We study directional relationships—in the driver-responder sense—in networks of coupled nonlinear oscillators using a phase modeling approach. Specifically, we focus on the identification of drivers in clusters with varying levels of synchrony, mimicking dynamical interactions between the seizure generating region (epileptic focus) and other brain structures. We demonstrate numerically that such an identification is not always possible in a reliable manner. Using the same analysis techniques as in model systems, we study multichannel electroencephalographic recordings from two patients suffering from focal epilepsy. Our findings demonstrate that—depending on the degree of intracluster synchrony—certain subsystems can spuriously appear to be driving others, which should be taken into account when analyzing field data with unknown underlying dynamics.

We argue that the results published by Ai et al. [Phys. Rev. E 67, 022903 (2003)] on “correlated noise in logistic growth” are not correct. Their conclusion that, for larger values of the correlation parameter $\lambda$, the cell population is peaked at $x=0$, which denotes a high extinction rate, is also incorrect. We find the reverse behavior to their results, that increasing $\lambda$ promotes the stable growth of tumor cells. In particular, their results for the steady-state probability, as a function of cell number, at different correlation strengths, presented in Figs. 1 and 2 of their paper show different behavior than one would expect from the simple mathematical expression for the steady-state probability. Additionally, their interpretation that at small values of cell number the steady-state probability increases as the correlation parameter is increased is also questionable. Another striking feature in their Figs. 1 and 3 is that, for the same values of the parameters $\lambda$ and $\alpha$, their simulation produces two different curves, both qualitatively and quantitatively.

We respond to the preceding Comment by Behera and O’Rourke, which points out an error in our earlier work [Phys. Rev. E 67, 022903 (2003)], and argues that our results are not correct. We agree with Behera and O’Rourke: a sign error led us to solve the model for the opposite (positive) sign of the correlation parameter from that which we intended. In order to improve this problem, we extend the range of the correlation parameter $\lambda$ from (0,1) to (–1,1].

The influence of uniaxial small-scale anisotropy on the stability of the scaling regimes and on the anomalous scaling of the structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator product expansion within one-loop approximation. Possible scaling regimes are found and classified in the plane of exponents $\epsilon -\eta$, where $\epsilon$ characterizes the energy spectrum of the velocity field in the inertial range $E\propto k^{1-2\epsilon }$, and $\eta$ is related to the correlation time of the velocity field at the wave number $k$ which is scaled as $k^{-2+\eta }$. It is shown that the presence of anisotropy does not disturb the stability of the infrared fixed points of the renormalization group equations, which are directly related to the corresponding scaling regimes. The influence of anisotropy on the anomalous scaling of the structure functions of the passive scalar field is studied as a function of the fixed point value of the parameter $u$, which represents the ratio of turnover time of scalar field and velocity correlation time. It is shown that the corresponding one-loop anomalous dimensions, which are the same (universal) for all particular models with a concrete value of $u$ in the isotropic case, are different (nonuniversal) in the case with the presence of small-scale anisotropy and they are continuous functions of the anisotropy parameters, as well as the parameter $u$. The dependence of the anomalous dimensions on the anisotropy parameters of two special limits of the general model, namely, the rapid-change model and the frozen velocity field model, are found when $u\to \infty$ and $u\to 0$, respectively.

Fast electron emission from the interaction of femtosecond laser pulses with shaped solid targets has been studied. It is found that the angular distributions of the forward fast electrons are highly dependent upon the target shapes. The important roles played by the electrostatic fields built up at the non-laser-irradiated target surfaces and the collisions in the target are identified. Our two-dimensional particle-in-cell simulations with binary collisions included reproduce the main experimental observations.

The linear dashpot model for the inelastic normal force between colliding spheres leads to a constant coefficient of normal restitution, ${\epsilon }_n=\mathrm{const}$, which makes this model very popular for the investigation of dilute and moderately dense granular systems. For two frequently used models for the tangential interaction force we determine the coefficient of tangential restitution, ${\epsilon }_t$, both analytically and by numerical integration of Newton’s equation. Although ${\epsilon }_n=\mathrm{const}$ for the linear-dashpot model, we obtain pronounced and characteristic dependences of the tangential coefficient on the impact velocity, ${\epsilon }_t={\epsilon }_t\left(\vec{g}\right)$. The results may be used for event-driven simulations of granular systems of frictional particles.

By pouring a mixture of two types of grains into a large vertical cell with a narrow space, we discovered a dual stratification pattern consisting of two different wavelengths at the upper and lower regions of the resulting sand pile. In the formation of this pattern, we also observed an additional type of kink—a wave that moves toward the top of the sand pile along the slope. The kink, herein called a trapped kink, is essential for the formation of dual stratification patterns. Asymmetric probability distributions are obtained from measurement of the position where the kinks are generated. We proposed a phenomenological model to describe the kink generation process. The results analyzed by this model agree with experimental distributions.

Results on the rheological behavior of Chinese hamster ovary cell suspensions in a large range of concentrations are reported. The concentration-dependent yield stress and elastic plateau modulus are formalized in the context of fractal aggregates under shear, and quite different exponents are found as compared to the case of red blood cell suspensions. This is explained in terms of intrinsic microscopic parameters such as the cell-cell adhesion energy and cell elasticity but also the cell’s individual dynamic properties, found to correlate well with viscoelastic data at large concentrations $(\varphi \ge 0.5)$.

The bilateral simultaneous generation of sound in some oscine songbirds leads to complex sounds that cannot be described in terms of a superposition of the isolated sources alone. In this work, we study the appearance of complex solutions in a model for the acoustic interaction between the two sound sources in birdsong. The origin of these complex oscillations can be traced to the nonlinear mode-mode interaction arising when both sources are active. As an example, we analyze a remarkable sound produced by an oscine songbird and show that the proposed dynamical scenario is compatible with the observed behavior.

We consider the problem of fuzzy community detection in networks, which complements and expands the concept of overlapping community structure. Our approach allows each vertex of the graph to belong to multiple communities at the same time, determined by exact numerical membership degrees, even in the presence of uncertainty in the data being analyzed. We create an algorithm for determining the optimal membership degrees with respect to a given goal function. Based on the membership degrees, we introduce a measure that is able to identify outlier vertices that do not belong to any of the communities, bridge vertices that have significant membership in more than one single community, and regular vertices that fundamentally restrict their interactions within their own community, while also being able to quantify the centrality of a vertex with respect to its dominant community. The method can also be used for prediction in case of uncertainty in the data set analyzed. The number of communities can be given in advance, or determined by the algorithm itself, using a fuzzified variant of the modularity function. The technique is able to discover the fuzzy community structure of different real world networks including, but not limited to, social networks, scientific collaboration networks, and cortical networks, with high confidence.

A system of coupled chaotic bistable maps on a lattice with randomly distributed impurities is investigated as a model for studying the phenomenon of phase growth in nonuniform media. The statistical properties of the system are characterized by means of the average size of spatial domains of equivalent spin variables that define the phases. It is found that the rate at which phase domains grow becomes smaller when impurities are present and that the average size of the resulting domains in the inhomogeneous state of the system decreases when the density of impurities is increased. The phase diagram showing regions where homogeneous, heterogeneous, and chessboard patterns occur on the space of parameters of the system is obtained. A critical boundary that separates the regime of slow growth of domains from the regime of fast growth in the heterogeneous region of the phase diagram is calculated. The transition between these two growth regimes is explained in terms of the stability properties of the local phase configurations. Our results show that the inclusion of spatial inhomogeneities can be used as a control mechanism for the size and growth velocity of phase domains forming in spatiotemporal systems.

In this paper, we provide a numerical approximation to the occurrence of the process of nonlinear supratransmission in semiunbounded, discrete, $\left(2+1\right)$-dimensional systems of sine-Gordon equations subject to harmonic Neumann boundary data irradiating with a frequency in the forbidden band gap. The model is a generalization of the one describing semi-infinite, discrete, $\left(1+1\right)$-dimensional, parallel arrays of Josephson junctions connected through superconducting wires, subject to the action of an ac current at the end. The computational results are obtained using a finite-difference scheme for sine-Gordon and nonlinear Klein-Gordon media, and the method is applied to systems of harmonic oscillators when Dirichlet data are imposed to the boundary. Our numerical results show that energy is transmitted into the medium in the form of discrete breathers.

We investigate the effective permittivity $\epsilon$ of two-phase two-dimensional heterostructures, consisting of an inclusion (or cross section of infinite parallel, infinitely long, identical, cylinders, where the properties and characteristics are invariant along the perpendicular cross sectional plane), of permittivity ${\epsilon }_2={\epsilon }_2^{\prime }+{\epsilon }_2^{″}i$ with ${\epsilon }_2^{\prime }$ being positive or negative, in a matrix of permittivity ${\epsilon }_1$ (hereafter, assumed to be real valued and positive). Our method for computing $\epsilon ={\epsilon }^{\prime }+{\epsilon }^{″}i$ is based on formulating the conservation of electric displacement flux through the interface separating the two media on systems with periodic boundary conditions in one direction. We identify two distinct behaviors in the surface fraction ${\varphi }_2$ dependence of the effective permittivity according the value of $\frac{\mid {\epsilon }_2^{\prime }\mid }{{\epsilon }_1}$ relative to 1, which is a consequence of the duality symmetry. The incorporation of negative values of ${\epsilon }_2^{\prime }$ into our calculations leads to a peak in ${\epsilon }^{″}\left({\varphi }_2\right)$ whereas ${\epsilon }^{\prime }\left({\varphi }_2\right)$ decreases to zero, which are both results of an electrostatic resonance (ER) phenomenon. We demonstrate that one can generate heterostructures characterized by an upward shift in the ER position as ${\epsilon }_2^{″}$ is increased. This suggests that, in principle, this property can be used to provide a wide range of innovative structures from specially designed composite materials, e.g., reconfigurable composite device. The comparison of our data with Maxwell Garnett (MG) and Bruggeman (SBG) homogenization formalisms permits a quantitative assessment of the ability of the two methods to capture the effects of surface fraction on $\epsilon$. These methods have severe inadequacies, which arise physically from an incorrect treatment of the higher multipoles than dipole moments. We argue that the inappropriateness of SBG formula can originate from its prerogative that phase 1 and phase 2 are treated symmetrically. Our calculations show that MG formula may provide reasonable estimates for $\epsilon$, even close to the ER position, of homogenized two-phase heterostructures with the real part of the complex-valued permittivities of phases having opposite signs and provided that $\mid {\epsilon }_2^{\prime }\mid ⩽{\epsilon }_2^{″}$.

This paper addresses issues related to weights and acceptance rates in generalized ensemble simulations, while comparing two algorithms: serial (e.g., simulated tempering or expanded ensemble method) and parallel (e.g., parallel tempering or replica exchange). We derive a cumulant approximation for weights and discuss its effectiveness in practical applications. We compare the acceptance rates of the serial and parallel algorithms and prove that the serial algorithm always has higher acceptance rates. The duality between forward and backward transitions plays a crucial role in the derivations throughout the paper.

The phenomenon of glass transition, such as the anomalous divergence in viscosity without apparent structural change, remains inadequately understood. We employ spatial confinement to probe length scale dependence on structural relaxation and concomitant glassy dynamics of a hard-sphere poly-(methyl methacrylate) colloidal suspension via confocal microscopy. Remarkable film thickness dependent scaling behavior is observed, where the mobility and relaxation processes of a “fluid” suspension are found to be significantly impeded as film thickness is reduced below 15–20 particle layers.

We investigate the occurrence of exponential relaxation in a certain class of closed, finite systems on the basis of a time-convolutionless projection operator expansion for a specific class of initial states with vanishing inhomogeneity. It turns out that exponential behavior is to be expected only if the leading order predicts the standard separation of time scales and if, furthermore, all higher orders remain negligible for the full relaxation time. The latter, however, is shown to depend not only on the perturbation (interaction) strength, but also crucially on the structure of the perturbation matrix. It is shown that perturbations yielding exponential relaxation have to fulfill certain criteria, one of which relates to the so-called “Van Hove structure.” All our results are verified by the numerical integration of the full time-dependent Schrödinger equation.

High-resolution quasielastic neutron scattering spectroscopy was used to measure ${\text{H}}_2\text{O}$ and ${\text{D}}_2\text{O}$ hydrated RNA samples. The contribution of scattering from RNA was subtracted out by taking the difference of the signals between the two samples. The measurements were made at a series of temperatures from 270 K down to 180 K. The relaxing-cage model was used to analyze the difference quasielastic spectra. We observed clear evidence of a fragile-to-strong dynamic crossover (FSC) at $T_L=220\text{K}$ in RNA hydration water. We further show that the mean-square displacements of the hydrogen atoms in both RNA and its hydration water exhibit a sharp change in slope at approximately the same temperature 220 K. This latter fact suggests that the dynamic transition in RNA is triggered by the abrupt change of mobility of the hydration water at its FSC temperature.

We report on the surface rheology of cross-linked F-actin networks associated with a lipid monolayer at the air-water interface of a Langmuir monolayer. The rheological measurements are made using a Couette cell. These data demonstrate that the network has a finite elastic modulus that grows as a function of the cross-linking concentration. We also note that under steady-state flow the system behaves as a power-law fluid in which the effective viscosity decreases with imposed shear.

The expected firing probability of a stochastic neuron is approximated by a function of the expected subthreshold membrane potential, for the case of colored noise. We propose this approximation in order to extend the recently proposed white noise model [A. V. Chizhov and L. J. Graham, Phys. Rev. E 75, 011924 (2007)] to the case of colored noise, applying a refractory density approach to conductance-based neurons. The uncoupled neurons of a single population receive a common input and are dispersed by the noise. Within the framework of the model the effect of noise is expressed by the so-called hazard function, which is the probability density for a single neuron to fire given the average membrane potential in the presence of a noise term. To derive the hazard function we solve the Kolmogorov-Fokker-Planck equation for a mean voltage-driven neuron fluctuating due to colored noisy current. We show that a sum of both a self-similar solution for the case of slow changing mean voltage and a frozen stationary solution for fast changing mean voltage gives a satisfactory approximation for the hazard function in the arbitrary case. We demonstrate the quantitative effect of a temporal correlation of noisy input on the neuron dynamics in the case of leaky integrate-and-fire and detailed conductance-based neurons in response to an injected current step.

The elytra of male beetles Chlorophila obscuripennis (Coleoptera) display an inconspicuous iridescent bluish green color. By structural characterizations we find that the outermost elytral surface comprises a sculpted multilayer, which is the origin of structural coloration. In elytra both structural green and cyan colors are observed which arise from the modulations imposed on the multilayer, leading to a bluish green color by color mixing. The adoption of the sculpted multilayer can render structural coloration inconspicuous, which could be advantageous for camouflage. In addition, it can cause light emergence at nonspecular angles.