The effect of time delay on nonlinear oscillators is an important problem in the study of dynamical systems. The dynamics of an erbium-doped fiber ring laser with an extra loop providing time-delayed feedback is studied experimentally by measuring the intensity of the laser. The delay time for the feedback is varied from $\sim 0.3$ to $\sim 900$ times the cavity round-trip time, over four orders of magnitude, by changing the length of fiber in the delay line. Depending on the delay, we observe either regular oscillations or complex dynamics. The size of the fluctuations increases for delays long compared with the round-trip time of the laser cavity. The complexity of the fluctuations is quantified by creating spatiotemporal representations of the time series and performing a Karhunen-Loève decomposition. The complexity increases with increasing delay time. The experiment is extended by mutually coupling two fiber ring lasers together. The delay time for the mutual coupling is varied from $\sim 0.2$ to $\sim 600$ times the cavity round-trip time, over four orders of magnitude again. In this case the fluctuations are generally larger than the single laser case. The complexity of the dynamics for the mutually coupled system is less at short delays and larger at long delays when compared to the uncoupled case. The width of the optical spectra of the coupled lasers also narrows.

We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in systems with spatiotemporal chaos. We focus on characteristic LVs and compare the results with backward LVs obtained via successive Gram-Schmidt orthonormalizations. Systems of a very different nature such as coupled-map lattices and the (continuous-time) Lorenz ‘96 model exhibit the same features in quantitative and qualitative terms. Additionally, we propose a minimal stochastic model that reproduces the results for chaotic systems. Our work supports the claims about universality of our earlier results [I. G. Szendro et al., Phys. Rev. E 76, 025202(R) (2007)] for a specific coupled-map lattice.

A modified version of the usual viscous fingering problem in a radial Hele-Shaw cell with immiscible fluids is studied by intensive numerical simulations. We consider the situation in which the fluids involved are miscible, so that the diffusing interface separating them can be driven unstable through the injection or suction of the inner fluid. The system is allowed to rotate in such a way that centrifugal and Coriolis forces come into play, imposing important changes on the morphology of the arising patterns. In order to bridge from miscible to immiscible pattern forming structures, we add the surface tensionlike effects due to Korteweg stresses. Our numerical experiments reveal a variety of interesting fingering behaviors, which depend on the interplay between injection (or suction), diffusive, rotational, and Korteweg stress effects. Whenever possible the features of the simulated miscible fronts are contrasted to existing experiments and other theoretical or numerical studies, usually resulting in close agreements. A number of additional complex morphologies, whose experimental realization is still not available, are predicted and discussed.

We adress the question of the stability of a confined coflowing jet at low Reynolds number in various geometries. Our study is motivated by recent experiments in microfluidic devices. When immiscible fluids flow in microchannels, either monodisperse droplets or parallel flows are obtained depending upon the flow rate of the aqueous phase and the oil phase. In these experiments, the confining and the shape of the geometry play a fundamental role. In a previous paper [Guillot et al., Phys. Rev. Lett 99, 104502 (2007)], we analyzed the stability of the jet in the framework of the lubrication approximation at low Reynolds number in a cylindrical geometry, and we related the transition between the droplets regime and the jet regime to the absolute-convective transition of the Rayleigh plateau instability. In this work, the effect of the channel geometry and the jet position within the microfluidic device are discussed. New flow patterns are pointed out. Bidimensional jets are encountered in square and rectangular geometry. Contrary to jets occuring in circular geometry, these two-dimensional jets are absolutely stable. Focusing on situations where the inner fluid is more viscous than the outer one, we evidence a range of parameters where droplets are produced through a blocking and pinching mechanism. In this particular case, the flow is unstable, the growing perturbations are convected upstream. This induces the clogging of the channel by the internal phase and its pinching by the external one. In a future presentation we will give a comparison between this model and experimental data.

The formation and evolution of a collisional aluminum plasma jet created by optical laser irradiation of triangular grooves with pulses of $120\mathrm{ps}$ duration at an intensity of $1\times {10}^{12}\mathrm{W}{\mathrm{cm}}^{-2}$ were studied with experiments and simulations. Series of high-contrast soft x-ray laser interferograms obtained with a $46.9\mathrm{nm}$ laser mapped the plasma density evolution of an initially narrow plasma jet that expands along the symmetry plane and evolves into a broader plasma plume with significant side lobes. Two-dimensional simulations performed using the radiation hydrodynamic code HYDRA reveal that the jet formation is initiated by accelerated material ablated from the vertex and is augmented by the continual sequential arrival of wall material along the symmetry plane, where it collides and is redirected outward. Radiative cooling is identified as an important process in maintaining the collimation of the jet. These results demonstrate that well collimated collisional plasma jets with parameters in a range of interest can be generated with low-energy laser pulses $(<1\mathrm{J})$, opening the possibility of studying relevant plasma phenomena in a small laboratory setting.

We present the analysis of a higher-order lattice Boltzmann (LB) method based on the fourth-order Gauss-Hermite quadrature, with emphasis on the slip velocity and the Knudsen layer. The exact solution of the slip velocity for the higher-order LB equation is obtained for Poiseuille flows with finite Knudsen numbers. Due to increased accuracy in velocity space discretization, the higher-order scheme gives much improved slip coefficients as compared with the standard LB method based on the third-order Gauss-Hermite quadrature. A multiple relaxation time model is investigated to show the effects of the relaxation times for higher-order moments on the slip phenomena.

Previous numerical investigations of the stability and bifurcation properties of different nonlinear combination structures of spiral vortices in a counter-rotating Taylor-Couette system that were done for fixed axial wavelengths are supplemented by exploring the dependence of the vortex phenomena waves on their wavelength. This yields information about the experimental and numerical accessibility of the various bifurcation scenarios. Also backward bifurcating standing waves with oscillating amplitudes of the constituent traveling waves are found.

To elucidate slow dynamics in glassy materials, we introduce the figure-8 model in which $N$ hard blocks undergo Brownian motion around a circuit in the shape of a figure 8. This system undergoes kinetic arrest at a critical packing fraction $\varphi ={\varphi }_g<1$, and for $\varphi \approx {\varphi }_g$ long-time diffusion is controlled by rare, cooperative, “junction-crossing” particle rearrangements. We find that the average time between junction crossings ${\tau }_{\mathrm{JC}}$, and hence the structural relaxation time, does not simply scale with the configurational volume ${\Omega }_c$ of transition states, because ${\tau }_{\mathrm{JC}}$ also depends on the time to complete a junction crossing. The importance of these results in understanding cage-breaking dynamics in glassy systems is discussed.

We consider the dynamics of a single tagged particle in a two-dimensional system governed by Lennard-Jones interactions. Previous work based on the Mori-Zwanzig projection operator formalism has shown that the single-particles dynamics can be described via a generalized Langevin equation (GLE) which is exact within the harmonic approximation, that is, for a low-temperature solid [J. M. Deutch and R. Silbey, Phys. Rev. A 3, 2049 (1971)]. In the present work we explore to what an extent the GLE reproduces the effective dynamics under thermodynamic conditions where the harmonic approximation is no longer justified. To this end we compute characteristic time autocorrelation functions for the tagged particle in molecular dynamics simulations of the full system and compare these functions with those obtained from solving the GLE. At low temperatures we find excellent agreement between both data sets. Deviations emerge at higher temperatures which are, however, surprisingly small even in the high-temperature liquid phase.

Broadband dielectric measurements for triethyleneglycol (3EG)-water mixtures with various concentrations were performed in the frequency range of $10\mu \mathrm{Hz}–10\mathrm{GHz}$ and in the temperature range of $130–298\mathrm{K}$. For each mixture, the separation of the primary $\left(\alpha \right)$ and secondary processes is observed below the crossover temperature, $T_C$. In the case of $80–100\mathrm{wt}\%$ 3EG-water mixtures, the Kohlrausch-Williams-Watts–type primary process above $T_C$ continues to the $\alpha$ process below $T_C$, and an additional secondary process is observed in the frequency range higher than that of the $\alpha$ process below $T_C$. On the other hand, the primary process for 65 and $70\mathrm{wt}\%$ 3EG-water mixtures above $T_C$ continues to the higher-frequency secondary process below $T_C$, and an additional $\alpha$ process appears at a frequency lower than that of the secondary process. The contribution of water to relaxation processes is discussed, to clarify the molecular mechanism of the separation behavior. The characteristic separation behavior of the relaxation processes for high-water-content 3EG-water mixtures is due to the existence of excess water, which cannot move cooperatively with solute 3EG molecules below $T_C$.

Recent experiments report that the long-looked-for thermotropic biaxial nematic phase has been finally detected in some thermotropic liquid crystalline systems. Inspired by these experimental observations, we concentrate on some elementary theoretical issues concerned with the classical sixth-order Landau–de Gennes free energy expansion in terms of the symmetric and traceless tensor order parameter $Q_{\alpha \beta }$. In particular, we fully explore the stability of the biaxial nematic phase giving analytical solutions for all distinct classes of the phase diagrams that theory allows. This includes diagrams with triple, critical, and tricritical points and with multiple (reentrant) biaxial and uniaxial phase transitions. A brief comparison with predictions of existing molecular theories is also given.

A model of self-avoiding walks with suitable constraint has been developed to study the effect of temperature on a single-stranded DNA (ssDNA) in the constant force ensemble. Our exact calculations for small chains show that the extension (reaction coordinate) may increase or decrease with the temperature depending on the applied force. The simple model developed here, which incorporates semimicroscopic details of base direction, provides an explanation of the force-induced transitions in ssDNA as observed in experiments.

We studied microrheological properties of $F$-actin across the isotropic-nematic phase transition region by video particle tracking (VPT) and by laser deflection particle tracking (LDPT). Both methods track the motion of thermally driven micron-sized beads, and convert the temporal mean square displacement (MSD) to shear moduli. The two methods give consistent results for the elastic modulus $G^{\prime }$ and less so for the loss modulus $G^{″}$. As the nematic order parameter increases with actin concentration, $G_{\parallel }^{\prime }$ (measured parallel to the nematic director) and $G_{\perp }^{\prime }$ (perpendicular to the director) grow apart, with $G_{\perp }^{\prime }$ larger than $G_{\parallel }^{\prime }$. The moduli scale with actin concentration as $G_{\parallel }^{\prime }\sim c^{0.54\pm 0.13}$ and $G_{\perp }^{\prime }\sim c^{1.38\pm 0.15}$. Furthermore, $G^{\prime }$ and $G^{″}$ dependence on $\left[{\mathrm{Mg}}^{2+}\right]$ were measured and compared for $1\mathrm{mg}∕\mathrm{ml}$ isotropic and $4\mathrm{mg}∕\mathrm{ml}$ nematic $F$-actin solutions, respectively. In the isotropic phase, $G^{\prime }$ increases with $\left[{\mathrm{Mg}}^{2+}\right]$ up to $6\mathrm{mM}$ and then plateaus. In the nematic phase, $G_{\perp }^{\prime }$ is larger than $G_{\parallel }^{\prime }$, and both $G_{\perp }^{\prime }$ and $G_{\parallel }^{\prime }$ increase with $\left[{\mathrm{Mg}}^{2+}\right]$ progressively up to $16\mathrm{mM}$, above which $F$-actin form large bundles. In both isotropic and nematic phases, $G^{″}$ only weakly depends on $\left[{\mathrm{Mg}}^{2+}\right]$. In conclusion, particle tracking microrheology reveals rich rheological features of $F$-actin affected by the isotropic-nematic phase transition and by tuning weak electrostatic interactions among the protein filaments.

Extensive restricted canonical ensemble Monte Carlo simulations [D. S. Corti and P. Debenedetti, Chem. Eng. Sci. 49, 2717 (1994)] for the supersaturated Lennard—Jones (LJ) vapor were performed. These simulations were conducted at different densities and reduced temperatures from 0.7 to 1.0 and the radial density distribution functions were obtained, most of which are unavailable via integral equation theory due to phase separations. Among different constraints imposed on the system studied, the one with the local minimum of the excess free energy was taken to be the one that approximates the equilibrium state of the metastable LJ vapor. For the slightly saturated state points, where integral equation theory does have a solution, compared with our simulations, differences of the radial density distribution functions were found and they are attributed to ignoring density fluctuations in the integral equation theory.

We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive nonlinear Schrödinger equation with a Gaussian random pulse as an initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We also calculate the distribution of a set of scattering data of the Zakharov-Shabat operator that determine the asymptotics of the eigenfunctions. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of information transmission through nonlinear optical fibers.

In a previous paper analytical equations were derived for the packing fraction of crystalline structures consisting of bimodal randomly placed hard spheres [H. J. H. Brouwers, Phys. Rev. E 76, 041304 (2007)]. The bimodal packing fraction was derived for the three crystalline cubic systems: viz., face-centered cubic, body-centered cubic, and simple cubic. These three equations appeared also to be applicable to all 14 Bravais lattices. Here it is demonstrated, accounting for the number of distorted bonds in the building blocks and using graph theory, that one general packing equation can be derived, valid again for all lattices. This expression is validated and applied to the process of amorphization.

The magnetic field of planets or stars is generated by the motion of a conducting fluid through a dynamo instability. The saturation of the magnetic field occurs through the reaction of the Lorentz force on the flow. In relation to this phenomenon, we study the effect of a magnetic field on a turbulent flow of liquid gallium. The measurement of electric potential differences provides a signal related to the local velocity fluctuations. We observe a reduction of velocity fluctuations at all frequencies in the spectrum when the magnetic field is increased.

In this work, we use a dissipative-particle-dynamics-based model for two-phase flows to simulate the breakup of liquid nanocylinders. Rayleigh’s criterion for capillary breakup of inviscid liquid cylinders is shown to apply for the cases considered, in agreement with prior molecular dynamics (MD) simulations. Also, as shown previously through MD simulations, satellite drops are not observed, because of the dominant role played by thermal fluctuations which lead to a symmetric breakup of the neck joining the two main drops. The parameters varied in this study are the domain size, cylinder radius, thermal length scale, viscosity, and surface tension. The breakup time does not show the same scaling dependence as in capillary breakup of liquid cylinders at the macroscale. The time variation of the radius at the point of breakup agrees with prior theoretical predictions from expressions derived with the assumption that thermal fluctuations lead to breakup.

We report in this paper the observation of a transition between two different dendritic growth mechanisms in the electrodeposition of a metal from a binary electrolyte. Our results, in particular concerning the dendritic growth velocities, enable us to explain this behavior in terms of models previously proposed in the literature.

By considering the eigenratio of the Laplacian of the connection graph as a synchronizability measure, we propose a procedure for weighting dynamical networks to enhance their synchronizability. The method is based on node and edge betweenness centrality measures and is tested on artificially constructed scale-free, Watts-Strogatz, and random networks as well as on some real-world graphs. It is also numerically shown that the same procedure could be used to enhance the phase synchronizability of networks of nonidentical oscillators.