We show that pairwise soliton collisions in $N>2$ intensity-coupled nonlinear Schrödinger equations can be reduced to pairwise soliton collisions in two coupled equations. The reduction applies to a wide class of systems, including the $N$-component Manakov system. This greatly simplifies the analysis of such systems and has important implications for the application of soliton collisions to all-optical computing.

Multiphoton fluorescence is used for the direct observation of a new class of breathers in waveguide arrays, which are a coherent superposition of Floquet-Bloch solitons of different bands. These Floquet-Bloch breathers oscillate along their spatial propagation axis, and possess several novel properties. Some behavior of these breathers is readily understood intuitively in terms of the band structure of the waveguide array and the properties of discrete solitons.

A two-dimensional photonic crystal with a rectangular symmetry and low contrast ($<1$) of the dielectric constant is considered. We demonstrate that, despite the absence of a band gap, strong localization of a photon can be achieved for certain “magic” geometries of a unit cell by introducing two $\pi /2$ phase slips along the major axes. The long-living photon mode is bound to the intersection of the phase slips. We calculate analytically the lifetime of this mode for the simplest geometry—a square lattice of cylinders of a radius, $r$. We find the magic radius $r_c$ of a cylinder to be 43.10% of the lattice constant. For this value of $r$, the quality factor of the bound mode exceeds ${10}^6$. A small ($\sim 1\%$) deviation of $r$ from $r_c$ results in a drastic damping of the bound mode.

We use symbolic dynamics to examine the flow of information in unidirectionally coupled chaotic oscillators exhibiting synchronization. The theory of symbolic dynamics reduces chaos to a shift map that acts on a discrete set of symbols, each of which contains information about the system state. Using this transformation we explore so-called achronal synchronization, in which the response lags or leads the drive by a fixed amount of time. We find fundamental tradeoffs between the precision to which the drive state is detected, the quality of synchronization attained, and the delay or anticipation exhibited by the response system. To illustrate these tradeoffs, we provide a physical example using electronic circuits.

We carry out a detailed comparison of soft-particle molecular dynamics simulations with the theory of partially fluidized shear granular flows. We verify by direct simulations a constitutive relation based on the separation of the shear stress tensor into a fluid part proportional to the strain rate tensor, and a remaining solid part. The ratio of these two components is determined by the order parameter. Based on results of the simulations we construct the “free energy” function for the order parameter. We also present the simulations of the stationary deep 2D granular flows driven by an upper wall and compare it with the continuum theory.

The breakdown of turbulent eddies can be characterized by sets of “multipliers,” defined as ratios of velocity increments at successively smaller scales. These quantities were introduced by Kolmogorov, who hypothesized their self-similar statistics and independence at distant scales. Here we report experimental and numerical results on the statistics of these multipliers, for both their magnitude and sign. We show that the multipliers at adjacent scales are not independent but that their correlations decay rapidly in scale separation. New scaling laws are thereby predicted and verified for both roughness and sign of turbulent velocity increments. The sign oscillations per cascade step are found to decrease at points of increasing roughness or singularity of the velocity.

The observation of a novel noncollinear optical second-harmonic generation mechanism is reported. In strontium barium niobate crystals, a circular cone of second-harmonic light is generated when a fundamental beam of intensive laser light is directed along the crystallographic $c$ axis. It can be shown that the effect is caused by the nonlinear polarization of antiparallel ordered ferroelectric microdomains.

We introduce a cycle-expansion (fully deterministic) technique to compute the asymptotic behavior of arbitrary order transport moments. The theory is applied to different kinds of one-dimensional intermittent maps and Lorentz gas with an infinite horizon, confirming the typical appearance of phase transitions in the transport spectrum.

We elaborate the physics of systems of unconstrained, reconnecting vortex filaments with dynamic finite cores of uniform (“quantized”) circulation interacting via Biot-Savart and viscous forces. The phenomenology of this purely structured turbulent system includes an inertial range with Kolmogorov’s $k^{-5/3}$ scaling for the energy spectrum, as well as Kolmogorov’s linear in $r$ scaling for the third order longitudinal structure function.

We report an experimental study of the scattering of sound by sound in the vicinity of the liquid-vapor critical point of carbon dioxide. We measure the amplitude of the scattered difference frequency wave generated by acoustic bulk nonlinearities. We observe that it is strongly increased in the vicinity of the critical point.

We investigate experimentally the subcritical behavior of the Kelvin-Helmholtz instability for a gas-liquid shearing flow in a Hele-Shaw cell. The subcritical curve separating the solutions of a stable plane interface and a fully saturated nonlinear wave train is determined. Experimental results are fitted by a fifth order complex Ginzburg-Landau equation whose linear coefficients are compared to theoretical ones.

We describe broad new classes of three-dimensional (3D) structures which, when made of silicon, exhibit robust 3D photonic band gaps of up to $25\%$ of the gap center frequency. The proposed photonic crystals are readily amenable to very high precision microfabrication using established techniques such as x-ray lithography and template inversion. Each architecture consists of a set of oriented cylindrical pores emanating from a two-dimensional (2D) square lattice mask with a two-point basis. Large bandwidth, microcircuits for light may be incorporated within the resulting photonic band gaps using an intercalated 2D photonic crystal layer.

We show that enhanced wave function localization due to the presence of short unstable orbits and strong scarring can rely on completely different mechanisms. Specifically we find that in quantum networks the shortest and most stable orbits do not support visible scars, although they are responsible for enhanced localization in the majority of the eigenstates. Scarring orbits are selected by a criterion which does not involve the classical stability. We obtain predictions for the energies of visible scars and the distributions of scarring strengths and inverse participation numbers.

Liquid ${}^4\mathrm{H}\mathrm{e}$ at pressures $P_0=0.5–30\mathrm{\text{bars}}$ and temperatures $T_0=1.5–4.2\mathrm{K}$ is discharged into vacuum through two different $2\mu \mathrm{m}$ nozzles. The velocities of the beam of particles obey the Bernoulli equation down to $15\mathrm{m}\mathrm{/}\mathrm{s}\mathrm{e}\mathrm{c}$. With decreasing $T_0$ and increasing $P_0$ the velocity and angular distributions become exceedingly narrow with $\Delta v/v\lesssim 1\%$ and $\Delta \vartheta \lesssim 1\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$. Optical observations indicate that the beam consists of micron-sized droplets ($N\gtrsim {10}^9\mathrm{\text{atoms}}$). This new droplet source provides opportunities for novel experimental studies of superfluid behavior.

We present a unified model of shear-induced demixing and “mechanical” shear banding instabilities in polymeric and surfactant solutions, by combining a simple flow instability with a two-fluid approach to concentration fluctuations. Within this model, we calculate the “spinodal” limit of stability of initially homogeneous shear states to demixing/banding, and predict the selected length and time scales at which inhomogeneity first emerges after a shear start-up “quench” into the unstable region, finding qualitative agreement with experiment. Our analysis is the counterpart, for this driven phase transition, of the Cahn-Hilliard calculation for unsheared fluid-fluid demixing.

Phase-and-polarization coherent control is applied to control the nonlinear response of a quantum system. We use it to obtain high-resolution background-free single-pulse coherent anti-Stokes Raman spectra. The ability to control both the spectral phase and the spectral polarization enables measurement of a specific off-diagonal susceptibility tensor element while exploiting the different spectral response of the resonant Raman signal and the nonresonant background to achieve maximal background suppression.

Carbon nanotubes are potential building blocks for nanofluidic devices. The way fluids flow into and fill nanotubes is therefore of wide interest; however, there are currently no experimental data or theoretical models for this nanoscale process. We have carried out molecular dynamics simulations of nanotubes imbibing oil at an oil/vapor interface at 298 K. We find that nanotubes imbibe very rapidly ($\le 445\mathrm{m}/\mathrm{s}$) via complex imbibition dynamics. The filling does not obey the macroscopic Washburn equation; the penetration length is a linear function of time.

Free gas bubbles in water with radii between 7 and $55\mu \mathrm{m}$ subjected to a shock wave exhibit a liquid jetting phenomenon with the jet pointing in the direction of the propagating shock wave. With increasing bubble radius, the length of the jet tip increases and a lower estimate of the averaged jet velocity increases linearly from 20 to $150\mathrm{m}/\mathrm{s}$. At a later stage, the jet breaks up and releases micron-size bubbles. In the course of shock wave permeabilization and transfection of biological cells, this observation suggests a microinjection mechanism when the cells are near bubbles exposed to a shock wave.

The statistics of the energy and helicity fluxes in isotropic turbulence are studied using high resolution direct numerical simulation. The scaling exponents of the energy flux agree with those of the transverse velocity structure functions through refined similarity hypothesis, consistent with Kraichnan’s prediction. The helicity flux is even more intermittent than the energy flux. Consistent with this observation, the spatial helicity-flux structures are finer than those of energy flux and more tubelike in geometry.

In this Letter, we explore transmission properties of a single subwavelength slit flanked by a finite array of grooves made on a thick metallic film. We identify three main mechanisms that can enhance optical transmission: groove cavity mode excitation (controlled by the depth of the grooves), in-phase groove reemission (controlled by the period of the groove array), and slit waveguide mode (controlled by the thickness of the metal film). By tuning these geometrical parameters, enhancements of transmission of light by up to 2 orders of magnitude can be achieved when all three mechanisms coincide. Experimental verification of these findings is also shown for structured silver films fabricated by focused-ion-beam milling.