauss quadrature rule, the method only requires the evaluation of the potential at some mesh points. The eigenfunctions are expanded in terms of regularized Lagrange functions, which vanish at all mesh points except one. Using the peculiarities of the method, it is shown that the Fourier transform of the eigenfunctions, computed in the configuration space, can easily be obtained with good accuracy in the physical domain of the momentum space. Also, observables in this space can easily be computed with good accuracy only using matrix elements and eigenfunctions computed in the configuration space.

Monte Carlo algorithms such as the Wang-Landau algorithm and similar “entropic” methods are able to accurately sample the density of states of model systems and thereby give access to thermal equilibrium properties at any temperature. Thermal equilibrium is, however, unachievable at low temperatures in glassy systems. Such systems are characterized by a multitude of metastable configurations pictorially referred to as “valleys” of an energy landscape. Geometrical properties of the landscape, e.g., the local density of states describing the distribution in energy of the states belonging to a single valley, are key to understanding the dynamical properties of such systems. In this paper we combine the lid algorithm, a tool for landscape exploration previously applied to a range of models, with the Wang-Swendsen algorithm. To test this improved exploration tool, we consider a paradigmatic complex system, the Edwards-Anderson model in two and three spatial dimensions. We find a striking difference between the energy dependence of the local density of states in two dimensions and three dimensions—nearly linear in the first case, and nearly exponential in the second. The dynamical consequences of these findings are discussed.

Memory effects in quantum dynamical processes involving structured environments are presently difficult, if not impossible, to investigate using standard approaches. Progress can be made by transforming the environmental variables to a suitable chain representation which effectively performs a Markovian embedding of the dynamics. Here, we show that this effective-mode chain representation provides a unique way of unraveling the memory kernel $\kappa \left(t\right)$ as a function of time. Truncated or Markov-closed chains with $n$ effective modes exactly reproduce $\kappa \left(t\right)$ to the $4n$th order in time, up to an irrelevant constant of order $\kappa \left(0\right)/n$. These favorable convergence properties pave the way for efficient quantum simulations of fast (non-Markovian) processes by reduced dynamical models.

We present an alternate method for finding the communities in a complex network. We introduce two concepts named the seed of the community and the absorption power of the seed in complex networks. First, we find the seeds and then develop them by considering their absorption power to achieve the communities. We compare the modularity and the computational complexity of this algorithm with some other existing methods, and we show that this algorithm is very fast and efficient in comparison with some recently fast algorithms.

We show by nonequilibrium molecular dynamics simulations that the Navier-Stokes equation does not correctly describe water flow in a nanoscale geometry. It is argued that this failure reflects the fact that the coupling between the intrinsic rotational and translational degrees of freedom becomes important for nanoflows. The coupling is correctly accounted for by the extended Navier-Stokes equations that include the intrinsic angular momentum as an independent hydrodynamic degree of freedom.

We consider the quintic one-dimensional nonlinear Schrödinger equation with forcing and both linear and nonlinear dissipation. Quintic nonlinearity results in multiple collapse events randomly distributed in space and time, forming forced turbulence. Without dissipation each of these collapses produces finite-time singularity, but dissipative terms prevent actual formation of singularity. In statistical steady state of the developed turbulence, the spatial correlation function has a universal form with the correlation length determined by the modulational instability scale. The amplitude fluctuations at that scale are nearly Gaussian while the large-amplitude tail of the probability density function (PDF) is strongly non-Gaussian with powerlike behavior. The small-amplitude nearly Gaussian fluctuations seed formation of large collapse events. The universal spatiotemporal form of these events together with the PDFs for their maximum amplitudes define the powerlike tail of the PDF for large-amplitude fluctuations, i.e., the intermittency of strong turbulence.

A reformulated lattice Boltzmann model is described for incompressible axisymmetric flows with or without swirling. It is a further development and improvement on the author’s axisymmetric lattice Boltzmann method. The main features of the revised scheme are (a) all the macroscopic variables such as velocities are determined in the same formulas as those in the conventional lattice Boltzmann approach to the Navier-Stokes equations and (b) the added sink or source and force terms are simple with no calculation for a derivative. Such features distinguish the present method from the other existing simplified schemes, leading to a simple and efficient model. The scheme is naturally suitable for generic incompressible axisymmetric rotational flows involving more physical phenomena. The numerical solutions to Womersley and cylindrical cavity flows are presented to demonstrate its accuracy and capability.

We show that there is a disparity in fractal scaling behavior of the core and peripheral parts of empirical small-world scale-free networks. We decompose the network into a core and a periphery and measure the fractal dimension of each part separately using the box-counting method. We find that the core of small-world scale-free networks has a nonfractal structure, whereas the periphery exhibits either fractal or nonfractal scaling. The fractal dimension of the periphery is found to coincide with one for the whole network.

We consider the thermodynamic geometry of an ideal non-Abelian gas. We show that, for a certain value of the fractional parameter and at the relevant maximum value of fugacity, the thermodynamic curvature has a singular point. This indicates a condensation such as Bose-Einstein condensation for non-Abelian statistics and we work out the phase transition temperature in various dimensions.

We study the coordinate-velocity couple of the harmonic oscillator with $\alpha$-stable noise. As previously shown by Sokolov et al., the distribution of this couple is bivariate $\alpha$-stable. In this work, we determine explicitly its associated spectral measure, exhibiting directly both the non-independence and non-ellipticity of the coordinate-velocity couple. Knowledge of the spectral measure allows to analyze and quantify the deviation from ellipticity.

We study fluctuation theorems for open quantum systems with a non-Markovian heat bath using the approach of quantum master equations and examine the physical quantities that appear in those fluctuation theorems. The approach of Markovian quantum master equations to the fluctuation theorems was developed by Esposito and Mukamel [Phys. Rev. E 73, 046129 (2006)]. We show that their discussion can be formally generalized to the case of a non-Markovian heat bath when the local system is linearly connected to a Gaussian heat bath with the spectrum distribution of the Drude form. We found by numerically simulating the spin-boson model in non-Markovian regime that the “detailed balance” condition is well satisfied except in a strongly nonequilibrium transient situation, and hence our generalization of the definition of the “entropy production” is almost always legitimate. Therefore, our generalization of the fluctuation theorem seems meaningful in wide regions.

We formulate and investigate the nonlinear $q$-voter model (which as a special case includes the linear voter and the Sznajd model) on a one-dimensional lattice. We derive an analytical formula for the exit probability and show that it agrees perfectly with Monte Carlo simulations. The puzzle that we deal with here may be summarized by a simple question: Why does the mean-field approach give the exact formula for the exit probability in the one-dimensional nonlinear $q$-voter model? To answer this question, we test several hypotheses proposed recently for the Sznajd model, including the finite size effects, the influence of the range of interactions, and the importance of the initial step of the evolution. On the one hand, our work is part of a trend of the current debate on the form of the exit probability in the one-dimensional Sznajd model, but on the other hand, it concerns the much broader problem of the nonlinear $q$-voter model.

Several studies have shown that the performance of different chemical processes can be improved by means of periodic operation. An accurate modeling and simulation of these processes requires accounting for the dependence of the system parameters with the operating frequency. This work uses the method of volume averaging to study the behavior of dispersion with frequency (i.e., dynamic dispersion) in homogeneous porous media. In the absence of convection, the dynamic dispersion is reduced to the dynamic diffusivity, showing a decreasing behavior with frequency. In contrast, the dynamic dispersion can be either an increasing or decreasing function of frequency, depending on the particle Péclet number values. At sufficiently high frequency values, the dispersion coefficient approaches the molecular diffusivity. Comparisons with direct numerical simulations for idealized porous medium models evidence the extents and limitations of the upscaling approach.