The restrictions on the resolution of transmission devices formed by wire media (arrays of conductive cylinders) recently proposed in Phys. Rev. B 71, 193105 (2005) and experimentally tested in Phys. Rev. B 73, 033108 (2006) are studied in this paper using both analytical and numerical modeling. It is demonstrated that such transmission devices have subwavelength resolution that can in principle be made as fine as required by a specific application by controlling the lattice constant of the wire medium. This confirms that slabs of the wire medium are unique imaging devices at the microwave frequency range, and are capable of transmitting distributions of TM-polarized electric fields with nearly unlimited subwavelength resolution to practically arbitrary distances.

We predict the existence of lattice solitons made of incoherent white light: lattice solitons made of light originating from an ordinary incandescent light bulb. We find that the intensity structure and spatial power spectra associated with different temporal frequency constituents of incoherent white-light lattice solitons (IWLLSs) arrange themselves in a characteristic fashion, with the intensity structure more localized at higher frequencies, and the spatial power spectrum more localized at lower frequencies; the spatial correlation distance is larger at lower frequency constituents of IWLLSs. This characteristic shape of incoherent white-light lattice solitons reflects the fact that diffraction is stronger for lower temporal frequency constituents, while higher frequencies experience stronger effective nonlinearity and deeper lattice structure.

We study energy localization in a finite one-dimensional ${\Phi }^4$ oscillator chain with initial energy in a single oscillator of the chain. We numerically calculate the effective number of degrees of freedom sharing the energy on the lattice as a function of time. We find that for energies smaller than a critical value, energy equipartition among the oscillators is reached in a relatively short time. On the other hand, above the critical energy, a decreasing number of particles sharing the energy is observed. We give an estimate of the effective number of degrees of freedom as a function of the energy. Our results suggest that localization is due to the appearance, above threshold, of a breather-like structure. Analytic arguments are given, based on the averaging theory and the analysis of a discrete nonlinear Schrödinger equation approximating the dynamics, to support and explain the numerical results.

The DNLS model including Kac-Baker long-range interactions and nonlinear damping exhibits prominent effects in computer simulations. The combination of long-range forces and damping yields a periodic pattern of stationary breathers from an originally uniformly distributed background. The inverse interaction radius determines the periodicity which can be understood in the quasicontinuum approximation of the system. For the undamped system, we investigate the impact of the long-range interactions on the transition to the persistent-breather phase, which only depends on the energy and the norm of the DNLS. Using Monte Carlo techniques, we can monitor the localization strength as a function of the the long-range radius and the system temperature, which is formally negative in the persistent-breather phase.

We investigate the equation of state, diffusion coefficient, and structural order of a family of spherically symmetric potentials consisting of a hard core and a linear repulsive ramp. This generic potential has two characteristic length scales: the hard and soft core diameters. The family of potentials is generated by varying their ratio, $\lambda$. We find negative thermal expansion (thermodynamic anomaly) and an increase of the diffusion coefficient upon isothermal compression (dynamic anomaly) for $0⩽\lambda <6∕7$. As in water, the regions where these anomalies occur are nested domes in the $(T,\rho )$ or $(T,P)$ planes, with the thermodynamic anomaly dome contained entirely within the dynamic anomaly dome. We calculate translational and orientational order parameters ($t$ and $Q_6$), and project equilibrium state points onto the $(t,Q_6)$ plane, or order map. The order map evolves from waterlike behavior to hard-sphere-like behavior upon varying $\lambda$ between $4∕7$ and $6∕7$. Thus, we traverse the range of liquid behavior encompassed by hard spheres $(\lambda =1)$ and waterlike $(\lambda \sim 4∕7)$ with a family of tunable spherically symmetric potentials by simply varying the ratio of hard to soft-core diameters. Although dynamic and thermodynamic anomalies occur almost across the entire range $0⩽\lambda ⩽1$, waterlike structural anomalies (i.e., decrease in both $t$ and $Q_6$ upon compression and strictly correlated $t$ and $Q_6$ in the anomalous region) occur only around $\lambda =4∕7$. Waterlike anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, with their ratio $\lambda$ being the single control parameter, orientation-dependent interactions being absent by design.

Using Gibbs ensemble Monte Carlo simulations and density functional theory we investigate the fluid-fluid demixing transition in inhomogeneous colloid-polymer mixtures confined between two parallel plates with separation distances between one and ten colloid diameters covering the complete range from quasi-two-dimensional to bulklike behavior. We use the Asakura-Oosawa-Vrij model in which colloid-colloid and colloid-polymer interactions are hard-sphere like, while the pair potential between polymers vanishes. Two different types of confinement induced by a pair of parallel walls are considered—namely, either through two hard walls or through two semipermeable walls that repel colloids but allow polymers to freely penetrate. For hard (semipermeable) walls we find that the capillary binodal is shifted towards higher (lower) polymer fugacities and lower (higher) colloid fugacities as compared to the bulk binodal; this implies capillary condensation (evaporation) of the colloidal liquid phase in the slit. A macroscopic treatment is provided by a symmetric Kelvin equation for general binary mixtures based on the proximity in chemical potentials of statepoints at capillary coexistence and the reference bulk coexistence. Results for capillary binodals compare well with those obtained from the classic version of the Kelvin equation due to [Evans and Marini Bettolo Marconi, J. Chem. Phys. 86, 7138 (1987)] and are quantitatively accurate away from the fluid-fluid critical point, even at small wall separations. However, the significant shift of the critical polymer fugacity towards higher values upon increasing confinement, as found in simulations, is not reproduced. For hard walls the density profiles of polymers and colloids inside the slit display oscillations due to packing effects for all statepoints. For semipermeable walls either similar structuring or flat profiles are found, depending on the statepoint considered.

We investigate both theoretically and experimentally the rotational dynamics of micrometric droplets of dye-doped and pure liquid crystal induced by circularly and elliptically polarized laser light. The droplets are dispersed in water and trapped in the focus of the laser beam. Since the optical torque acting on the molecular director is known to be strongly enhanced in light-absorbing dye-doped materials, the question arises whether a similar enhancement takes place also for the overall optical torque acting on the whole droplets. We searched for such enhancement by measuring and comparing the rotation speed of dye-doped droplets induced by a laser beam having a wavelength either inside or outside the dye absorption band, and also comparing it with the rotation of pure liquid crystal droplets. No enhancement was found, confirming that photoinduced dye effects are only associated with an internal exchange of angular momentum between orientational and translational degrees of freedom of matter. Our result provides also direct experimental proof of the existence of a photoinduced stress tensor in the illuminated dye-doped liquid crystal. Finally, peculiar photoinduced dynamical effects are predicted to occur in droplets in which the molecular director is not rigidly locked to the flow, but so far they could not be observed.

We consider a nematic liquid crystal confined by two parallel flat substrates whose anchoring conditions vary periodically in one lateral direction. Within the Gaussian approximation, we study the effective forces between the patterned substrates induced by the thermal fluctuations of the nematic director. The shear force oscillates as a function of the lateral shift between the patterns on the lower and the upper substrates. We compare the strength of this fluctuation-induced lateral force with the lateral van der Waals force arising from chemically structured adsorbed monolayers. The fluctuation-induced force in the normal direction is either repulsive or attractive, depending on the model parameters.

We calculate the correction-to-scaling exponent ${\omega }_T$ that characterizes the approach to the scaling limit in multicomponent polymer solutions. A direct Monte Carlo determination of ${\omega }_T$ in a system of interacting self-avoiding walks gives ${\omega }_T=0.415\pm 0.020$. A field-theory analysis based on five- and six-loop perturbative series leads to ${\omega }_T=0.41\pm 0.04$. We also verify the renormalization-group predictions for the scaling behavior close to the ideal-mixing point.

We present a model of microfluidic flow of several completely immiscible fluids and use it to simulate a whole flow focusing device chamber. Our efficient, practical model supports a large parameter space, spanned by surface wetting, surface tension, liquid-liquid wetting, viscosity ratio, and inlet velocity. It is based upon an N-component lattice Boltzmann method with interrupted coalescence [Dupin et al., Philos. Trans. R. Soc. London, Ser. A 362, 1885 (2004)], here adapted for calculations at low capillary and Reynolds numbers, with wetting and significantly reduced spurious flow. Results over 2 orders of magnitude in Reynolds number are presented.

We present a numerical study of the order-parameter probability density function (PDF) of the square Ising model for lattices with linear sizes $L=80–140$. A recent efficient entropic sampling scheme, combining the Wang-Landau and broad histogram methods and based on the high levels of the Wang-Landau process in dominant energy subspaces is employed. We find that for large lattices there exists a stable window of the scaled order-parameter in which the full ansatz including the pre-exponential factor for the tail regime of the universal PDF is well obeyed. This window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal PDF. The probability densities are used to estimate the universal Privman-Fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime.

We study the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. We propose a preferential-attachment scheme, in which a new node attaches to an existing node $i$ with probability $\Pi \left(k_i\right)\propto k_i^{-1}$, where $k_i$ is the number of outgoing links at $i$. We calculate the degree distribution for the outgoing links in the asymptotic regime $(t\to \infty )$, $n_k^{*}$, both analytically and by Monte Carlo simulations. The distribution decays like $k{\mu }^k∕\Gamma \left(k\right)$ for large $k$, where $\mu$ is a constant. We investigate the effect of this preferential-attachment scheme, by comparing the results to an equivalent growth model with a degree-independent probability of attachment, which gives an exponential outdegree distribution. Also, we relate this mechanism to simple food-web models by implementing it in the cascade model. We show that the low-degree preferential-attachment mechanism breaks the symmetry between in- and outdegree distributions in the cascade model. It also causes a faster decay in the tails of the outdegree distributions for both our network growth model and the cascade model.

We investigate the simultaneous formation and propagation of coupled ultraslow optical soliton pairs in a cold, lifetime-broadened three-state double-$\Lambda$ atomic system. Starting from the equations of motion of atomic response and two-mode probe-control electromagnetic fields, we derive coupled nonlinear Schrödinger equations that govern the nonlinear evolution of the envelopes of the probe fields in this four-wave mixing scheme by means of the standard method of multiple scales. We demonstrate that for weak probe fields and with suitable operation conditions, a pair of coupled optical solitons moving with remarkably slow propagating velocity can be established in such a highly resonant atomic medium. The key elements to such a shape preserving, well matched yet interacting soliton pair is the balance between dispersion effect and self- and cross-phase modulation effects of the system.

The relative performances of different implementations of the Wang-Landau method are assessed on two classes of systems with continuous degrees of freedom, namely, two polypeptides and two atomic Lennard-Jones clusters. Parallel tempering Monte Carlo simulations serve as a reference, and we pay particular attention to the variations of the multiplicative factor $f$ during the course of the simulation. For the systems studied, the Wang-Landau method is found to be of comparable accuracy as parallel tempering, but has significant difficulties in reproducing low-temperature transitions exhibited by the Lennard-Jones clusters at low temperature. Using a complementary order parameter and calculating a two-dimensional joint density of states significantly improves the situation, especially for the notoriously difficult ${\mathrm{LJ}}_{38}$ system. However, while parallel tempering easily converges for ${\mathrm{LJ}}_{31}$, we have not been able to get data of comparable accuracy with Wang-Landau multicanonical sampling.

The shape of a granular pile in a rotating drum is investigated. Using discrete elements method (DEM) simulations we show that the “$\mathsf{S}$ shape” obtained for high rotation speed can be accounted for by the friction on the end plates. A theoretical model which accounts for the effect of the end plates is presented and the equation of the shape of the free surface is derived. The model reveals a dimensionless number which quantifies the influence of the end plates on the shape of the pile. Finally, the scaling laws of the system are discussed and numerical results support our conclusions.

An inertial Brownian motor with time-delayed feedback driven by an unbiased time-periodic force is investigated. It is found that the mean velocity and the rectification efficiency are decreased when the noise intensity is increased. While the shape of the mean velocity and the rectification efficiency can be changed from one peak to two peaks when the time delay is increased, the symmetry in the velocity probability distribution function is broken when the delay time is increased.

Orientational ordering of short and intermediate $n$-alkanes confined to silicon nanotubes has been studied using ${}^1\mathrm{H}$ NMR. The measured residual nuclear dipolar couplings characterizing the degree of molecular ordering were found to depend on the pore size and the molecular length in a complex way. It is inferred from the experimental results that the observed behavior is governed by concomitance of surface and intermolecular interactions as well as the effect of confinement.

We consider the coupling between the local curvature tensor of a membrane and the local two-dimensional nematic order parameter, deriving it from a quasi-microscopic argument. This coupling makes the nematic director aligned along the lowest curvature eigenvector in a local metric. Local bending of a membrane may then generate nematic ordering. Alternatively, emerging nematic order leads to shape instabilities of closed vesicles. The theory is applied to a spherical isotropic vesicle, which turns into a prolate shape with two $+1$ disclinations on its poles as the nematic order sets in the membrane, described within the Landau-de Gennes continuum model.

A neuron that is stimulated repeatedly by the same time-dependent stimulus exhibits slightly different spike timing at each trial. We compared the exact solution of the time-dependent firing rate for a stochastically spiking neuron model with refractoriness (spike response model) with that of an inhomogeneous Poisson process subject to the same stimulus. To arrive at a mapping between the two models we used alternatively (i) a systematic parameter-free Volterra expansion of the exact solution or (ii) a linear filter combined with nonlinear Poisson rate model (linear-nonlinear Poisson cascade model) with a single free parameter. Both the cascade model and the second-order Volterra model showed excellent agreement with the exact rate dynamics of the spiking neuron model with refractoriness even for strong and rapidly changing input. Cascade rate models are widely used in systems neuroscience. Our method could help to connect experimental rate measurements to the theory of spiking neurons.

Core percolation and maximum independent set on random graphs have recently been characterized using the methods of statistical physics. Here we present a statistical physics study of these problems on bond diluted triangular lattices. Core percolation critical behavior is found to be consistent with the standard percolation values, though there are strong finite size effects. A transfer matrix method is developed and applied to find accurate values of the density and degeneracy of the maximum independent set on lattices of limited width but large length. An extrapolation of these results to the infinite lattice limit yields high precision results, which are tabulated. These results are compared to results found using both vertex based and edge based local probability recursion algorithms, which have proven useful in the analysis of hard computational problems, such as the satisfiability problem.