Propagation of solitary waves activated in thin ferroelectric liquid crystal cells under external, sinusoidally alternating electric fields is investigated using the electro-optic technique. It is shown that solitons give contributions only to the loss component of the response spectrum, within rather narrow ranges of frequencies and in sufficiently strong fields. The limit frequency, at which the amplitude of the velocity of the solitary waves is greatest, is found to be related to material constants of liquid crystals. Measuring this threshold frequency provides the capability to determine the elastic constant of surface stabilized liquid crystalline materials in the bookshelf or chevron layer geometries.

The disease epilepsy is related to hypersynchronous activity of networks of neurons. While acute epileptic seizures are the most extreme manifestation of this hypersynchronous activity, an elevated level of interdependence of neuronal dynamics is thought to persist also during the seizure-free interval. In multichannel recordings from brain areas involved in the epileptic process, this interdependence can be reflected in an increased linear cross correlation but also in signal properties of higher order. Bivariate time series analysis comprises a variety of approaches, each with different degrees of sensitivity and specificity for interdependencies reflected in lower- or higher-order properties of pairs of simultaneously recorded signals. Here we investigate which approach is best suited to detect putatively elevated interdependence levels in signals recorded from brain areas involved in the epileptic process. For this purpose, we use the linear cross correlation that is sensitive to lower-order signatures of interdependence, a nonlinear interdependence measure that integrates both lower- and higher-order properties, and a surrogate-corrected nonlinear interdependence measure that aims to specifically characterize higher-order properties. We analyze intracranial electroencephalographic recordings of the seizure-free interval from 29 patients with an epileptic focus located in the medial temporal lobe. Our results show that all three approaches detect higher levels of interdependence for signals recorded from the brain hemisphere containing the epileptic focus as compared to signals recorded from the opposite hemisphere. For the linear cross correlation, however, these differences are not significant. For the nonlinear interdependence measure, results are significant but only of moderate accuracy with regard to the discriminative power for the focal and nonfocal hemispheres. The highest significance and accuracy is obtained for the surrogate-corrected nonlinear interdependence measure.

This study is motivated in part by the discrepancy that exists in the literature with regard to the dependence of the tank-treading frequency of red blood cells on the shear rate and suspending medium viscosity. Here we consider three-dimensional numerical simulations of deformable capsules of initially spherical and oblate spheroidal shapes and biconcave discoid representing the red blood cell resting shape. By considering a much broader range of the viscosity ratio (ratio of capsule or cell interior to suspending fluid viscosity), shear rate, and aspect ratio (ratio of minor to major axes) than that considered in the previous experiments, we find several new characteristics of the tank-treading and tumbling frequencies that have not been reported earlier. These new characteristics are the result of the large shape deformation and the coupling between shape and angular oscillations of the capsules or cells. For the spherical and oblate spheroidal capsules, the tank-treading frequency shows a nonmonotonic trend that is characterized by an initial decrease leading to a minimum followed by an increase with increasing viscosity ratio. For red blood cells, we find two regimes of the viscosity dependence of the tank-treading frequency: an exponential regime in which the tank-treading frequency decreases at a slower rate with increasing viscosity ratio, and a logarithmic range in which it decreases at a much faster rate. While this trend agrees well with different theoretical models of shape-preserving capsules, it was not evident in previous experimental results. When the shear rate dependence is considered, the tank-treading frequency of red blood cells and capsules of highly elongated initial shapes exhibits a nonmonotonic trend that is characterized by an initial increase leading to a maximum followed by a sharp decrease with decreasing shear rate. This anomalous behavior of the tank-treading frequency is shown to be due to a breathing-like dynamics of the capsule or cell that is characterized by a repeated emergence and absence of deep, crater-like dimples, and a large swinging motion. We further observe that the tumbling frequency exhibits a decreasing trend with increasing viscosity ratio that is in contrast to the theoretical result for the shape-preserving capsules and is due to the periodic deformation and preferential alignment of the capsules in the extensional quadrant of the flow.

The luminescence pulses emitted from collapsing laser-induced bubbles in water-glycerol mixtures are studied as a function of the mixture concentration and applied hydrostatic pressure. The primary effect of increasing the glycerol concentration is to increase the viscosity of the fluid. The pulse duration of the luminescence is found to increase by more than a factor of two as the concentration increases up to $33\%$ glycerol by volume, where the viscosity is nearly four times that of pure water. At higher glycerol concentrations the pulse duration remains nearly unchanged, until no luminescence can be observed at concentrations above $60\%$, corresponding to a viscosity greater than 15 times that of water. The pulse duration further increases with applied pressures up to 8 bar, similar to that observed earlier in pure water.

An extension of the pseudopotential lattice Boltzmann method is introduced to simulate heat transfer problems involving phase transition. Using this model, evaporation through a plane interface and two-phase Poiseuille flow were simulated and the macroscopic jump conditions were utilized to evaluate the accuracy of the method. We have found that the simulation results are in very good agreement with the analytical solutions as far as we take into account the extent of the interface during the evaluation. Using the same model heterogeneous boiling was simulated taking into account the geometry of a cavity and the important features of the boiling process could be observed in the simulation results.

Numerical simulations with previous formulations of the quantum lattice Boltzmann (QLB) scheme in three spatial dimensions showed significant lack of isotropy. In two or more spatial dimensions the QLB approach relies upon operator splitting to decompose the time evolution into a sequence of applications of the one-dimensional QLB scheme along coordinate axes. Each application must be accompanied by a rotation of the wave function into a basis of chiral eigenstates aligned along the relevant axis. The previously observed lack of isotropy was due to an inconsistency in the application of these rotations. Once this inconsistency is removed, the QLB scheme is shown to exhibit isotropic behavior to within a numerical error that scales approximately linearly with the lattice spacing. This establishes the viability of the QLB approach in two and three spatial dimensions.

Thin-film dewetting can be exploited to self-assemble and organize nanoparticles. Crucial to this effort is the understanding of the nanoscale liquid phase dynamics, and molecular dynamics simulations (MD) provide a powerful tool in this respect. In this paper we demonstrate that MD simulations utilizing a Lennard-Jones (LJ) interface potential can be effectively used to study various wetting regimes of nanoscale Cu disks on graphite. It was found that both the dewetting velocity and the equilibrium contact angle increase with a decrease in the Cu-C potential, and that the retraction velocities obtained are characteristic of dewetting phenomena governed by inertial and capillary forces. This phenomena leads to a change in morphology, from disks to nanodroplets, which, in turn, when using the most accurate LJ potential, jump off the graphitic substrate with a velocity on the order of 140 m/s. This ejection velocity is consistent with the previous experimental observation that nanoscale Au triangles deposited on graphite or glass jump when exposed to a pulsed laser above the melting threshold. Interestingly, the Cu ejection velocity decreases when the liquid Cu disks are deposited on a suspended graphene membrane. Finally, a Rayleigh-Plateau-like instability, which leads to the breakup of a pseudo-one-dimensional liquid Cu nanowire in nanodroplets, is revealed when the MD simulations are performed using different LJ interface potentials.

Maier-Saupe theory is the canonical mean field description of thermotropic nematic liquid crystals. In this paper, we examine the predictions of the theory in four spatial dimensions. Representations of the order parameter tensor and the existence of new phases are discussed. The phase diagram, based on numerical solution of the self-consistent equations and Landau theory, is presented. Orientational order decreases as the number of spatial dimensions is increased.

We report effects of disorder due to random cross-linking on the nematic to smectic-A phase transition in smectic elastomers. Thermoelastic data, stress-strain relations and high-resolution x-ray scattering profiles have been analyzed for two related compounds with a small and a larger nematic range, respectively, each for 5% as well as 10% cross-links. At 5% cross-link density the algebraic decay of the positional correlations of the smectic layers survives in finite-size domains, providing a sharp smectic-nematic transition. At an increased cross-link concentration of 10% the smectic order disappears and gives way to extended short-range layer correlations. In this situation neither a smectic-nematic nor a nematic-isotropic transition is observed anymore. The occurrence of disorder at a relatively large cross-link concentration only, indicates that smectic elastomers are rather resistant to a random field. The temperature dependence of the correlation lengths and thermoelastic behavior suggest a shift to a “parasmectic” regime of a first-order smectic-isotropic transition.

We numerically study the phase diagram of a three-state host-parasite model on the square lattice motivated by population biology. The model is an extension of the contact process, and the three states correspond to an empty site, a host, and a parasite. We determine the phase diagram of the model by scaling analysis. In agreement with previous results, three phases are identified: the phase in which both hosts and parasites are extinct ($S_0$), the phase in which hosts survive but parasites are extinct ($S_{01}$), and the phase in which both hosts and parasites survive ($S_{012}$). We argue that both the $S_0$–$S_{01}$ and $S_{01}$–$S_{012}$ boundaries belong to the directed percolation class. In this model, it has been suggested that an excessively large reproduction rate of parasites paradoxically extinguishes hosts and parasites and results in $S_0$. We show that this paradoxical extinction is a finite size effect; the corresponding parameter region is likely to disappear in the limit of infinite system size.

We report observations of wave turbulence on the surface of a ferrofluid submitted to a magnetic field parallel to the fluid surface. The magnetic wave turbulence shows several differences compared to the normal field case reported recently. The inertial zone of the magnetic wave turbulence regime is notably found to be strongly increased with respect to the normal field case and to be well described by our theoretical predictions. The dispersion relation of linear waves is also measured and differs from the normal field case due to the absence of the Rosensweig instability.

Symmetry-breaking bifurcations have been studied for convection in a nonrotating spherical shell whose outer radius is twice the inner radius, under the influence of an externally applied central force field with a radial dependence proportional to $1/r^5$. This work is motivated by the GeoFlow experiment, which is performed under microgravity condition at the International Space Station where this particular central force can be generated. In order to predict the observable patterns, simulations together with path-following techniques and stability computations have been applied. Branches of axisymmetric, octahedral, and seven-cell solutions have been traced. The bifurcations producing them have been identified and their stability ranges determined. At higher Rayleigh numbers, time-periodic states with a complex spatiotemporal symmetry are found, which we call breathing patterns.

We present and use an algorithm based on convex conic optimization to design two-dimensional photonic crystals with large absolute band gaps. Among several illustrations we show that it is possible to design photonic crystals which exhibit multiple absolute band gaps for the combined transverse electric and magnetic modes. The optimized crystals show complicated patterns which are far different from existing photonic crystal designs. We employ subspace approximation and mesh adaptivity to enhance computational efficiency. For some examples involving two band gaps, we demonstrate the tradeoff frontier between two different absolute band gaps.

Colloidal solutions posses a wide range of time and length scales so that it is unfeasible to keep track of all of them within a single simulation. As a consequence, some form of coarse graining must be applied. In this work we use the multiparticle collision dynamics scheme. We describe a particular implementation of no-slip boundary conditions upon a solid surface, capable of providing correct forces on the solid bypassing the calculation of the velocity profile or the stress tensor in the fluid near the surface. As an application we measure the friction on a spherical particle when it is placed in a bulk fluid and when it is confined in a slit. We show that the implementation of the no-slip boundary conditions leads to an enhanced Enskog friction, which can be understood analytically. Because of the long-range nature of hydrodynamic interactions, the Stokes friction obtained from the simulations is sensitive of the simulation box size. We address this topic for the slit geometry, showing that the dependence on the system size differs very much from what is expected in a three-dimensional system where periodic boundary conditions are used in all directions.

The spectral, dissipative, and statistical properties of the damped quantum oscillator are studied in the case of non-Markovian and nonstationary system-heat bath coupling. The dissipation of collective energy is shown to be slowed down, and the decoherence rate and entropy grow with modulation frequency.

We study the probability distribution of the index $N_{+}$, i.e., the number of positive eigenvalues of an $N\times N$ Gaussian random matrix. We show analytically that, for large $N$ and large $N_{+}$ with the fraction $0⩽c=N_{+}/N⩽1$ of positive eigenvalues fixed, the index distribution $P(N_{+}=\mathit{cN},N)~\exp [-\beta N^2\Phi (c)]$ where $\beta$ is the Dyson index characterizing the Gaussian ensemble. The associated large deviation rate function $\Phi (c)$ is computed explicitly for all $0⩽c⩽1$. It is independent of $\beta$ and displays a quadratic form modulated by a logarithmic singularity around $c=1/2$. As a consequence, the distribution of the index has a Gaussian form near the peak, but with a variance $\Delta (N)$ of index fluctuations growing as $\Delta (N)~\ln N/\beta {\pi }^2$ for large $N$. For $\beta =2$, this result is independently confirmed against an exact finite-$N$ formula, yielding $\Delta (N)=\ln N/2{\pi }^2+C+O(N^{-1})$ for large $N$, where the constant $C$ for even $N$ has the nontrivial value $C=(\gamma +1+3\ln 2)/2{\pi }^2\simeq 0.185\hspace{0.5em}248\dots$ and $\gamma =0.5772\dots$ is the Euler constant. We also determine for large $N$ the probability that the interval $[{\zeta }_1,{\zeta }_2]$ is free of eigenvalues. Some of these results have been announced in a recent letter [Phys. Rev. Lett. 103, 220603 (2009)].

The present paper is concerned with the global asymptotic theory of steady deep-cellular growth in directional solidification of binary mixtures. We consider the two-dimensional model with nonzero isotropic surface tension and obtain the global uniformly valid asymptotic solutions for the steady state of the system in the limit of the Péclet number $\epsilon \to 0$; $\epsilon$ is defined as the ratio of the radius of the cell's tip and mass diffussion length. The whole physical space is divided into the outer region and root region; the solutions in each subregion are solved, respectively, and matched with each other in the intermediate region. The results show that given growth conditions and material properties, the global solutions for steady state of the system contain two free parameters: the Péclet number and asymptotic width parameter ${\lambda }_0$, which are related to the geometry of cellular structure: the cell tip radius and primary spacing. One of the most important conclusions drawn from this analysis is that the steady-state solutions of cellular growth have a complicated structure with three internal layers in the root region; for given $(\epsilon ,{\lambda }_0)$, there exists a discrete set of the global steady-state solutions subject to the quantization condition that are profoundly affected by the surface tension. Each eigenvalue calculated from this quantization condition determines the total length of the finger described by the corresponding global steady-state solution.

Thermal conductivity of interfacial layers is an essential parameter for determining how the ordered liquid layering around the particle-liquid interface contributes to the unusual high thermal conductivity of nanofluids. However, so far there is no experimental data regarding this parameter. Using nonequilibrium molecular dynamics simulations of an inhomogeneous Au-Ar system in which the solid-liquid interactions are assumed to be much stronger than the liquid-liquid interactions, we show explicitly that the thermal conductivity of a 1-nm-thick interfacial layer is 1.6 ∼ 2.5 times higher than that of the base fluid. The simulation results are incorporated into a three-level clustering model to calculate the effective thermal conductivity of nanofluids. The results show that the contribution of the interfacial layer to thermal conductivity enhancements should be considered if there are particle clusters in nanofluids.

We discuss the Lebwohl-Lasher model of nematic liquid crystals in a confined geometry, using Monte Carlo simulation and mean-field theory. A film of material is sandwiched between two planar, parallel plates that couple to the adjacent spins via a surface strength ${\epsilon }_s$. We consider the cases where the favored alignments at the two walls are the same (symmetric cell) or different (asymmetric cell). In the latter case, we demonstrate the existence of a single phase transition in the slab for all values of the cell thickness. This transition has been observed before in the regime of narrow cells, where the two structures involved correspond to different arrangements of the nematic director. By studying wider cells, we show that the transition is in fact the usual isotropic-to-nematic (capillary) transition under confinement in the case of antagonistic surface forces. We show results for a wide range of values of film thickness and discuss the phenomenology using a mean-field model.

The chaotic phase synchronization transition is studied in connection with the zero Lyapunov exponent. We propose a hypothesis that it is associated with a switching of the maximal finite-time zero Lyapunov exponent, which is introduced in the framework of a large deviation analysis. A noisy sine circle map is investigated to introduce this hypothesis and it is tested in an unidirectionally coupled Rössler system by using the covariant Lyapunov vector associated with the zero Lyapunov exponent.