We study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the time-dependent order parameter, which characterizes the synchronization between the oscillators. The known critical coupling strength is exactly recovered by the Gaussian theory. Extensive numerical experiments further show that the analytical results are very accurate below and sufficiently above the critical value. We obtain the asymptotic order parameter in closed form, which suggests a tighter upper bound for the corresponding scaling. As a last point, we elaborate the Gaussian approximation in complex networks with distributed degrees.

The yield stress is a defining feature of amorphous materials which is difficult to analyze theoretically, because it stems from the strongly nonlinear response of an arrested solid to an applied deformation. Mode-coupling theory predicts the flow curves of materials undergoing a glass transition and thus offers predictions for the yield stress of amorphous solids. We use this approach to analyze several classes of disordered solids, using simple models of hard-sphere glasses, soft glasses, and metallic glasses for which the mode-coupling predictions can be directly compared to the outcome of numerical measurements. The theory correctly describes the emergence of a yield stress of entropic nature in hard-sphere glasses, and its rapid growth as density approaches random close packing at qualitative level. By contrast, the emergence of solid behavior in soft and metallic glasses, which originates from direct particle interactions is not well described by the theory. We show that similar shortcomings arise in the description of the caging dynamics of the glass phase at rest. We discuss the range of applicability of mode-coupling theory to understand the yield stress and nonlinear rheology of amorphous materials.

The properties of fluids can be significantly altered by the geometry of their confining environments. While there has been significant work on the properties of such confined fluids, the properties of fluids under ultraconfinement, environments where, at least in one plane, the dimensions of the confining environment are similar to that of the confined molecule, have not been investigated. This paper investigates the dynamic properties of water in beryl (Be${}_3$Al${}_2$Si${}_6$O${}_{18}$), the structure of which contains approximately 5-Å-diam channels parallel to the $c$ axis. Three techniques, inelastic neutron scattering, quasielastic neutron scattering, and dielectric spectroscopy, have been used to quantify these properties over a dynamic range covering approximately 16 orders of magnitude. Because beryl can be obtained in large single crystals we were able to quantify directional variations, perpendicular and parallel to the channel directions, in the dynamics of the confined fluid. These are significantly anisotropic and, somewhat counterintuitively, show that vibrations parallel to the $c$-axis channels are significantly more hindered than those perpendicular to the channels. The effective potential for vibrations in the $c$ direction is harder than the potential in directions perpendicular to it. There is evidence of single-file diffusion of water molecules along the channels at higher temperatures, but below 150 K this diffusion is strongly suppressed. No such suppression, however, has been observed in the channel-perpendicular direction. Inelastic neutron scattering spectra include an intramolecular stretching O-H peak at ∼465 meV. As this is nearly coincident with that known for free water molecules and approximately 30 meV higher than that in liquid water or ice, this suggests that there is no hydrogen bonding constraining vibrations between the channel water and the beryl structure. However, dielectric spectroscopic measurements at higher temperatures and lower frequencies yield an activation energy for the dipole reorientation of 16.4 ± 0.14 kJ/mol, close to the energy required to break a hydrogen bond in bulk water. This may suggest the presence of some other form of bonding between the water molecules and the structure, but the resolution of the apparent contradiction between the inelastic neutron and dielectric spectroscopic results remains uncertain.

Experiments have shown that elasticity of disordered filamentous networks with compliant crosslinks is very different from networks with rigid crosslinks. Here, we model and analyze filamentous networks as a collection of randomly oriented rigid filaments connected to each other by flexible crosslinks that are modeled as wormlike chains. For relatively large extensions we allow for enthalpic stretching of crosslink backbones. We show that for sufficiently high crosslink density, the network linear elastic response is affine on the scale of the filaments’ length. The nonlinear regime can become highly nonaffine and is characterized by a divergence of the elastic modulus at finite strain. In contrast to the prior predictions, we do not find an asymptotic regime in which the differential elastic modulus scales linearly with the stress, although an approximate linear dependence can be seen in a transition from entropic to enthalpic regimes. We discuss our results in light of recent experiments.

We propose a method for obtaining the intrinsic, long-time mean square displacement (MSD) of atoms and molecules in proteins from finite-time molecular dynamics (MD) simulations. Typical data from simulations are limited to times of 1 to 10 ns, and over this time period the calculated MSD continues to increase without a clear limiting value. The proposed method consists of fitting a model to MD simulation-derived values of the incoherent intermediate neutron scattering function, $I_{\mathrm{inc}}(\mathbf{Q},t)$, for finite times. The infinite-time MSD, $\langle r^2\rangle$, appears as a parameter in the model and is determined by fits of the model to the finite-time $I_{\mathrm{inc}}(\mathbf{Q},t)$. Specifically, the $\langle r^2\rangle$ is defined in the usual way in terms of the Debye-Waller factor as $I(\mathbf{Q},t=\infty )=\exp (-Q^2\langle r^2\rangle /3)$. The method is illustrated by obtaining the intrinsic MSD $\langle r^2\rangle$ of hydrated lysozyme powder ($h=0.4$ g water/g protein) over a wide temperature range. The intrinsic $\langle r^2\rangle$ obtained from data out to 1 and to 10 ns is found to be the same. The intrinsic $\langle r^2\rangle$ is approximately twice the value of the MSD that is reached in simulations after times of 1 ns which correspond to those observed using neutron instruments that have an energy resolution width of 1 $\mu$eV.

The chaotic dynamics of pointlike, spherical particles in cylindrical Poiseuille flow is theoretically characterized and numerically confirmed when their own intrinsic swimming velocity undergoes temporal fluctuations around an average value. Two dimensionless ratios associated with the three significant temporal scales of the problem are identified that fully determine the chaos scenario. In particular, small but finite periodic fluctuations of swimming speed result in chaotic or regular motion depending on the position and orientation of the microswimmer with respect to the flow center line. Remarkably, the spatial extension of chaotic microswimmers is found to depend crucially on the fluctuations' period and amplitude and to be highly sensitive to the Fourier spectrum of the fluctuations. This has implications for the design of artificial microswimmers.

We study a chain of anharmonic springs with tunable power law interactions as a minimal model to explore the propagation of strongly nonlinear solitary wave excitations in a background of thermal fluctuations. By treating the solitary waves as quasiparticles, we derive an effective Langevin equation and obtain their damping rate and thermal diffusion. These analytical findings compare favorably against numerical results from a Langevin dynamic simulation. In our chains composed of two-sided nonlinear springs, we report the existence of an expansion solitary wave (antisoliton) in addition to the compressive solitary waves observed for noncohesive macroscopic particles.

In this work we apply point canonical transformations to solve some classes of two coupled nonautonomous nonlinear Schrödinger equations with specific cubic and quintic—time- and space-dependent—nonlinearities. The method applied here allows us to find a class of wide localized (in space) vector soliton solutions of nonautonomous nonlinear Schrödinger equations. The vector solitons found here can be applied to theoretical studies of Bose-condensed atoms in two different internal states and of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities.

Optical properties of periodic structures can be calculated using the transfer-matrix approach, which establishes a relation between amplitudes of the wave incident on a structure with transmitted or reflected waves. The transfer matrix can be used to obtain transmittance and reflectance spectra of finite periodic structures as well as eigenmodes of infinite structures. Traditionally, calculation of the transfer matrix is performed in the frequency domain and involves linear algebra. In this work, we present a technique for calculation of the transfer matrix using the finite-difference time-domain (FDTD) method and show the way of its implementation in FDTD code. To illustrate the performance of our technique we calculate the transmittance spectra for opal photonic crystal slabs consisting of multiple layers of spherical scatterers. Our technique can be used for photonic band structure calculations. It can also be combined with existing FDTD methods for the analysis of periodic structures at an oblique incidence, as well as for modeling point sources in a periodic environment.

Based on numerical simulations with a stochastic three-phase traffic flow model, we reveal that moving queues (moving jams) in oversaturated city traffic dissolve at some distance upstream of the traffic signal while transforming into synchronized flow. It is found that, as in highway traffic [Kerner, Phys. Rev. E 85, 036110 (2012)], such a jam-absorption effect in city traffic is explained by a strong driver's speed adaptation: Time headways (space gaps) between vehicles increase upstream of a moving queue (moving jam), resulting in moving queue dissolution. It turns out that at given traffic signal parameters, the stronger the speed adaptation effect, the shorter the mean distance between the signal location and the road location at which moving queues dissolve fully and oversaturated traffic consists of synchronized flow only. A comparison of the synchronized flow in city traffic found in this Brief Report with synchronized flow in highway traffic is made.

Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching types in coupled nonlinear oscillators. The transition from AD to OD has been recently realized due to the interplay between heterogeneity and coupling strength [A. Koseska et al., Phys. Rev. Lett. 111, 024103 (2013)]. We identify here the transition from AD to OD in nonlinear oscillators with couplings of distinct natures. It is demonstrated that the presence of time delay in the coupling cannot induce such a transition in identical oscillators, but it can indeed facilitate its occurrence with a low degree of heterogeneity. Moreover, it is further shown that the AD to OD transition is reliably observed in identical oscillators with dynamic and conjugate couplings. The coexistence of AD and OD and rich stable OD configurations after the transition are revealed, which are of great significance for potential applications in physics, biology, and control studies.

We study localization properties of the eigenstates and wave transport in a one-dimensional system consisting of a set of barriers and/or wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced Anderson localization is the presence of the resonances emerging due to the coherent interaction of the waves reflected from the interfaces between the wells and/or barriers. Our theoretical approach allows to derive the localization length in infinite samples both out of the resonances and close to them. We examine how the transport properties of finite samples can be described in terms of this length. It is shown that the analytical expressions obtained by standard methods for continuous random potentials can be used in our discrete model, in spite of the presence of resonances that cannot be described by conventional theories. All our results are illustrated with numerical data manifesting an excellent agreement with the theory.

The Green-Kubo formula for linear response coefficients is modified when dealing with nonequilibrium dynamics. In particular, negative differential conductivities are allowed to exist away from equilibrium. We give a unifying framework for such a negative differential response in terms of the frenetic contribution in the nonequilibrium formula. It corresponds to a negative dependence of the escape rates and reactivities on the driving forces. Partial caging in state space and reduction of dynamical activity with increased driving cause the current to drop. These are time-symmetric kinetic effects that are believed to play a major role in the study of nonequilibria. We give various simple examples treating particle and energy transport, which all follow the same pattern in the dependence of the dynamical activity on the nonequilibrium driving, made visible from recently derived nonequilibrium response theory.

We generalize the linearized Gouy-Chapman-Stern theory of an electric double layer for morphologically complex and disordered electrodes. An equation for capacitance is obtained using a linear Gouy-Chapman or Debye-Hückel equation for the potential near the complex-geometry electrode-electrolyte interface. The effect of the surface morphology of an electrode on an electric double layer is obtained using multiple scattering formalism in surface curvature. The result for capacitance is expressed in terms of the ratio of Gouy screening length to the local principal radii of curvatures of the surface. We also include a contribution of a compact layer, which is significant in the overall prediction of capacitance. Our general results are analyzed in detail for two special morphologies of electrodes, i.e., a nanoporous membrane and a forest of nanopillars. Variations of local shapes and global size variations due to residual randomness in morphology are accounted for as curvature fluctuations over a reference shape element. In particular, the theory shows that the presence of geometrical fluctuations in porous systems causes an enhanced dependence of capacitance on mean pore sizes and suppresses the magnitude of capacitance. This theory is further extended to include contributions to capacitance from adsorption of ions and electrode material due to electronic screening. Our predictions are in reasonable agreement with recent experimental measurements on supercapacitive microporous and mesoporous systems.

Temperature dependence of the configurational fluctuation of water confined in a reverse micellar solution has been studied by absorption spectroscopy of a probe molecule. We have found that the configurational fluctuation is liquidlike below the homogeneous nucleation temperature. This is proposed to be due to a large reduction in the confinement of water, and is explained in terms of water shedding from the reverse micelle. Further, the configurational fluctuation is frozen at ∼210 K. A reverse micellar solution is considered to be a promising candidate for studies of supercooled water.

Frictional properties of contacts between a smooth viscoelastic rubber and rigid surfaces are investigated using a torsional contact configuration where a glass lens is continuously rotated on the rubber surface. From the inversion of the displacement field measured at the surface of the rubber, spatially resolved values of the steady state frictional shear stress are determined within the nonhomogeneous pressure and velocity fields of the contact. For contacts with a smooth lens, a velocity-dependent but pressure-independent local shear stress is retrieved from the inversion. On the other hand, the local shear stress is found to depend on both velocity and applied contact pressure when a randomly rough (sand-blasted) glass lens is rubbed against the rubber surface. As a result of changes in the density of microasperity contacts, the amount of light transmitted by the transparent multicontact interface is observed to vary locally as a function of both contact pressure and sliding velocity. Under the assumption that the intensity of light transmitted by the rough interface is proportional to the proportion of area into contact, it is found that the local frictional stress can be expressed experimentally as the product of a purely velocity-dependent term, $k\left(v\right)$, by a term representing the pressure and velocity dependence of the actual contact area, $A/A_0$. A comparison between $k\left(v\right)$ and the frictional shear stress of smooth contacts suggests that nanometer scale dissipative processes occurring at the interface predominate over viscoelastic dissipation at microasperity scale.

Real data show that interdependent networks usually involve intersimilarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent [Parshani et al. Europhys. Lett. 92, 68002 (2010)]. For example, the coupled worldwide port network and the global airport network are intersimilar since many pairs of linked nodes (neighboring cities), by direct flights and direct shipping lines, exist in both networks. Nodes in both networks in the same city are regarded as interdependent. If two neighboring nodes in one network depend on neighboring nodes in the other network, we call these links common links. The fraction of common links in the system is a measure of intersimilarity. Previous simulation results of Parshani et al. suggest that intersimilarity has considerable effects on reducing the cascading failures; however, a theoretical understanding of this effect on the cascading process is currently missing. Here we map the cascading process with intersimilarity to a percolation of networks composed of components of common links and noncommon links. This transforms the percolation of intersimilar system to a regular percolation on a series of subnetworks, which can be solved analytically. We apply our analysis to the case where the network of common links is an Erdős-Rényi (ER) network with the average degree $K$, and the two networks of noncommon links are also ER networks. We show for a fully coupled pair of ER networks, that for any $K⩾0$, although the cascade is reduced with increasing $K$, the phase transition is still discontinuous. Our analysis can be generalized to any kind of interdependent random network systems.

Current periodic structures are constrained to have fixed energy transmission behavior unless active control or component replacement is used to alter their wave propagation characteristics. The introduction of nonlinearity to generate multiple stable equilibria is an alternative strategy for realizing distinct energy propagation behaviors. We investigate the creation of a reconfigurable band-gap system by implementing passive switching between multiple stable states of equilibrium, to alter the level of energy attenuation in response to environmental stimuli. The ability to avoid potentially catastrophic loads is demonstrated by tailoring the bandpass and band-gap regions to coalesce for two stable equilibria and varying an external load parameter to trigger a bifurcation. The proposed phenomenon could be utilized in remote or autonomous applications where component modifications and active control are impractical.

We implement a method to identify the deterministic nature of specific events in the dynamics of a semiconductor laser subject to time-delayed optical feedback. Specifically, we study the power dropouts in the low-frequency fluctuations regime on an individual event basis and identify whether the underlying dominant mechanism is deterministic. Our approach is based on sychronization with a twin system in a symmetric relay configuration. We investigate the dependence of the fraction of deterministically driven (i.e., synchronized) dropouts on the laser's pump current as a key parameter. Our experimental results are corroborated by numerical modeling based on rate equations. Our numerical findings also provide insights into the influence of spontaneous emission noise.

It is well known that the transient behavior during drainage or imbibition in multiphase flow in porous media strongly depends on the history and initial condition of the system. However, when the steady-state regime is reached and both drainage and imbibition take place at the pore level, the influence of the evolution history and initial preparation is an open question. Here, we present an extensive experimental and numerical work investigating the history dependence of simultaneous steady-state two-phase flow through porous media. Our experimental system consists of a Hele-Shaw cell filled with glass beads which we model numerically by a network of disordered pores transporting two immiscible fluids. From measurements of global pressure evolution, histograms of saturation, and cluster-size distributions, we find that when both phases are flowing through the porous medium, the steady state does not depend on the initial preparation of the system or on the way it has been reached.