We study static and dynamic correlations of two fluctuations, the charge density fluctuation and height fluctuation (undulation), on a fluid membrane with a finite excess charge in a viscous fluid. For a planar and symmetrical membrane, we consider a model Hamiltonian inclusive of the fluctuations at the Gaussian level, and construct their equations of motion. Within the model, there exists no coupling, either static or dynamic, between the two fluctuations. The correlation function of the charge density has a short-range damped oscillation over the size of lipid heads due to Coulomb attraction between unlike-charged lipids. Its dynamic correlation function is shown to decay much faster in time than that in simple diffusion. The correlation function of height undulation, on the other hand, has a long-range damped oscillation (bud) over the membrane size, due to Coulomb repulsion among the excess charges. As the excess charge density increases to a critical value, a bending instability sets in, where a minute perturbation on the membrane can cause a large bud to form. Due to the excess charge, the dynamic correlation of the undulation decays slowly in time; at the critical density of the instability, the decay becomes infinitely slow.

Since the observation of antispirals by Vanag et al. in a reaction-diffusion system, the study of its origin becomes a focus of nonlinear science and pattern formation. It was shown that antispirals may exist in a reaction-diffusion system when the system is near the onset of Hopf bifurcation. Here, we demonstrate that antispiral waves can also exist in a relaxational oscillatory medium, which is far from Hopf onset. Furthermore, we clarify the previously unclear concept of group velocity in inharmonic nonlinear waves, and prove that the group velocity $v_g=d\omega ∕dk$ is physically significant and valid both for excitable media and for oscillatory media. From this formula, we identify two types of wave propagating fronts: gentle mode front and steep mode front. Finally, we discuss the origin of counterpropagating waves and propose necessary conditions for antispiral formation. A direct deduction from these criteria is that antispirals cannot exist in an excitable medium.

A temporal linear stability analysis is carried out for a coflowing jet with two immiscible inviscid liquids under a uniform axial electric field. According to the electrical properties of the inner and outer liquids, four cases, i.e., IDOC (inner: dielectric; outer: conductor), ICOD (inner: conductor; outer: dielectric), ICOC (inner and outer: conductor), and IDOD (inner and outer: dielectric), are considered. The analytical dimensionless dispersion relation is derived for both axisymmetric and nonaxisymmetric perturbations and is solved for axisymmetric ones. Three unstable modes, i.e., the paravaricose, parasinuous and transitional modes, are identified in the Rayleigh regime. The influences of the axial electric field, liquid electrical properties, and Weber number are studied at length. The results show that the axial electric field has a generally stabilizing effect on the unstable modes. The effects of the liquid electrical properties are quite different but all great for each case. The change of dominant mode is detected with the variation of the electric field intensity, electrical properties or Weber number. It is found that the parasinuous instability is the easiest to realize in IDOC. And the comparison with the experiment validates that the parasinuous mode is predominant in coaxial electrospray.

The collective and single-electron amplification regimes of a noncollinear free-electron laser (FEL) are studied within the framework of dispersion equations. In the limit of small-signal gain the growth rates and the conditions for self-amplified excitations are found for the collective (Raman) and single-electron (Thompson) regimes. The Raman regime is shown to be preferable for the coherent spontaneous second harmonic generation by ultrarelativistic electron beams. Raman excitations in a noncollinear FEL, e.g., in an FEL without inversion, are favored by the noncollinear geometry of the electron and the laser beams, and by the relativity of the beam electrons.

We investigate the modulational instability of Stokes wave solutions on a system of coupled nonlinear electrical transmission lines with dispersive elements. In the continuum limit, and in suitable scaled coordinates, the voltage on the system is described by the two-dimensional coupled nonlinear Schrödinger equations. The set of coupled nonlinear Schrödinger equations obtained is analyzed via a perturbation approach. No assumption is made on the signs of the relevant coefficients such as the coefficients of nonlinearity and the coupling coefficients. A set of explicit criteria of modulational stability and modulational instability is derived and analyzed. It is numerically shown that the effect of the dispersive elements in the line is to decrease the instability region and the instability growth rate.

We perform direct thermal emission calculations for three-dimensionally periodic photonic crystal slabs using stochastic electrodynamics following the Langevin approach, implemented via a finite-difference time-domain algorithm. We demonstrate that emissivity and absorptivity are equal, by showing that such photonic crystal systems emit as much radiation as they absorb, for every frequency, up to statistical fluctuations. We also study the effect of surface termination on absorption and emission spectra from these systems.

We present a method for calculating the transmission spectra, dispersion, and time delay characteristics of optical-waveguide gratings based on Green’s functions and Dyson’s equation. Starting from the wave equation for transverse electric modes we show that the method can solve exactly both the problems of coupling of counterpropagating waves (Bragg gratings) and co-propagating waves (long-period gratings). In both cases the method applies for gratings with arbitrary dielectric modulation, including all kinds of chirp and apodization and possibly also imperfections in the dielectric modulation profile of the grating. Numerically, the method scales as $O\left(N\right)$ where $N$ is the number of points used to discretize the grating along the propagation axis. We consider optical fiber gratings although the method applies to all one-dimensional (1D) optical waveguide gratings including high-index contrast gratings and 1D photonic crystals.

Photonic-crystal fibers are employed to demonstrate widely tunable frequency down-conversion of unamplified $6\text{−}\mathrm{fs}$ Ti:sapphire laser pulses through the soliton self-frequency shift induced by the Raman effect. Wavelength shifts as large as $500\mathrm{nm}$ are achieved for input few-cycle pulses with broadband spectra centered at approximately $820\mathrm{nm}$. The central wavelength of the redshifted output of a photonic-crystal fiber is smoothly tuned from the low-frequency edge in the spectrum of the $6\text{−}\mathrm{fs}$ Ti:sapphire laser pulse up to $1.35\mu \mathrm{m}$ by varying the input energy in the fundamental mode of the fiber.

We study the behavior of a heuristic for solving random satisfiability problems by stochastic local search near the satisfiability threshold. The heuristic for average satisfiability (ASAT), is similar to the Focused Metropolis Search heuristic, and shares the property of being focused, i.e., only variables in unsatisfied clauses are updated in each step. It is significantly simpler than the benchmark WALKSAT heuristic. We show that ASAT solves instances as large as $N={10}^6$ in linear time, on average, up to a ratio of 4.21 clauses per variable in random three-satisfiability. For $K$ higher than 3, ASAT appears to solve instances of $K$-satisfiability up to the Montanari-Ricci-Tersenghi-Parisi full replica symmetry breaking (FSRB) threshold denoted ${\alpha }_s\left(K\right)$ in linear time.

Motivated by aggregation phenomena in gliding bacteria, we study collective motion in a two-dimensional model of active, self-propelled rods interacting through volume exclusion. In simulations with individual particles, we find that particle clustering is facilitated by a sufficiently large packing fraction $\eta$ or length-to-width ratio $\kappa$. The transition to clustering in simulations is well captured by a mean-field model for the cluster size distribution, which predicts that the transition values ${\kappa }_c$ of the aspect ratio for a fixed packing fraction $\eta$ are given by ${\kappa }_c=C∕\eta -1$ where $C$ is a constant.

The random-energy model is studied in the presence of random fields. The problem is solved exactly both in the microcanonical ensemble, without recourse to the replica method, and in the canonical ensemble using the replica formalism. The phase diagrams for bimodal and Gaussian random fields are investigated in detail. In contrast to the Gaussian case, the bimodal random field may lead to a tricritical point and a first-order transition. An interesting feature of the phase diagram is the possibility of a first-order transition from paramagnetic to mixed phase.

The effect of three-body interactions on the solid-liquid phase boundaries of argon, krypton, and xenon is investigated via a novel technique that combines both nonequilibrium and equilibrium molecular dynamics. The simulations involve the evaluation of two- and three-body forces using accurate two-body and three-body intermolecular potentials. The effect of three-body interactions is to substantially increase the coexistence pressure and to lower the densities of liquid and solid phases. Comparison with experiment indicates that three-body interactions are required to accurately determine the total pressure. In contrast to vapor-liquid phase equilibria, the relative contribution of three-body interactions to the freezing pressure exceeds the contribution of two-body interactions at all temperatures.

Phase separation in a capillary tube with one of the phases fully wetting the capillary wall is arrested when the typical size of the phase domains reaches the value of the diameter of the tube. The arrested state consists of an alternating sequence of concave-capped and convex-capped cylindrical domains, called “plugs,” “bridges,” or “lenses,” of wetting and nonwetting phase, respectively. A description of this arrested plug state for an aqueous mixture of two polymer solutions is the subject of this work. A phase separating system consisting of two incompatible polymers dissolved in water was studied. The phase volume ratio was close to unity. The initial state from which plugs evolve is characterized by droplets of wetting phase in a continuous nonwetting phase. Experiments show the formation of plugs by a pathway that differs from the theoretically well-described instabilities in the thickness of a fluid thread inside a confined fluid cylinder. Plugs appear to form after the wetting layer (the confined fluid cylinder) has become unstable after merging of droplet with the wetting layer. The relative density of the phases could be set by the addition of salt, enabling density matching. As a consequence, the capillary length can in principle be made infinitely large and the Bond number (which represents the force of gravity relative to the capillary force) zero, without considerably changing the interfacial tension. Using the possibility of density matching, the relations among capillary length and capillary diameter on the one hand, and the presence of plugs and their average size on the other were studied. It was found that stable plugs are present when the capillary radius does not exceed a certain value, which is probably smaller than the capillary length. However, the average plug size is independent of capillary length. At constant capillary length, average plug size was found to scale with the capillary diameter to a power 1.3, significantly higher than the expected value of 1. Plug sizes had a polydispersity between 1.1 and 1.2 for all capillary radii for which this number could be reliably determined, suggesting a universal plug size distribution. Within plug sequences, size correlations were found between plugs with one to three plugs in between. This suggests the presence of an additional length scale.

Quasicrystal growth remains an unsolved problem in condensed matter. The dynamics of the process is studied by means of synchrotron live imaging all along the solidification of icosahedral AlPdMn quasicrystals. The lateral motion of ledges driving faceted growth at the solid-melt interface is conclusively shown. When the solidification rate is increased, nucleation and free growth of new faceted grains occur in the melt due to the significant interface recoil induced by slow attachment kinetics. The detailed analysis of the evolution of these grains reveals the crucial role of aluminum rejection, both in the poisoning of their growth and driving fluid flow.

Using x-ray photon correlation spectroscopy, we studied the layer fluctuations in the lamellar phase of an ionic lyotropic system. We measured the relaxation rate of in-plane (undulation) fluctuations as a function of the wave vector. Static and dynamic results obtained during the same experiment were combined to yield the values of both elastic constants of the lamellar phase (compression and bending moduli) as well as that of the sliding viscosity. The results are in very good agreement with dynamic light-scattering data, validating the use of the technique in ordered phases.

The (pre)wetting behavior of an annealed polyelectrolyte (PE) brush by an electrolyte solution that is strongly segregated from an apolar phase is analyzed. In this complex interface, there are interactions on various length scales. There are short-range interactions with the (uncharged) surface, and there are interactions on the length scale of the brush height. Using either the ionic strength or the water-surface interaction strength as the control parameters, it is possible to approach and induce a wetting transition in this system. The first-order wetting transition, promoted by favorable short-range substrate interactions with the surface, is in competition with the wetting transition controlled by the detachment of the fluid interface from the periphery of the PE brush. The electric double layer on top of the PE brush contributes with a repulsive forces to the disjoining pressure that tends to thicken the wetting film, and therefore, the transition in all cases is first order. Various phase portraits of the wetting phase diagram are envisioned. One of these features the crossing of two prewetting lines. At the crossing point three surface states coexist. This triple point is analyzed in some detail with the help of a molecular-level self-consistent field model.

We express community detection as an inference problem of determining the most likely arrangement of communities. We then apply belief propagation and mean-field theory to this problem, and show that this leads to fast, accurate algorithms for community detection.

We provide compelling evidence for the presence of quantum chaos in the unitary part of the operator usually employed in Shor’s factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the eigenangles as well as the distribution of the eigenvector components follow the circular unitary ensemble of random matrices, of relevance to quantized chaotic systems that violate time-reversal symmetry. However, as the algorithm tracks the evolution of a single state, it is possible to employ other operators; in particular, it is possible that the generic quantum chaos found above becomes of a nongeneric kind such as is found in the quantum cat maps and in toy models of the quantum baker’s map.

Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behavior, which are known to depend on topology, can also be explored by tuning the form of the interactions at fixed topology. For a model of opinion formation, simple mean field and scaling arguments show that a mapping ${\gamma }^{\prime }=(\gamma -\mu )∕(1-\mu )$ describes how a shift of the standard exponent $\gamma$ of the degree distribution can absorb the effect of degree-dependent pair interactions $J_{ij}\propto {\left(k_i{k}_j\right)}^{-\mu }$, where $k_i$ stands for the degree of vertex $i$. This prediction is verified by extensive numerical investigations using the cavity method and Monte Carlo simulations. The critical temperature of the model is obtained through the Bethe-Peierls approximation and with the replica technique. The mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network.

We analyze gap solitons in trapped Bose-Einstein condensates (BECs) in optical lattice potentials under Feshbach resonance management. Starting with an averaged Gross-Pitaevsky equation with a periodic potential, we employ an envelope-wave approximation to derive coupled-mode equations describing the slow BEC dynamics in the first spectral gap of the optical lattice. We construct exact analytical formulas describing gap soliton solutions and examine their spectral stability using the Chebyshev interpolation method. We show that these gap solitons are unstable far from the threshold of local bifurcation and that the instability results in the distortion of their shape. We also predict the threshold of the power of gap solitons near the local bifurcation limit.