We perform experiments on the chlorine dioxide-iodine-malonic acid (CDIMA) reaction forced with light with a pattern of moving stripes in which the spatiotemporal behavior is the oscillating movement of stripes (waving). This behavior is seen for different relative wavelengths between stationary and moving patterns. Different velocities of forcing may produce different modes of relaxation of the pattern in order to get to the natural Turing wavelength. Zigzag or Eckhaus instabilities may affect the symmetry of the pattern but do not influence the waving movement of stripes.

The dynamical behavior of a weakly diluted fully inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochasticlike regime is observed. In the weak-coupling phase, a periodic dynamics is rapidly approached, with all neurons firing with the same rate and mutually phase locked. The strong-coupling phase is characterized by an irregular pattern, even though the maximum Lyapunov exponent is negative. The paradox is solved by drawing an analogy with the phenomenon of “stable chaos,” i.e., by observing that the stochasticlike behavior is “limited” to an exponentially long (with the system size) transient. Remarkably, the transient dynamics turns out to be stationary.

Recently, it was shown that using an ellipsoidal mesh in an einzel-type lens, spherical aberration can be corrected over a wide acceptance angle of up to 120°. The present paper creates the possibility for beam analysis by achieving dramatic improvements in deceleration lens capabilities. This provides a scheme for simultaneous angular distribution measurement suitable for application to high-energy charged-particle beams up to around $10\mathrm{keV}$. We consider the behavior of wide-angle charged-particle beams in electrostatic fields given by simple solutions of the Laplace equation, starting with a discussion on a spherically symmetric deceleration field. A beam focusing over a wide acceptance angle of 100° is found in a special spherically symmetric field. However, in many cases of the spherically symmetric field, focusing of wide-angle beams is obstructed by the presence of spherical aberration. We show that the spherical aberration can be corrected by two kinds of deformation of the spherically symmetric field, a deformation of the field under a spherical boundary condition and an ellipsoidal deformation of the field. We study practical realization of such fields under the use of a few electrodes and a curved mesh (spherical or ellipsoidal mesh). Some variations of the arrangement of electrodes are considered, and simple designs of deceleration lenses with wide acceptance angles of up to 120° are obtained. Here fine focusing of wide-angle beams can be achieved in a three-electrode deceleration lens with an ellipsoidal mesh.

We introduce an inhomogeneously nonlinear Schrödinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such inhomogeneous settings present vastly different dynamical behavior in the vicinity of the interface than the one expected in their homogeneous counterparts. We analyze the relevant stationary states, as well as their stability, by means of perturbation theory and linear stability analysis. We find good agreement with the numerical findings in the vicinity of the anticontinuum limit. For larger values of the coupling, we follow the relevant branches numerically and show that they terminate at values of the coupling strength which are larger for more extended solutions. The dynamical development of relevant instabilities is also monitored in the case of unstable solutions.

The well-established procedure of deriving lattice Boltzmann schemes using the trapezoidal rule for time integration is generalized to the recently introduced lattice Fokker-Planck method.

We consider the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further the issue of the “imaginary” Langevin noise that appears in the context of reaction-diffusion processes. Our procedure applies to a wide class of problems and is related to large deviation functional techniques developed recently to describe fluctuations of nonequilibrium systems in the hydrodynamic limit.

We studied the pair correlation function $g\left(r\right)$ of silica particles with a fluorescent core and a nonfluorescent shell which were confined between two glass plates by optical video microscopy. To investigate the possible role of optical artifacts due to overlapping particle images, we compared experiments, where, first, the whole particle (white image) and then, only the fluorescent core (fluorescent image) was used for determining particle positions. While under white-image conditions the observed $g\left(r\right)$ exhibits a main peak at about 1.2 times the particle’s diameter; under fluorescent image conditions the obtained $g\left(r\right)$ resembles a short-ranged repulsive system where the main peak is close to contact. This discrepancy points towards artifacts of video microscopy, leading to erroneous $g\left(r\right)$ and in turn to erroneous effective-pair potentials.

Binary mixtures growing on small-world networks under far-from-equilibrium conditions are studied by means of extensive Monte Carlo simulations. For any positive value of the shortcut fraction of the network $(p>0)$, the system undergoes a continuous order-disorder phase transition, while it is noncritical in the regular lattice limit $(p=0)$. Using finite-size scaling relations, the phase diagram is obtained in the thermodynamic limit and the critical exponents are evaluated. The small-world networks are thus shown to trigger criticality, a phenomenon analogous to similar observations reported recently in the investigation of equilibrium systems.

We have studied a bent-core liquid crystal where two different optically isotropic phases can be induced by a strong electric field. Depending on the field treatment the phases can present optical rotation or be optically inactive. The switching dynamics of the phases is studied by means of electrooptic and optical second-harmonic generation measurements. It is found that the ground state of the phases is locally antiferroelectric. The structure of the phases is consistent with a disordered version of the kind of structures recently proposed for the smectic blue phase: layered systems with high Gaussian curvature. The origin of the smectic layer distortion is discussed. It is concluded that the direct reason for the curvature of planes is of steric nature.

An experimental study of the $B_1$-$B_2$ transition is carried out in a bent-core liquid crystal. The study is essentially based on x-ray measurements as a function of temperature. The $B_1$-$B_2$ transition is extremely unusual and implies a deep structural change from a columnar phase to a lamellar phase. We have found that the $B_1$ phase in our compound is similar to the so-called $B_1$ reversed phase, with an additional splay of the polarization in the columns. On approaching the $B_2$ phase the width of the cross section of the columns increases. The transition is clearly first order, with a large hysteresis though the enthalpy content is very small. A possible mechanism for the transition is briefly sketched.

We have studied the collective calcium signaling behavior of an array of coupled $N$ cells, taking into account the internal noises resulting from the small cell size $V$. The system’s performance was characterized by the reciprocal coefficient of variance (RCV) of the calcium spike train. Two system-size resonances were observed, namely, the RCV value shows a clear peak when both $N$ and $V$ are optimal. Therefore, an optimal number of cells of optimal size work the best as a whole.

The theory of Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] is extended to include the effect of a magnetic field on convection of an electrically conducting fluid. Different scaling laws are obtained depending on whether the bulk or the boundary layers make the major contribution to the dissipation. Scalings are obtained for both weak and strong magnetic fields. The predictions are shown to be in better agreement with experimental data than earlier theoretical models.

We study the condensation phenomenon in a zero range process on weighted scale-free networks in order to show how the weighted transport influences the particle condensation. Instead of the approach of grand canonical ensemble which is generally used in a zero range process, we introduce an alternate approach of the mean-field equations to study the dynamics of particle transport. We find that the condensation on the scale-free network is easier to occur in the case of weighted transport than in the case of weight-free networks. In the weighted transport, especially, a dynamical condensation is even possible for the case of no interaction among particles, which is impossible in the case of weight-free networks.

We consider a model system of two coupled Hopfield neurons, which is described by delay differential equations taking into account the finite signal propagation and processing times. When the delay exceeds a critical value, a limit cycle emerges via a supercritical Hopf bifurcation. First, we calculate its frequency and trajectory perturbatively by applying the Poincaré-Lindstedt method. Then, the perturbation series are resummed by means of the Shohat expansion in good agreement with numerical values. However, with increasing delay, the accuracy of the results from the Shohat expansion worsens. We thus apply variational perturbation theory (VPT) to the perturbation expansions to obtain more accurate results, which moreover hold even in the limit of large delays.

We show that arrival times for electromagnetic pulses measured through the rate of absorption in an ideal impedance matched detector are equivalent to the arrival times using the average flow of optical energy as proposed by Peatross et al. [Phys. Rev. Lett. 84, 2370 (2000)]. We then investigate the transport of optical pulses through dispersive media with negative dielectric permittivity and negative refractive index choosing the geometry such that no resonant effects come into play. For evanescent waves, the definitions of the group delay, and the reshaping delay get interchanged in comparison to propagating waves. The total delay times for the evanescent waves can be negative in an infinite plasma medium even for broadband pulses. The total delay time is, however, positive for broadband pulses in the presence of an interface when the radiation is detected outside the plasma. We find evidence of the Hartman effect for pulses when the distance traversed in the plasma is much smaller than the free space pulse length. We also show that for a negative refractive index medium (NRM) with $\epsilon \left(\omega \right)=\mu \left(\omega \right)$ the reshaping delay for propagating waves is identically zero. The total delay time in NRM is otherwise dominated by the reshaping delay time, and for broadband pulses in NRM the total delay time is subluminal.

A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general path integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid ${}^4\mathrm{He}$ in two and three dimensions, as well as the calculation of the chemical potential of hcp ${}^4\mathrm{He}$.

The orientational order of liquid crystals (LCs) induced by periodic patterned substrates has been investigated with cells coated by azopolymer films that could be photoaligned in a controlled way. Two regimes were observed depending on the period of the patterns: (i) above $3.0\mathrm{\mu }\mathrm{m}$ the LC follows the direction imposed by the patterned substrate since the energy stored in the surface potential minimizes the elastic energy of the LC medium. (ii) For periods smaller than $1.0\mathrm{\mu }\mathrm{m}$ a homogeneous in-plane state was induced and the LC did not follow the orientation imposed by the surface. This in-plane transition could be explained qualitatively by a theoretical model based on the competition between the Frank-Oseen elastic energy and the phenomenological surface potential. The results also suggest an out-of-plane transition for the LC director as the period was reduced. These results agree with data in the literature for patterned substrates with completely distinct architectures. This indicates that for a particular LC sample the overall behavior depends basically on the texture period instead of the texture architecture. The textures were characterized with a scanning near-field optical microscope (SNOM), which allowed simultaneous morphological and optical images in the submicrometer range.

Photonic-crystal-type nanostructures occurring in the scales of the butterfly Cyanophrys remus were investigated by optical and electron microscopy (scanning and transmission electron microscopy), reflectance measurements (specular, integrated, and goniometric), by fast Fourier transform analysis of micrographs, by modeling, and by numerical simulation of the measured reflectance data. By evaluating the collected data in a cross-correlated way, we show that the metallic blue dorsal coloration originates from scales which individually are photonic single crystals of $50\times 120\mu {\mathrm{m}}^2$, while the matt pea-green coloration of the ventral side arises from the cumulative effect of randomly arranged, bright photonic crystallites (blue, green, and yellow) with typical diameters in the $3–10\text{−}\mu \mathrm{m}$ range. Both structures are based on a very moderate refractive index contrast between air and chitin. Using a bleached specimen in which the pigment has decayed with time, we investigated the role of pigment in photonic-crystal material in the process of color generation. The possible biologic utility of the metallic blue (single-crystal) and dull green (polycrystal) textures both achieved with photonic crystals are briefly discussed. Potential applications in the field of colorants, flat panel displays, smart textiles, and smart papers are surveyed.

We consider a semi-infinite nematic in contact with a periodic patterned surface with alternate planar and homeotropic stripes. Extending the work of Barbero et al., we find the free energy (assuming $K_1=K_3$) for the situations where the easy direction on the planar stripe is either perpendicular or parallel to the length of the stripes. We find the bulk free energy difference between the structures to be proportional to $\sqrt{K_2∕K_1}$ and so we consider the possibility of a spontaneous transition between the two states if the azimuthal anchoring energy is sufficiently weak and $K_1\ne K_2$. We compute the critical azimuthal anchoring energy for such a transition in terms of the relative width of the stripes and the period of the pattern and find it to be $\sim {10}^{-6}\mathrm{J}{\mathrm{m}}^{-2}$, comparable to experimental values.

This paper orders certain important issues related to both uncorrelated and correlated networks with hidden variables, in which hidden variables correspond to desired node degrees. In particular, we show that networks being uncorrelated at the hidden level are also lacking in correlations between node degrees. The observation supported by the depoissonization idea allows us to extract a distribution of hidden variables from a given node degree distribution. It completes the algorithm for generating uncorrelated networks that was suggested by other authors. In this paper we also carefully analyze the interplay between hidden attributes and node degrees. We show how to extract hidden correlations from degree correlations. Our derivations provide a mathematical background for the algorithm for generating correlated networks that was proposed by Boguñá and Pastor-Satorras.