We present exact calculations of the spatial correlation of the blackbody radiation in the presence of spheres whose dimensions are smaller or comparable to the radiation wavelength. By going beyond the standard scalar coherence theory, we show that the spatial correlation function of a spherical thermal source is not universal but depends on the material properties of the source and exhibits near-field-induced features. Near-field effects are also manifested in the case of a linear chain of dielectric spheres where the correlation function probes the inhomogeneity of the chain. For this latter system we have established the conditions when the near-field effects cancel out and the correlation function takes the typical form of a conventional Lambertian source. For the case of a chain of metallic nanospheres, the increased spatial correlation of the far field leads to a directional thermal emission spectrum.

We investigate the formation of collisionless shocks along the spatial profile of a Gaussian laser beam propagating in nonlocal nonlinear media. For defocusing nonlinearity the shock survives the smoothing effect of the nonlocal response, though its dynamics is qualitatively affected by the latter, whereas for focusing nonlinearity it dominates over filamentation. The patterns observed in a thermal defocusing medium are interpreted in the framework of our theory.

We show that by placing a metal plate next to a two-dimensional phononic crystal, acoustic waves can tunnel through the combined structure at a specific frequency that lies inside the band gap of the phononic crystal. The enhanced transmission is attributed to the coupling of the input waves with the acoustically resonant states created between the metal plate and the phononic crystal. Experiments are in excellent agreement with the theoretical predictions.

In this Letter, we show that the energy equivalent to that incident on a $4.7\mu \mathrm{m}$ wide strip can be squeezed through a 50 nm wide slit in a metal film surrounded by grooves. This corresponds to a transmission efficiency of 9400%, which can be even further enhanced by increasing the number of grooves. We use the phase of the magnetic field to explain that the ideal slit-to-groove distance is just over half the plasmon wavelength. In addition, we also optimize the groove depth and width. Such optimized transmission enhancement is very important for near-field devices.

A perm-selective nanochannel could initiate concentration polarization near the nanochannel, significantly decreasing (increasing) the ion concentration in the anodic (cathodic) end of the nanochannel. Such strong concentration polarization can be induced even at moderate buffer concentrations because of local ion depletion (therefore thicker local Debye layer) near the nanochannel. In addition, fast fluid vortices were generated at the anodic side of the nanochannel due to the nonequilibrium electro-osmotic flow (EOF), which was at least $\sim 10\times$ faster than predicted from any equilibrium EOF. This result corroborates the relation among induced EOF, concentration polarization, and limiting-current behavior.

A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on fully nonlinear equations describing weakly three-dimensional potential flows of an ideal fluid with a free surface in terms of conformal variables. Spontaneous formation of zigzag patterns for wave amplitude is observed in a nonlinear stage of the instability. If initial wave steepness is sufficiently high ($ka>0.06$), these coherent structures produce rogue waves. The most tall waves appear in turns of the zigzags. For $ka<0.06$, the structures decay typically without formation of steep waves.

We examine the time-dependent distortion of a nearly circular viscous domain in an infinite viscous sheet when suction occurs. Suction, the driving force of the instability, can occur everywhere in the two phases separated by an interface. The model assumes a two-dimensional Stokes flow; the selection of the wavelength at short times is determined by a variational procedure. Contrary to the viscous fingering instability, undulations of the boundary may be observed for enough pumping, whatever the sign of the viscosity contrast between the two fluids involved. We apply our model to the suction by lipoproteins of cholesterol-enriched domains in giant unilamellar vesicles. Comparison of the number of undulations given by the model and by the experiments gives reasonable values of physical quantities such as the viscosities of the domains.

We have demonstrated nonlinear cross-phase modulation in electro-optic crystals using intense, single-cycle terahertz (THz) radiation. Individual THz pulses, generated by coherent transition radiation emitted by subpicosecond electron bunches, have peak energies of up to $100\mu \mathrm{J}$ per pulse. The time-dependent electric field of the intense THz pulses induces cross-phase modulation in electro-optic crystals through the Pockels effect, leading to spectral shifting, broadening, and modulation of copropagating laser pulses. The observed THz-induced cross-phase modulation agrees well with a time-dependent phase-shift model.

The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the edge of chaos which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in Skufca et al., Phys. Rev. Lett. 96, 174101 (2006), we show that superimposed on an overall $1/\mathrm{Re}$ scaling predicted and studied previously there are small, nonmonotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.

We develop a kinetic Boltzmann equation for describing filtered fluid turbulence applicable for continuum and noncontinuum effects. The effect of unresolved turbulent motion on the resolved distribution function is elucidated and closure modeling issues of kinetic Boltzmann and Navier-Stokes descriptions are reconciled. This could pave the way for unifying turbulence modeling at kinetic and continuum levels and the development of numerical methods that are valid over a wide range of flow physics.

We report on the experimental observation of coherence resonance in a bistable system with delay. Our system consists of a vertical-cavity surface-emitting laser subject to time-delayed optical feedback simultaneously from a long and from an extremely short external cavity. Coherence resonance is experimentally proven by analysis of the residence time distribution of the polarization mode-hopping regime and of the signal to noise ratio in the power spectrum.

A nonlinear optical medium results by the collective orientation of liquid crystal molecules tightly coupled to a transparent photoconductive layer. We show that such a medium can give a large gain; thus, if inserted in a ring cavity, it results in an unidirectional optical oscillator. We report new dynamical regimes characterized by the generation of spatiotemporal pulses, localized in three dimensions and arising from the random superposition of many longitudinal and transverse modes with different frequencies.

Through a new rigorous Bloch-mode formalism, we theoretically study the generation of photons in single-row-defect photonic-crystal waveguides. In contrast with previous related works relying on a reinforcement of the spontaneous emission (SE) through microcavity effects, we explore situations for which the SE into radiation modes is reduced to a very low level while the SE into the guided mode is maintained at a level comparable to that in the bulk material. Remarkably large SE $\beta$ factors in excess of 95% are obtained, and since no resonance effect is involved, this efficiency is achieved over a 40-nm-large spectral interval at $\lambda \approx 950\mathrm{nm}$.

Overall homogeneity of temperature is a condition for thermal equilibrium, but, as is demonstrated by classical molecular dynamics simulations, the local temperatures of atoms in small, isolated crystalline clusters in microcanonical equilibrium are not uniform. The effective temperature determined from individual atomic velocity decreases with distance from the cluster center. It is argued that these effects are due to the conservation of angular and translational momentum. A general microcanonical expression is derived for the spatial dependence of the statistics of the kinetic energies of individual atoms; this fits the numerical observations well.

The leading Pollicott-Ruelle resonance is calculated analytically for a general class of two-dimensional area-preserving maps. Its wave number dependence determines the normal transport coefficients. In particular, a general exact formula for the diffusion coefficient $D$ is derived without any high stochasticity approximation, and a new effect emerges: The angular evolution can induce fast or slow modes of diffusion even in the high stochasticity regime. The behavior of $D$ is examined for three particular cases: (i) the standard map, (ii) a sawtooth map, and (iii) a Harper map as an example of a map with a nonlinear rotation number. Numerical simulations support this formula.

An $H$ theorem for the linearized Grad 13 moment equations leads to regularizing constitutive equations for higher fluxes and to a complete set of boundary conditions. Solutions for Couette and Poiseuille flows show good agreement with direct simulation Monte Carlo calculations. The Knudsen minimum for the relative mass flow rate is reproduced.

We present an experimental study of the statistics of surface gravity wave turbulence in a flume of a horizontal size $12\times 6\mathrm{m}$. For a wide range of amplitudes the wave energy spectrum was found to scale as $E_{\omega }\sim {\omega }^{-\nu }$ in a frequency range of up to one decade. However, $\nu$ appears to be nonuniversal: it depends on the wave intensity and ranges from about 6 to 4. We discuss our results in the context of existing theories and argue that at low wave amplitudes the wave statistics is affected by the flume finite size, and at high amplitudes the wave breaking effect dominates.

We show that ballistic transport of optically excited atoms in an atomic vapor provides a nonlocal nonlinearity which stabilizes the propagation of vortex beams and higher order modes in the presence of a self-focusing nonlinearity. Numerical experiments demonstrate stable propagation of higher order nonlinear states (dipole, vortices, and rotating azimuthons) over a hundred diffraction lengths, before dissipation leads to decay of these structures.

We demonstrate an isotropic phase matching in properly designed nonlinear two-dimensional photonic crystals. In addition, by combining left- and right-handed properties at the fundamental and second-harmonic frequencies, we obtain a backward second-harmonic generation. These two properties lead to an unusual second-harmonic localization effect in perfect lattice photonic crystals.

High-order harmonic generation from muonic atoms exposed to intense laser fields is considered. Our particular interest lies in effects arising from the finite nuclear mass and size. We numerically perform a fully quantum mechanical treatment of the muon-nucleus dynamics by employing modified soft-core and hard-core potentials. It is shown that the position of the high-energy cutoff of the harmonic spectrum depends on the nuclear mass, while the height of the spectral plateau is sensitive to the nuclear radius. We also demonstrate that $\gamma$-ray harmonics can be generated from muonic atoms in ultrastrong VUV fields, which have potential to induce photonuclear reactions.