The evolution of a spherical gaseous interface accelerated by a plane weak shock wave has been investigated in a square cross section shock tube via a multiple exposure shadowgraph diagnostic. Different gaseous bubbles, i.e., helium, nitrogen, and krypton, were introduced in air at atmospheric pressure in order to study the Richtmyer-Meshkov instability in the spherical geometry for negative, close to zero, and positive initial density jumps across the interface. We show that the bubble distortion is strongly different for the three cases and we present the experimental velocity and volume of the developed vortical structures. We prove that at late times the bubble velocities reach constant values which are in good agreement with previous calculations. Finally, we point out that, in our flow conditions, the gaseous bubble motion and shape are mainly influenced by vorticity and aerodynamic forces.

The mixing of passive scalars of decreasing diffusivity, advected in each case by the same three-dimensional Navier-Stokes turbulence, is studied. The mixing becomes more isotropic with decreasing diffusivity. The local flow in the vicinity of steepest negative and positive scalar gradients is in general different, and its behavior is studied for various values of the scalar diffusivity. Mixing approaches monofractal properties with diminishing diffusivity. We consider these results in the context of possible singularities of scalar dissipation.

The transient nature of spatiotemporal chaos is examined in reaction-diffusion systems with coexisting stable states. We find the apparent asymptotic spatiotemporal chaos of the Gray-Scott system to be transient, with the average transient lifetime increasing exponentially with medium size. The collapse of spatiotemporal chaos arises when statistical spatial correlations produce a quasihomogeneous medium, and the system obeys its zero-dimensional dynamics to relax to its stable asymptotic state.

The distribution of reflection coefficients $P(R)$ for chaotic microwave cavities with time-reversal symmetry is investigated in different absorption and antenna coupling regimes. For all regimes the agreement between experimental distributions and random-matrix theory predictions is very good, provided both the antenna coupling $T_a$ and the wall absorption strength $T_w$ are taken into account in an appropriate way. These parameters are determined by independent experimental quantities.

We demonstrate generalized synchronization of chaos in a two-mode laser system. The total intensity of the laser output (the sum of the individual mode intensities) is used as the drive signal. This lumped variable transmitted to the identical response system does not generate identical synchronization. Generalized synchronization is observed instead of identical synchronization because of the hidden internal degrees of freedom.

Production of extreme-ultraviolet radiation by high-order harmonic generation is demonstrated to yield unprecedented spectral purity of $\lambda /\Delta \lambda =2.5\times {10}^5$ at wavelengths covering the entire range 40–100 nm. Tunability and sub-${\mathrm{c}\mathrm{m}}^{-1}$ bandwidth of the harmonics are demonstrated in recordings of the He ($1s4p$) and Ar ($3p^{5}3d^{\prime }$) resonance lines at 52.2 and 86.6 nm. Frequency shift of the harmonics due to chirp-induced phenomena are investigated and found to be small, resulting in a frequency accuracy of about $5\times {10}^{-7}$ in the domain of extreme-ultraviolet radiation.

We report the first experimental observation of a shock transverse wave propagating in an elastic medium. This observation was possible because the propagation medium, a soft solid, allows one to reach a very high Mach number. In this extreme configuration, the shock formation is observed over a distance of less than a few wavelengths, thanks to a prototype of an ultrafast scanner (that acquires 5000 frames per second). A comparison of these new experimental data with theoretical predictions, based on a modified Burger’s equation, shows good agreement.

We report the full spectrum of the evolution of the wrinkle pattern formation in a thin bilayer film of an elastic metal on a viscoelastic polymer. Although the origin is different, the transition of an initial islandlike pattern to a labyrinthine structure without any change in the wavelength ($q\sim t^0$) and the overall evolutionary process is strikingly similar to that in the spinodal system but the process is robust and takes place on a long time scale (about 10 days). The change into a mountainous topography in the late stages is accompanied by an increase in the length scale from an initial wavelength to another. This change, due to the relaxation of the confined polymer that results in a transition from elastic- to viscouslike behavior, induces wave coarsening ($q\sim t^{-1.04\pm 0.08}$) and macroscopic roughening.

We introduce novel optical solitons that consist of a periodic and a spatially localized component coupled nonlinearly via cross-phase modulation. The spatially localized optical field can be treated as a gap soliton supported by the optically induced nonlinear grating. We find different types of these band-gap composite solitons and demonstrate their dynamical stability.

We present a conjecture relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. Mathematical arguments justifying this conjecture are discussed. Numerical evidence based on computation of resonances of systems of $n$ disks on a plane are presented supporting this conjecture. The result generalizes the Weyl law for the density of states of a closed system to chaotic open systems.

We show that the strength of the central electric field peaks in a few-cycle laser pulse can be recovered from a frequency-time image of the high harmonic spectrum generated in a gas volume. Pulse intensity, duration, and also the carrier-envelope phase ${\phi }_{\mathrm{C}\mathrm{E}}$ can be determined. A simple and robust observable is defined that provides a gauge of ${\phi }_{\mathrm{C}\mathrm{E}}$ for pulse durations up to three optical cycles, corresponding to 7.8 fs FWHM at the Ti:sapphire wavelength of 800 nm.

We report on the first experimental observation of a concentric-ring pattern in a short planar dielectric barrier gas-discharge system and study its spatiotemporal behavior. While increasing the gas pressure the destabilization of the rings into a filamentary structure is observed. The charge carriers deposited on the dielectric electrodes determine the spatiotemporal behavior of the pattern.

We report the first experimental observation of discrete vector solitons in AlGaAs nonlinear waveguide arrays. These self-trapped states are possible through the coexistence of two orthogonally polarized fields and are stable in spite of the presence of four-wave mixing effects. We demonstrate that at sufficiently high power levels the two polarizations lock into a highly localized vector discrete soliton that would have been otherwise impossible in the absence of either one of these two components.

The time-domain response of highly conducting targets following a rapidly terminated electromagnetic pulse displays three distinct regimes: early, intermediate, and late time. The intermediate and late times are characterized by a superposition of exponentially decaying eigenmodes. At early time an ever increasing number of rapidly decaying modes contribute, with the result that the scattered electric field displays a universal $t^{-1/2}$ power law which emerges from the diffusive decay of a pattern of surface currents induced by the pulse. The power law amplitude reflects the surface geometry of the target, a property that may prove useful in buried target classification in geophysical remote sensing applications.

DNS and laboratory experiments show that the spatial distribution of straining stagnation points in homogeneous isotropic 3D turbulence has a fractal structure with dimension $D_s=2$. In kinematic simulations the exponent $\gamma$ in Richardson’s law and the fractal dimension $D_s$ are related by $\gamma =6/D_s$. The Richardson constant is found to be an increasing function of the number density of straining stagnation points in agreement with pair diffusion occurring in bursts when pairs meet such points in the flow.

We present an experimental and theoretical study of a simple, passive system consisting of a birefringent, two-dimensional photonic crystal and a polarizer in series, and show that superluminal dispersive effects can arise even though no incident radiation is absorbed or reflected. We demonstrate that a vector formulation of the Kramers-Kronig dispersion relations facilitates an understanding of these counterintuitive effects.

Stable embedded solitons are discovered in the generalized third-order nonlinear Schrödinger equation. When this equation can be reduced to a perturbed complex modified Korteweg–de Vries equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numerical simulations. These results establish that, contrary to previous beliefs, embedded solitons can be robust despite being in resonance with the linear spectrum.

Optical multistability in an optical ring cavity filled with a collection of three-level $\Lambda$-type rubidium atoms has been experimentally demonstrated. The observed multistability is very sensitive to the induced atomic coherence in the system and can evolve from a normal bistable behavior with the change of the coupling field as well as the atomic number density. The underlying mechanism for the formation of such multistability is also discussed.

We investigate experimentally the competition between spatial and temporal breakup due to modulational instability in ${\chi }^{(2)}$ nonlinear mixing. The modulation of the wave packets caused by the energy exchange between fundamental and second-harmonic components is found to be the prevailing trigger mechanism which, according to the relative weight of diffraction and dispersion, leads to the appearance of a multisoliton pattern in the low-dimensional spatial or temporal domain.

We report spatial domain measurements of the damping of surface-plasmon excitations in metal films with periodic nanohole arrays. The measurements reveal a short coherent propagation length of a few $\mu \mathrm{m}$ inside nanohole arrays, consistent with delays of about 10 fs in ultrafast transmission experiments. This implies that the transmission spectra of the entire plasmonic band-gap structure are homogeneously broadened by radiative damping of surface-plasmon excitations. We show that a Rayleigh-like scattering of surface plasmons by the periodic hole array is the microscopic origin of this damping, allowing the reradiation rate to be controlled.