Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.

Weakly chaotic or weakly interacting systems have a wide regime where the common random matrix theory modeling does not apply. As an example we consider cold atoms in a nearly integrable optical billiard with a displaceable wall (piston). The motion is completely chaotic but with a small Lyapunov exponent. The Hamiltonian matrix does not look like one taken from a Gaussian ensemble, but rather it is very sparse and textured. This can be characterized by parameters $s$ and $g$ which reflect the percentage of large elements and their connectivity, respectively. For $g$ we use a resistor network calculation that has a direct relation to the semilinear response characteristics of the system, hence leading to a prediction regarding the energy absorption rate of cold atoms in optical billiards with vibrating walls.

In the present work we focus on the case of (few-site) configurations respecting the parity-time ($\mathcal{PT}$) symmetry, i.e., with a spatially odd gain-loss profile. We examine the case of such “oligomers” with not only two sites, as in earlier works, but also the cases of three and four sites. While in the former case of recent experimental interest the picture of existing stationary solutions and their stability is fairly straightforward, the latter cases reveal a considerable additional complexity of solutions, including ones that exist past the linear $\mathcal{PT}$-symmetry breaking point in the case of the trimer, and symmetry-breaking bifurcations, as well as more complex, even asymmetric solutions in the case of the quadrimer with nontrivial properties in their linear stability and in their nonlinear dynamics. The linearization around the obtained solutions and their dynamical evolution, when unstable, are discussed.

The concept and experimental results of a light source given in a recent paper by Adamo et al. [Phys. Rev. Lett. 103, 113901 (2009)] are very interesting and attractive. Our paper presents detailed theoretical investigations on such a light source, and our results confirm that the mechanism of the light radiation experimentally detected in the published paper is a special kind of diffraction radiation in a waveguide with nanoscale periodic structure excited by an electron beam. The numerical calculations based on our theory and digital simulations agree well with the experimental results. This mechanism of diffraction radiation is of significance in physics and optics, and may bring good opportunities for the generation of electromagnetic waves from terahertz to light frequency regimes.

We investigate the stability of growing vesicles using the formalism of nonequilibrium thermodynamics. The vesicles are growing due to the accretion of lipids to the bilayer which forms the vesicle membrane. The thermodynamic description is based on the hydrodynamics of a water and lipid mixture together with a model of the vesicle as a discontinuous system in the sense of linear nonequilibrium thermodynamics. This formulation allows the forces and fluxes relevant to the dynamic stability of the vesicle to be identified. The method is used to analyze the stability of a spherical vesicle against arbitrary axisymmetric perturbations. It is found that there are generically two critical radii at which changes of stability occur. In the case where the perturbation takes the form of a single zonal harmonic, only one of these radii is physical and is given by the ratio $2L_p/L_{\gamma }$, where $L_p$ is the hydraulic conductivity and $L_{\gamma }$ is the Onsager coefficient related to changes in membrane area due to lipid accretion. The stability of such perturbations is related to the value of $l$ corresponding to the particular zonal harmonic: those with lower $l$ are more unstable than those with higher $l$. Possible extensions of the current work and the need for experimental input are discussed.

We study front propagation in the reaction-diffusion process $\{A\stackrel{\epsilon }{\to }2A,A\stackrel{{\epsilon }_t}{\to }3A\}$ on a one-dimensional lattice with hard-core interactions between the particles. Using the leading particle picture, the velocity of the front is computed using different approximate methods that yield results in good agreement with simulation results. We observe that the front dynamics exhibits temporal velocity correlations that must be accounted for to obtain accurate estimates of the front diffusion coefficient. Interestingly, these temporal correlations change sign depending upon the sign of ${\epsilon }_t-D$, where $D$ is the bare diffusion coefficient of $A$ particles. For ${\epsilon }_t=D$, we find analytically as well as numerically that the leading particle and thus the front move as an uncorrelated random walker.

We report on an observation of propagating compression waves in a quasi-two-dimensional monolayer of apolar granular rods fluidized by an upflow of air. The collective wave speed is an order of magnitude faster than the speed of the particles. This gives rise to anomalously large number fluctuations, $\Delta N~N^{0.72\pm 0.04}$, which are greater than ordinary number fluctuations of $N^{1/2}$. We characterize the waves by calculating the spatiotemporal power spectrum of the density. The position of observed peaks, as a function of frequency $\omega$ and wave vector $k$, yields a linear dispersion relationship in the long-time, long-wavelength limit and a wave speed $c=\omega /k$. Repeating this analysis for systems at different densities and air speeds, we observe a linear increase in the wave speed with increasing packing fraction with almost no dependence on the air flow. We also observe that the parallel and perpendicular root-mean-square speeds of the rods are identical when waves are present, but become different at low packing fractions where there are no waves. Based on this apparent exclusivity, we map out the phase behavior for the existence of waves vs speed anisotropy as a function of density and fluidizing air flow.

The phase-field-crystal model for liquid crystals is solved numerically in two spatial dimensions. This model is formulated with three position-dependent order parameters, namely the reduced translational density, the local nematic order parameter, and the mean local direction of the orientations. The equilibrium free-energy functional involves local powers of the order parameters up to fourth order, gradients of the order parameters up to fourth order, and different couplings between the order parameters. The stable phases of the equilibrium free-energy functional are calculated for various coupling parameters. Among the stable liquid crystalline states are the isotropic, nematic, columnar, smectic-$A$, and plastic crystalline phases. The plastic crystals can have triangular, square, and honeycomb lattices and exhibit orientational patterns with a complex topology involving a sublattice with topological defects. Phase diagrams were obtained by numerical minimization of the free-energy functional. Their main features are qualitatively in line with much simpler one-mode approximations for the order parameters.

The Landau-de Gennes free energy plays a central role in the macroscopic theory of anisotropic fluids. Here, the ideal, entropic contribution to this free energy—that is always present in these systems, irrespectively of the detailed form of interactions or applied fields—is derived within the quasiequilibrium ensemble and successfully tested. An explicit and compact form of the macroscopic, ideal entropy is derived. This entropy is nonpolynomial in the order parameter, diverging logarithmically near the fully oriented state and therefore restricting the order parameter to physical admissible values. As an application, it is shown that the isotropic-nematic transition within the Maier-Saupe model is described in a simple and very accurate manner.

We consider a single-end-grafted polymer chain covered by a membrane in contact with a flat and rigid surface in the context of supported membrane adhesion on surfaces carrying dilute polymer brushes. The fluid membrane adheres to the surface due to attractive interactions; the presence of a macromolecule locally hinders the membrane-surface contact and creates a protuberant membrane bulge. We study both the size and elevation of such membrane deformations as a function of curvature modulus, surface tension, adhesion energy, and chain size. Scaling results are derived, valid for both ideal and nonideal chain statistics, leading to complex diagrams of states depending on curvature modulus, tension, and adhesion values. We also compute quantitatively the membrane deformation profile for shallow bulges and make predictions for realistic systems involving DNA grafted chains covered by lipid membranes.

Using Brownian dynamics simulations, we investigate how hydrodynamic interaction (HI) affects the behavior of tethered polymers in uniform flow. While it is expected that the HI within the polymer will lead to a dependency of the polymer’s drag coefficient on the flow velocity, the interchain HI causes additional screening effects. For the case of two polymers in uniform flow with their tether points a finite distance apart, it is shown that the interchain HI not only causes a further reduction of the drag per polymer with decreasing distance between the tether points but simultaneously induces a polymer-polymer attraction as well. This attraction exhibits a characteristic maximum at intermediate flow velocities when the drag forces are of the order of the entropic forces. The effects uniquely attributed to the presence of HI can be verified experimentally.

We study the dynamics of the voter and Moran processes running on top of complex network substrates where each edge has a weight depending on the degree of the nodes it connects. For each elementary dynamical step the first node is chosen at random and the second is selected with probability proportional to the weight of the connecting edge. We present a heterogeneous mean-field approach allowing to identify conservation laws and to calculate exit probabilities along with consensus times. In the specific case when the weight is given by the product of nodes' degree raised to a power $\theta$, we derive a rich phase diagram, with the consensus time exhibiting various scaling laws depending on $\theta$ and on the exponent of the degree distribution $\gamma$. Numerical simulations give very good agreement for small values of $\left|\theta \right|$. An additional analytical treatment (heterogeneous pair approximation) improves the agreement with numerics, but the theoretical understanding of the behavior in the limit of large $\left|\theta \right|$ remains an open challenge.

A variety of metrics have been proposed to measure the relative importance of nodes in a network. One of these, alpha-centrality [P. Bonacich, Am. J. Sociol. 92, 1170 (1987)], measures the number of attenuated paths that exist between nodes. We introduce a normalized version of this metric and use it to study network structure, for example, to rank nodes and find community structure of the network. Specifically, we extend the modularity-maximization method for community detection to use this metric as the measure of node connectivity. Normalized alpha-centrality is a powerful tool for network analysis, since it contains a tunable parameter that sets the length scale of interactions. Studying how rankings and discovered communities change when this parameter is varied allows us to identify locally and globally important nodes and structures. We apply the proposed metric to several benchmark networks and show that it leads to better insights into network structure than alternative metrics.

Recommender systems have shown great potential in addressing the information overload problem, namely helping users in finding interesting and relevant objects within a huge information space. Some physical dynamics, including the heat conduction process and mass or energy diffusion on networks, have recently found applications in personalized recommendation. Most of the previous studies focus overwhelmingly on recommendation accuracy as the only important factor, while overlooking the significance of diversity and novelty that indeed provide the vitality of the system. In this paper, we propose a recommendation algorithm based on the preferential diffusion process on a user-object bipartite network. Numerical analyses on two benchmark data sets, MovieLens and Netflix, indicate that our method outperforms the state-of-the-art methods. Specifically, it can not only provide more accurate recommendations, but also generate more diverse and novel recommendations by accurately recommending unpopular objects.

We numerically investigate diffusion phenomena in quasiperiodically forced systems with spatially periodic potentials using a lift of the quasiperiodically forced circle map and a quasiperiodically forced damped pendulum. These systems exhibit several types of dynamics: quasiperiodic, strange nonchaotic, and chaotic. The strange nonchaotic and chaotic dynamics induce deterministic diffusion of orbits. The diffusion type gradually changes from logarithmic to subdiffusive within a strange nonchaotic regime and finally becomes normal in a chaotic regime. Fractal time-series analysis shows that the subdiffusion is caused by the antipersistence property of strange nonchaotic motion.

Classical Hamiltonian systems with a mixed phase space and some asymmetry may exhibit chaotic ratchet effects. The most significant such effect is a directed momentum current or acceleration. In known model systems, this effect may arise only for sufficiently strong chaos. In this paper, a Hamiltonian ratchet accelerator is introduced, featuring a momentum current for arbitrarily weak chaos. The system is a realistic, generalized kicked rotor and is exactly solvable to some extent, leading to analytical expressions for the momentum current. While this current arises also for relatively strong chaos, the maximal current is shown to occur, at least in one case, precisely in a limit of arbitrarily weak chaos.

This paper is an initial exploration of synchronizing a frequency-weighted network of Kuramoto oscillators, where the oscillators are asymmetrically coupled with the weights depending on their corresponding native frequencies. We find that with different categories of weighted couplings influenced by the native frequency distribution of the oscillators, one observes synchronous, asynchronous, and oscillatory phenomena, and the so-called chimera states, where the weighting exponent $\beta$ plays an important role.

Predicting three-phase relative permeability by network models requires reliable models for hydraulic conductance of films and layers stabilized by capillary forces at the pore level. We solve the creeping flow approximation of the Navier-Stokes equation for stable wetting and intermediate layers in the corner of angular capillaries by using a continuity boundary condition at the layer interface. We find significant coupling between the condensed phases and calculate the generalized mobilities by solving cocurrent and countercurrent flow of wetting and intermediate layers. Finally, we present a simple heuristic model for the generalized mobilities as a function of the geometry and viscosity ratio.