We investigate discrete light dynamics in the presence of a longitudinal defect of arbitrary extension, amplitude and position in a nonlinear waveguide array. We model and discuss the physics of the soliton-defect interaction, showing how to gain complete control over the system outcome for soliton-based data processing. We propose all-optical management in dye-doped liquid crystals.

A confined incompressible elastic film does not deform uniformly when subjected to adhesive interfacial stresses but with undulations which have a characteristic wavelength scaling linearly with the thickness of the film. In the classical peel geometry, undulations appear along the contact line below a critical film thickness or below a critical curvature of the plate. Perturbation analysis of the stress equilibrium equations shows that for a critically confined film the total excess energy indeed attains a minimum for a finite amplitude of the perturbations which grow with further increase in the confinement.

The thermal Casimir-like force in free-standing liquid crystal films close to the smectic-$A$–nematic transition temperature is computed using a quadratic functional approach. In the framework of a microscopic mean-field model of free-standing smectic-$A$ films, the temperature dependence of the order parameter profiles is computed and later used to estimate the elastic coupling variability in the vicinity of first- and second-order bulk smectic-$A$–nematic phase transitions. The strong nonuniformity of the coupling constant profiles promotes a significant increase of the fluctuation-induced force over three orders of magnitude, especially in thin films. This result reinforces the possible predominance of the thermal Casimir force as compared to the standard van der Waals interaction in thin smectic-$A$ liquid crystal films.

The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its three fundamental dynamical regimes: silence, bistability, and repetitive firing. Its response is characterized in terms of statistical indicators (interspike-interval distributions and their first moments) as well as of dynamical indicators (autocorrelation functions and conditional entropies). In the silent regime, the coexistence of two different coherence resonances is revealed: one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state; the second one (at intermediate noise variance) is associated with the regularization of the sequence of spikes emitted by the neuron. Bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations. In the repetitive firing regime a maximization of incoherence is observed at finite noise variance. Finally, the mechanisms responsible for the different features appearing in the interspike-interval distributions (like multimodality and exponential tails) are clearly identified in the various regimes.

In the last three decades, researchers have tried to identify universal patterns in the structure of food webs. It was recently proposed that the exponent $\eta$ characterizing the efficiency of the transport of energy in large and small food webs might have a universal value $(\eta =1.13)$. In this work we establish lower and upper bounds for this exponent in a general spanning tree with a fixed number of trophic species and levels. When the number of species is large, the lower and upper bounds are equal to 1, implying that the result $\eta =1.13$ is due to finite-size effects and that the value of this exponent depends on the size of the web. We also evaluate analytically and numerically the exponent $\eta$ for hierarchical and random networks. In all cases the exponent $\eta$ depends on the number of trophic species $K$, and when $K$ is large we have that $\eta \to 1$. Moreover, this result holds for any fixed number $M$ of trophic levels.

In the framework of Rayleigh’s description, we have investigated the eigenfrequencies of the capillary waves of a nonwetting droplet under forced oscillations (pointlike force). The theoretical model using the spherical harmonics $Y_{\ell ,m}(\theta ,\phi )$ as a part of the solution of the Laplace equation, is in good agreement with the experimental results. This model can be generalized for all kinds of excitations with a sitting or a levitating droplet due to the decomposition of the excitation on the spherical harmonics basis. From this study, a different theoretical way of interpreting droplet bouncing is presented motivating a wide range of industrial applications.

We propose a design of the equal time correlation matrix suitable for the analysis of multivariate time series with ill-defined phases. We present the cross-correlation analysis of model data sets taken from coupled stochastic oscillators and compare the concept with the results obtained from a conventional correlation matrix analysis. We show that the concept provides a higher sensitivity combined with a better statistical significance when quantifying weak cross correlations.

We show that the spurious current present near a curved interface in a class of multiphase lattice Boltzmann (LB) models is due to the insufficient isotropy of the discrete gradient operator. A method of obtaining highly isotropic gradient operators on a lattice is given. Numerical simulations show that both the magnitude and the spatial extent of the spurious current are significantly reduced as gradient operators of increasingly higher order of isotropy is adopted in multiphase LB models.

Confocal scanning laser microscopy has been used to quantitatively analyze the structure and dynamics of concentrated suspensions of spherical colloids in which the magnitude of the short-range attractive potential is increased by adding nonadsorbing polymers. These systems undergo a reentrant glass transition upon increasing polymer concentration. We find that melting of the glass is accompanied by significant changes in the displacement distribution and its moments. However, no significant variations have been detected in the shapes of the displacement distributions. Moreover, structural correlation functions and the magnitude of local density fluctuations do not vary significantly between the glass states and the fluid. Considering our experimental setup, these observations imply that local density fluctuations cannot be larger than a few percent of the average density.

The magnetic-field-induced orientational order in the isotropic phase of colloidal gibbsite $\left[\mathrm{Al}{\left(\mathrm{O}\mathrm{H}\right)}_3\right]$ platelets is studied by means of optical birefringence and small-angle x-ray scattering (SAXS) techniques. The suspensions display field-induced ordering at moderate field strengths (a few Tesla), which increases with increasing particle concentration. The gibbsite particles align their normals perpendicular to the magnetic field and hence possess a negative anisotropy of their diamagnetic susceptibility $\Delta \chi$. The results can be described following a simple, Onsager-like approach. A simplified model is derived that allows one to obtain the orientational distribution function directly from the scattering data. However, it leads to an underestimate of the diamagnetic susceptibility anisotropy $\Delta \chi$. This accounts for the difference between the $\Delta \chi$ values provided by the two experimental techniques (SAXS and magneto-optics). The order of magnitude $\Delta \chi \sim {10}^{-22}\mathrm{J}∕{\mathrm{T}}^2$ lies in between that of goethite suspensions and that of suspensions of organic particles.

We have simulated the two-dimensional growth of fractal aggregates produced in electrodeposition experiments with axial symmetry in the presence of electric and magnetic fields. A modified diffusion-limited aggregation algorithm based on the Monte Carlo method is used in order to simulate cluster growth under the action of Coulomb and Lorentz forces, taking into account the thermal energy. The ion-particle movement has each step biased by the resultant force; in the algorithm, it is mediated by the Boltzmann term. The electric voltage between the electrodes tends to compact the aggregates and reduce the effect of screening. The Lorentz force provides a spiral form for aggregates which twists according to the magnetic field direction and intensity. A function was defined to measure the chirality of the system. The fractal dimension was also calculated to measure the influence of the electric and magnetic fields as well as the temperature during the growth process. Good agreement with experimental results was observed.

A family of classical statistical-mechanical spin models, by now extensively studied in the literature, involves two-component unit vectors, associated with a two-dimensional lattice, with pair potentials restricted to nearest neighbors and possessing $O\left(2\right)$ symmetry—i.e., defined by some function of the scalar product between the two interacting spins; these studies often show the existence of a topological phase transition. We show here that, for a wide class of interaction models of the above type, available mathematical results entail the existence of a topological (Berezinskiĭ-Kosterlitz-Thouless-like) transition, as well as a rigorous lower bound on the transition temperature.

Equilibrium free energy differences are given by exponential averages of nonequilibrium work values; such averages, however, often converge poorly, as they are dominated by rare realizations. I show that there is a simple and intuitively appealing description of these rare but dominant realizations. This description is expressed as a duality between “forward” and “reverse” processes, and provides both heuristic insights and quantitative estimates regarding the number of realizations needed for convergence of the exponential average. Analogous results apply to the equilibrium perturbation method of estimating free energy differences. The pedagogical example of a piston and gas [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B 109, 6805 (2005)] is used to illustrate the general discussion.

We studied the effect of the turbulent heat flux on the Reynolds stresses in a rotating turbulent convection. To this end we solved a coupled system of dynamical equations which includes the equations for the Reynolds stresses, the entropy fluctuations, and the turbulent heat flux. We used a spectral $\tau$ approximation in order to close the system of dynamical equations. We found that the ratio of the contributions to the Reynolds stresses caused by the turbulent heat flux and the anisotropic eddy viscosity is of the order of $\sim 10{(L_{\rho }∕l_0)}^2$, where $l_0$ is the maximum scale of turbulent motions and $L_{\rho }$ is the fluid density variation scale. This effect is crucial for the formation of the differential rotation and should be taken into account in the theories of the differential rotation of the Sun, stars, and planets. In particular, we demonstrated that this effect may cause the differential rotation which is comparable with the typical solar differential rotation.

We study the properties of one-dimensional photonic crystals with an $\epsilon$-negative and a $\mu$-negative defect. With suitable parameters, the pair defect is equivalent to a transparent material with zero effective refractive index. This special pair defect has no influence on the spectral gap formed by the interference of propagating waves in positive-refractive-index materials. However, the field distribution is modified noticeably by the decaying wave in the pair defect. Particularly, the gap-edge field can be a highly localized wave instead of the usual standing wave as the size of the pair defect increases. The localized gap-edge field can reduce the switching thresholds for bistability greatly when Kerr-type nonlinear $\mu$-negative material is involved. A nonideal model when the $\epsilon$-negative and $\mu$-negative materials are dispersive and lossy is used to verify the unusual properties.

We address the issue of mobility of localized modes in two-dimensional nonlinear Schrödinger lattices with saturable nonlinearity. This describes, e.g., discrete spatial solitons in a tight-binding approximation of two-dimensional optical waveguide arrays made from photorefractive crystals. We discuss the numerically obtained exact stationary solutions and their stability, focusing on three different solution families with peaks at one, two, and four neighboring sites, respectively. When varying the power, there is a repeated exchange of stability between these three solutions, with symmetry-broken families of connecting intermediate stationary solutions appearing at the bifurcation points. When the nonlinearity parameter is not too large, we observe good mobility and a well-defined Peierls-Nabarro barrier measuring the minimum energy necessary for rendering a stable stationary solution mobile.

The derivative-based analysis for detecting regions of the validity of the Vogel-Fulcher-Tammann (VFT) dependence for superpressed and supercooled liquids is discussed. For the temperature $\left(T\right)$ path the analysis introduced by Stickel et al. [J. Chem. Phys. 104, 2043 (1996); J. Chem. Phys. 107, 1086 (1997)] is recalled. For the pressure $\left(P\right)$ path the derivation based on the counterpart of the VFT dependence proposed in Paluch et al. [J. Phys.: Condens. Mater 10, 4131 (1998)] is presented. The appearance of two ideal glass temperatures $\left(T_0\right)$ or pressures $\left(P_0\right)$, fragility strength coefficients $(D_T,D_P)$, and prefactors $({\tau }_0^T,{\tau }_0^P)$ for VFT equations in following dynamical domains, i.e., high-temperature $\left(\mathrm{\Delta }{T}_{high}\right)$ and low-temperature $\left(\mathrm{\Delta }{T}_{low}\right)$ or low-pressure $\left(\mathrm{\Delta }{P}_{low}\right)$ and high-pressure $\left(\mathrm{\Delta }{P}_{high}\right)$, is stressed. It is noteworthy that the values of $T_0\left(\mathrm{\Delta }{T}_{high}\right)>T_0\left(\mathrm{\Delta }{T}_{low}\right),D_T\left(\mathrm{\Delta }{T}_{high}\right)⪡D_T\left(\mathrm{\Delta }{T}_{low}\right)$, and ${\tau }_0^T\left(\mathrm{\Delta }{T}_{high}\right)⪢{\tau }_0^T\left(\mathrm{\Delta }{T}_{low}\right)$. Analogous behavior was noted for isothermal $\mathrm{\Delta }{P}_L$ and $\mathrm{\Delta }{P}_H$ dynamic domains. A similar derivative-based approach is also applied to test the validity of the mode coupling theory (MCT) critical-like equation $\tau \left(T\right)\propto (T-T_X{)}^{-\mathcal{g}}$. It yields the temperature $T_X$ and the MCT power (“critical”) exponent $\mathcal{g}$ exclusively from the simple linear regression. The extension of such an analysis for the pressure path is also given. The hardly discussed question of the error of estimations of $\mathcal{g}$ and $T_X$ is emphasized. The relation between the derivative based behavior mentioned above and the apparent activation enthalpy (temperature path) or the apparent activation volume (pressure path) is indicated. The presented analysis was applied to discuss the dynamic crossovers in supercooled and superpressed diethyl phthalate, based on experimental data supplemented by those given in Pawlus et al. [Phys. Rev. E 68, 021503 (2003)].

We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the quantum wave vector spectrum. A semiclassical derivation and numerical calculations are presented in support of the results. These classical eigenmodes can be observed in physical experiments through the autocorrelation of the transmission coefficient of waves in quantum billiards. Exact classical trace formulas of the resolvent are derived for the rectangle, equilateral triangle, and circle billiards. We also establish a correspondence between the classical periodic orbit length spectrum and the quantum spectrum for integrable polygonal billiards.