The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in the strongly connected component and those in the in and out components. Formal equations for the relative sizes in the number of edges of these giant structures are derived for arbitrary joint degree distributions in the presence of local and two-point correlations. The uncorrelated null model is fully solved analytically and compared against simulations, finding an excellent agreement. Interfaces, and their particular conformations giving place from “hairy ball” percolation landscapes to bottleneck straits, could bring new light to the discussion of how a structure is interwoven with functionality in flow networks.

We investigate the effect of common periodic drive applied to mean-field coupled oscillators and observe a specific realization of synchronization for particular ranges of drive frequency. This synchronization occurs when the phase difference variability between a pair of oscillators on a given cycle is larger than that between consecutive cycles. This synchrony may have implications for neural systems, in which case the apparent locking between neurons based on the magnitude of their interspike intervals may not be consistent with their dynamical locking.

In a recent study [Rempel and Chian, Phys. Rev. Lett. 98, 014101 (2007)], it has been shown that nonattracting chaotic sets (chaotic saddles) are responsible for intermittency in the regularized long-wave equation that undergoes a transition to spatiotemporal chaos (STC) via quasiperiodicity and temporal chaos. In the present paper, it is demonstrated that a similar mechanism is present in the damped Kuramoto-Sivashinsky equation. Prior to the onset of STC, a spatiotemporally chaotic saddle coexists with a spatially regular attractor. After the transition to STC, the chaotic saddle merges with the attractor, generating intermittent bursts of STC that dominate the post-transition dynamics.

Thermal instability in a horizontal Newtonian liquid layer with rigid boundaries is investigated in the presence of vertical quasiperiodic forcing having two incommensurate frequencies ${\omega }_1$ and ${\omega }_2$. By means of a Galerkin projection truncated to the first order, the governing linear system corresponding to the onset of convection is reduced to a damped quasiperiodic Mathieu equation. The threshold of convection corresponding to quasiperiodic solutions is determined in the cases of heating from below and heating from above. We show that a modulation with two incommensurate frequencies has a stabilizing or a destabilizing effect depending on the frequencies ratio $\omega ={\omega }_2∕{\omega }_1$. The effect of the Prandtl number in a stabilizing zone is also examined for different frequency ratios.

In the present work, first, plasma phase variables in a cylindrical radio-frequency (rf) plasma reactor are numerically solved using the local field approximation model. Then, equilibrium configurations of a few interacting (sub-)micron-sized dust particles are obtained by integrating the particles equations for their motion and charge, accounting for the various forces acting on each particle in a three-dimensional Lagrangian framework. Direct comparison of the results with experiment demonstrates excellent qualitative agreement. Based on the ion focus phenomenon, a physical model is formulated and proven successful in simulating the vertically aligned structures.

The first operation of a coaxial free-electron maser (FEM) based on two-dimensional (2D) distributed feedback has been recently observed. Analytical and numerical modeling, as well as measurements, of microwave radiation generated by a FEM with a cavity defined by coaxial structures with a 2D periodic perturbation on the inner surfaces of the outer conductor were carried out. The two-mirror cavity was formed with two 2D periodic structures separated by a central smooth section of coaxial waveguide. The FEM was driven by a large diameter $\left(7\mathrm{cm}\right)$, high-current $\left(500\mathrm{A}\right)$, annular electron beam with electron energy of $475\mathrm{keV}$. Studies of the FEM operation have been conducted. It has been demonstrated that by tuning the amplitude of the undulator or guide magnetic field, modes associated with the different band gaps of the 2D structures were excited. The Ka-band FEM generated $15\mathrm{MW}$ of radiation with a 6% conversion efficiency, in good agreement with theory.

Because of Euler buckling, a simple strut of length $L$ and Young modulus $Y$ requires a volume of material proportional to $L^3{f}^{1∕2}$ in order to support a compressive force $F$, where $f=F∕Y{L}^2$ and $f⪡1$. By taking into account both Euler and local buckling, we provide a hierarchical design for such a strut consisting of intersecting curved shells, which requires a volume of material proportional to the much smaller quantity $L^{3}f\text{exp}\left[2\sqrt{\left(\text{ln}3\right)\left(\text{ln}{f}^{-1}\right)}\right]$.

In this Brief Report, we study the synchronization of growing scale-free networks. An asymmetrical age-based coupling method is proposed with only one free parameter $\alpha$. Although the coupling matrix is asymmetric, our coupling method could guarantee that all the eigenvalues are non-negative reals. The eigenratio $R$ will approach 1 in the large limit of $\alpha$.

Quantum fluctuation of the energy is studied for an ultracold gas of interacting fermions trapped in a three-dimensional potential. Periodic-orbit theory is explored, and energy fluctuations are studied versus the particle number for generic regular and chaotic systems, as well as for a system defined by a harmonic confinement potential. Temperature effects on the energy fluctuations are investigated.

We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWNs). The SWNs are built from a one-dimensional ring of $N$ nodes by randomly introducing $B$ additional bonds between them. The exciton dynamics is modeled by continuous-time quantum walks, and we evaluate numerically the ensemble-averaged transition probability to reach any node of the network from the initially excited one. For sufficiently large $B$ we find that the quantum mechanical transport through the SWNs is, first, very fast, given that the limiting value of the transition probability is reached very quickly, and second, that the transport does not lead to equipartition, given that on average the exciton is most likely to be found at the initial node.

We study the formation of columnar structures of uniaxial dipoles in an external magnetic field both experimentally and theoretically. By applying an external magnetic field parallel to a thin layer of a magnetorheological fluid, we manipulate a single initial cluster of suspended colloidal particles. We find that the cluster breaks up into columns that have approximately uniform widths and intercolumnar spacings. Both the average column width and inter column spacing are observed to vary linearly with column length. The observed linear relationships between column width and spacing versus the column length are interpreted theoretically by computing the potential energy of an ensemble of closed-packed columns of spherical dipolar particles.

From magnetic resonance imaging rheometry we show that a pure emulsion can be turned from a simple yield stress fluid to a thixotropic material by adding a small fraction of colloidal particles. The two fluids have the same behavior in the liquid regime but the loaded emulsion exhibits a critical shear rate below which no steady flows can be observed. For a stress below the yield stress, the pure emulsion abruptly stops flowing, whereas the viscosity of the loaded emulsion continuously increases in time, which leads to an apparent flow stoppage. This phenomenon can be very well represented by a model assuming a progressive increase of the number of droplet links via colloidal particles.

We present the behavior of depletion-induced gels for vesicle-polymer mixtures when the ratio of the polymer radius of gyration to the mean vesicle radius is 0.09 and 0.27. As the polymer concentration increases, density gradients build up and an interface is developed between a highly turbid vesicle-rich phase and a polymer-rich phase. Increasing the polymer concentration further forms a gel ($C_P=0.3$ and $0.1\mathrm{wt}\%$ for $R_g∕a\approx 0.09$ and 0.27, respectively), which subsequently collapses. This collapse is characterized by a slow initial rising for a finite delay time, a rapid collapse, and a slow final compaction to an equilibrium height. However, we observe a remarkably different polymer concentration dependence on the collapse rate. Unlike other colloidal gels, we find that the delay time for the vesicle collapse decreases with increasing polymer concentration. We show that this behavior can be accounted for by considering the permeability for solvent backflow, which is directly related to the characteristic pore area of the gel obtained using confocal microscopy.

We numerically study the ground states of particles interacting via a repulsive Yukawa potential on two rigid substrates shaped as isolated and periodically arranged bumps characterized by a spatially varying Gaussian curvature. Below a critical aspect ratio that describes the substrate deformation, the lattice is frustrated, but defect free. A further increase of the aspect ratio triggers defect unbinding transitions that lower the total potential energy by introducing dislocations either in isolation or within grain boundaries. In the presence of very strong deformations, isolated disclinations are nucleated. We show that the character and spatial distribution of defects observed in the ground state reflect the symmetries and periodicity of the two model surfaces investigated in this study.

The orientational characterisitics and the temperature dependencies of the molecular apparent tilt angle of a partly fluorinated chiral smectic liquid crystal (/S/)-4-(1-methylheptyloxycarbonyl)phenyl $4^{\prime }$-[6-(3,4,4,4-tetrafluoro-3-trifluoromethylbutylcarbonyloxy)hexyloxy] biphenyl-4-carboxylate (acronym MHPHFHHOBC) are studied using the polarized Fourier transform infrared (FTIR) spectroscopy. The molecular orientational distributions and the orientational order parameters for a homogeneously aligned liquid crystalline sample at various temperatures and external electric fields are examined. The analysis uses the dichroic parameters of the phenyl and the carbonyl bands. For a temperature range of $65–80°\mathrm{C}$ corresponding to the antiferroelectric $\mathrm{Sm}C_A{}^{*}$ phase, the molecular apparent tilt angle lies within the range 43°–44°; antiferroelectric smectic structure being rather close to the orthoconic $\mathrm{Sm}C_A{}^{*}$ phase. An application of sufficiently high dc field across the cell in its $\mathrm{Sm}{A}^{*}$ phase surprisingly shows that the dichroism first increases slowly and then rapidly in two stages and finally a saturated apparent tilt angle of $\sim 30°$ is reached. The IR dichroic data is used to estimate the polar angles and the degree of rotational biasing of the carbonyl groups with respect to the molecular long axis. In the $\mathrm{Sm}{A}^{*}$ phase, the sample appears to demonstrate some of the typical properties of a de Vries material.

Calcium (Ca) plays an important role in regulating various cellular processes. In a variety of cell types, Ca signaling occurs within microdomains where channels deliver localized pulses of Ca activating a nearby collection of Ca-sensitive receptors. The small number of channels involved ensures that the signaling process is stochastic. The aggregate response of several thousand of these microdomains yields a whole-cell response which dictates the cell behavior. Here, we study the statistical properties of a population of these microdomains in response to a trigger signal. We use a first-passage-time approach to show analytically how Ca release in the whole cell depends on properties of Ca channels within microdomains. Using these results we explain for the first time the underlying mechanism for the graded relationship between Ca influx and Ca release in cardiac cells.

The largest eigenvalue of the adjacency matrix of a network plays an important role in several network processes (e.g., synchronization of oscillators, percolation on directed networks, and linear stability of equilibria of network coupled systems). In this paper we develop approximations to the largest eigenvalue of adjacency matrices and discuss the relationships between these approximations. Numerical experiments on simulated networks are used to test our results.

We studied a single bubble sonoluminescence system consisting of an argon bubble in a sulfuric acid aq. solution. We experimentally determined the relevant variables of the system. We also measured the bubble position, extent of the bubble orbits, and light intensity as a function of acoustic pressure for different argon concentrations. We find that the Bjerknes force is responsible for the bubble mean position and this imposes a limitation in the maximum acoustic pressure that can be applied to the bubble. The Rayleigh-Taylor instability does not play a role in this system and, at a given gas concentration, the SL intensity depends more on the bubble time of collapse than any other investigated parameter.

A two-dimensional model for the erosion generated by viscous free-surface flows, based on the shallow-water equations and the lubrication approximation, is presented. It has a family of self-similar solutions for straight erodible channels, with an aspect ratio that increases in time. It is also shown, through a simplified stability analysis, that a laminar river can generate various bar instabilities very similar to those observed in natural rivers. This theoretical similarity reflects the meandering and braiding tendencies of laminar rivers indicated by F. Métivier and P. Meunier [J. Hydrol. 27, 22 (2003)]. Finally, we propose a simple scenario for the transition between patterns observed in experimental erodible channels.

We find that a liquid jet can bounce off a bath of the same liquid if the bath is moving horizontally with respect to the jet. Previous observations of jets rebounding off a bath (e.g., the Kaye effect) have been reported only for non-Newtonian fluids, while we observe bouncing jets in a variety of Newtonian fluids, including mineral oil poured by hand. A thin layer of air separates the bouncing jet from the bath, and the relative motion replenishes the film of air. Jets with one or two bounces are stable for a range of viscosity, jet flow rate and velocity, and bath velocity. The bouncing phenomenon exhibits hysteresis and multiple steady states.