In this paper, we analyze a model of broad area vertical-cavity surface-emitting lasers subjected to frequency-selective optical feedback. In particular, we analyze the spatio-temporal regimes arising above threshold and the existence and dynamical properties of cavity solitons. We build the bifurcation diagram of stationary self-localized states, finding that branches of cavity solitons emerge from the degenerate Hopf bifurcations marking the homogeneous solutions with maximal and minimal gain. These branches collide in a saddle-node bifurcation, defining a maximum pump current for soliton existence that lies below the threshold of the laser without feedback. The properties of these cavity solitons are in good agreement with those observed in recent experiments.

Assuming the conventional Casimir setting with two thick parallel perfectly conducting plates of large extent with a homogeneous and isotropic medium between them, we discuss the physical meaning of the electromagnetic field energy $W_{\mathrm{disp}}$ when the intervening medium is weakly dispersive but nondissipative. The presence of dispersion means that the energy density contains terms of the form $d\left[\omega \epsilon \left(\omega \right)\right]∕d\omega$ and $d\left[\omega \mu \left(\omega \right)\right]∕d\omega$. We find that, as $W_{\mathrm{disp}}$ refers thermodynamically to a nonclosed physical system, it is not to be identified with the internal thermodynamic energy $U$ following from the free energy $F$, or the electromagnetic energy $W$, when the last-mentioned quantities are calculated without such dispersive derivatives. To arrive at this conclusion, we adopt a model in which the system is a capacitor, linked to an external self-inductance $L$ such that stationary oscillations become possible. Therewith the model system becomes a nonclosed one. As an introductory step, we review the meaning of the nondispersive energies, $F$, $U$, and $W$. As a final topic, we consider an anomaly connected with local surface divergences encountered in Casimir energy calculations for higher space-time dimensions, $D>4$, and discuss briefly its dispersive generalization. This kind of application is essentially a generalization of the treatment of Alnes et al. [J. Phys. A 40, F315 (2007)] to the case of a medium-filled cavity between two hyperplanes.

We conduct a numerical study of the dynamical behavior of a system of three-dimensional “crosses,” particles that consist of three mutually perpendicular line segments of length $\sigma$ rigidly joined at their midpoints. In an earlier study [W. van Ketel et al., Phys. Rev. Lett. 94, 135703 (2005)] we showed that this model has the structural properties of an ideal gas, yet the dynamical properties of a strong glass former. In the present paper we report an extensive study of the dynamical heterogeneities that appear in this system in the regime where glassy behavior sets in. On the one hand, we find that the propensity of a particle to diffuse is determined by the structure of its local environment. The local density around mobile particles is significantly less than the average density, but there is little clustering of mobile particles, and the clusters observed tend to be small. On the other hand, dynamical susceptibility results indicate that a large dynamical length scale develops even at moderate densities. This suggests that propensity and other mobility measures are an incomplete measure of the dynamical length scales in this system.

The transition to synchronization of a pair of coupled chaotic $\mathrm{C}{\mathrm{O}}_2$ lasers is investigated numerically in a model system. This system displays episodes of bursting of different predominant frequencies. Due to the multiple time scales present in this system, we use a complex continuous wavelet transform to perform the synchronization analysis. Thus it enables us to resolve the time of occurrence as well as the frequency of an event in a given time series up to an intrinsic uncertainty. Furthermore, due to the complex nature of that wavelet transform, it yields a direct estimate of the system’s phase. We show that, as the coupling strength of the laser system is increased, the mutual coherency increases differently for different frequencies. Additionally we test our method with experimental data.

In this paper we investigate the transition to chaos in the motion of particles advected by open flows with obstacles. By means of a topological argument, we show that the separation points on the surface of the obstacle imply the existence of a saddle point downstream from the obstacle, with an associated heteroclinic orbit. We argue that as soon as the flow becomes time periodic, these orbits give rise to heteroclinic tangles, causing passively advected particles to experience transient chaos. The transition to chaos thus coincides with the onset of time dependence in open flows with stagnant points, in contrast with flows with no stagnant points. We also show that the nonhyperbolic nature of the dynamics near the walls causes anomalous scalings in the vicinity of the transition. These results are confirmed by numerical simulations of the two-dimensional flow around a cylinder.

Formation of a cylindrical dust void in dust plasma crystals is simulated using the molecular dynamics method in a three-dimensional fluid sheath model with axisymmetry. The dust trajectories are integrated under a self-consistent field composed of the interactions with the electrostatic sheath field, gravity, drags, wakes, and nonlinear screened Coulomb forces. The simulation successfully explains how a uniform dust cloud transforms into a dust void as the dust particles grow to a sufficient size [D. Samsonov et al., Phys. Rev. E 59, 1047 (1999)] or the power supply and/or gas pressure increases to certain levels [R. P. Dahiya et al., Phys. Rev. Lett. 89, 125001 (2002)]. It is found that instead of the ion drag or thermophoretic force effect, the formation of the dust void in the axisymmetric three-dimensional sheath is due to a gentle potential bump in the central region of the electrode caused by the cylindrical geometry.

The viscosity and self-diffusion constant of particle-based mesoscale hydrodynamic methods, multiparticle collision dynamics (MPC), and dissipative particle dynamics, are investigated, both with and without angular-momentum conservation. Analytical results are derived for fluids with an ideal-gas equation of state and a finite-time-step dynamics, and compared with simulation data. In particular, the viscosity is derived in a general form for all variants of the MPC method. In general, very good agreement between theory and simulations is obtained.

Wall boundary conditions for the lattice Boltzmann equation (LBE) method for nonideal gases proposed by Lee and Fischer [Phys. Rev. E 74, 046709 (2006)] are examined. The LBE simulations of the contact line are typically contaminated by small but strong counter-rotating parasitic currents near solid surfaces. We find that these currents can be eliminated to round-off if the potential form of the intermolecular force is used with the boundary conditions based on the wall energy approach and the bounce-back rule. Numerical tests confirm the elimination of the parasitic currents in the vicinity of the contact line and the agreement of the calculated density, excess mass, and contact angle at the solid surfaces with theory.

The large deviation function for entropy production is calculated by solving a time-independent eigenvalue problem for a particle driven along a periodic potential. In an intermediate force regime, the large deviation function shows pronounced deviations from a Gaussian behavior with a characteristic “kink” at zero entropy production. Such a feature can also be extracted from the analytical solution of the asymmetric random walk to which the driven particle can be mapped in a certain parameter range.

In a recent Letter [N. D. Denkov et al., Phys. Rev. Lett. 100, 138301 (2008)] we calculated theoretically the macroscopic viscous stress of steadily sheared foam or emulsion from the energy dissipated inside the transient planar films, formed between neighboring bubbles or drops in the shear flow. The model predicts that the viscous stress in these systems should be proportional to ${\text{Ca}}^{1/2}$, where Ca is a capillary number and $n=1/2$ is the power-law index. In the current paper we explain our model in detail and develop it further in several aspects: First, we extend the model to account for the effects of viscous friction in the curved meniscus regions, surrounding the planar films, on the dynamics of film formation and on the total viscous stress. Second, we consider the effects of surface forces (electrostatic, van der Waals, etc.) acting between the surfaces of the neighboring bubbles or drops and show that these forces could be important in emulsions, due to the relatively small thickness of emulsion films (often comparable to the range of action of surface forces). In contrast, the surface forces are usually negligible in steadily sheared foams, because the dynamic foam films are thicker than the extent of surface forces, except for foams containing micrometer-sized bubbles and/or at very low shear rates. Third, additional consideration is made for bubbles or drops exhibiting high surface viscosity, for which we demonstrate an additional contribution to the macroscopic viscous stress, created by the surface dissipation of energy. The new upgraded model predicts that the energy dissipation at the bubble or drop surface leads to power-law index $n<1/2$, whereas the contribution of the surface forces leads to $n>1/2$, which explains the rich variety of foam or emulsion behaviors observed upon steady shear. Various comparisons are made between model predictions and experimental results for both foams and emulsions, and very good agreement is found.

A statistical analysis of random lasing events observed in dye-doped nematic-liquid-crystal films is reported. The occurrence of random laser action in such complex fluids is due to residual resonances in the multiple scattering of spontaneously emitted photons. The Shannon entropy and a local-Poisson test are used here in order to quantitatively characterize the chaotic behavior of laser spikes and gain further understanding of the mechanisms underlying the lasing effect in strongly scattering organized fluids arising by an unexpected interplay of localization and amplification.

The formation of bundles composed of actin filaments and cross-linking proteins is an essential process in the maintenance of the cells’ cytoskeleton. It has also been recreated by in-vitro experiments, where actin networks are routinely produced to mimic and study the cellular structures. It has been observed that these bundles seem to have a well-defined width distribution, which has not been adequately described theoretically. We propose here that packing defects of the filaments, quenched and random, contribute an effective repulsion that counters the cross-linking adhesion energy and leads to a well-defined bundle width. This is a two-dimensional strain-field version of the classic Rayleigh instability of charged droplets.

We show that Brownian motion is spatially not symmetric for mesoscopic particles embedded in a fluid if the particle is not in thermal equilibrium and its shape is not spherical. In view of applications to molecular motors in biological cells, we sustain nonequilibrium by stopping a nonspherical particle at periodic sites along a filament. Molecular dynamics simulations in a Lennard-Jones fluid demonstrate that directed motion is possible without a ratchet potential or temperature gradients if the asymmetric nonequilibrium relaxation process is hindered by external stopping. Analytical calculations in the ideal gas limit show that motion even against a fluid drift is possible and that the direction of motion can be controlled by the shape of the particle, which is completely characterized by tensorial Minkowski functionals.

Estimation of the input parameters of stochastic (leaky) integrate-and-fire neuronal models is studied. It is shown that the presence of a firing threshold brings a systematic error to the estimation procedure. Analytical formulas for the bias are given for two models, the randomized random walk and the perfect integrator. For the third model considered, the leaky integrate-and-fire model, the study is performed by using Monte Carlo simulated trajectories. The bias is compared with other errors appearing during the estimation, and it is documented that the effect of the bias has to be taken into account in experimental studies.

The parameters of heart rate variability and blood pressure variability have proved to be useful analytical tools in cardiovascular physics and medicine. Model-based analysis of these variabilities additionally leads to new prognostic information about mechanisms behind regulations in the cardiovascular system. In this paper, we analyze the complex interaction between heart rate, systolic blood pressure, and respiration by nonparametric fitted nonlinear additive autoregressive models with external inputs. Therefore, we consider measurements of healthy persons and patients suffering from obstructive sleep apnea syndrome (OSAS), with and without hypertension. It is shown that the proposed nonlinear models are capable of describing short-term fluctuations in heart rate as well as systolic blood pressure significantly better than similar linear ones, which confirms the assumption of nonlinear controlled heart rate and blood pressure. Furthermore, the comparison of the nonlinear and linear approaches reveals that the heart rate and blood pressure variability in healthy subjects is caused by a higher level of noise as well as nonlinearity than in patients suffering from OSAS. The residue analysis points at a further source of heart rate and blood pressure variability in healthy subjects, in addition to heart rate, systolic blood pressure, and respiration. Comparison of the nonlinear models within and among the different groups of subjects suggests the ability to discriminate the cohorts that could lead to a stratification of hypertension risk in OSAS patients.

Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali et al., Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation—the nine-bit model in two dimensions—in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.

We investigate experimentally a homogeneously driven granular medium. It consists of spheres, each one containing a magnetic dipole, rolling on a horizontally placed dish and subject to a magnetic field which is sinusoidal in time and spatially homogeneous. A gaslike state is obtained. Except for extremely low amplitudes of the magnetic field, non-Gaussian distributions are found for the translatory velocities, as well as for the horizontal components of the rotational velocities. However, the vertical component of the rotational velocity obeys an almost invariant Gaussian distribution within a large range of parameters, namely frequencies and amplitudes of the magnetic field and friction coefficients on the dish’s bottom. The results are close to predictions from simulations by Cafiero et al. [Europhys. Lett. 60, 854 (2002)].

We study fractal vesicle aggregates whose morphology is conditioned by the interaction between the lipid vesicle membranes and calcium and magnesium ions. These morphologies are probed by means of static light scattering using a cross-correlation scheme that avoids the multiple intracluster scattering. In contrast to the branched structures induced by calcium, we report a singular surface- to mass-fractal transition controlled by the magnesium concentration. From infrared spectroscopy data we conclude that the specific dehydration of the lipid membranes due to these cations plays an essential role in short-range intervesicle interactions.

We show that the dynamics of simple disordered models, like the directed trap model and the random energy model, takes place at a coexistence point between active and inactive dynamical phases. We relate the presence of a dynamic phase transition in these models to the extreme value statistics of the associated random energy landscape.