We present numerical simulations of coupled Ginzburg-Landau equations describing parametrically excited waves which reveal persistent dynamics due to the occurrence of phase slips in sequential pairs, with the second phase slip quickly following and negating the first. Of particular interest are solutions where these double phase slips occur irregularly in space and time within a spatially localized region. An effective phase diffusion equation utilizing the long-term phase conservation of the solution explains the localization of this new form of amplitude chaos.

We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications.

Hydrodynamic instabilities occur in the motion of non-Newtonian polymeric liquids at low flow rates that are entirely absent in the corresponding motions of Newtonian fluids. We develop a dimensionless criterion that characterizes the critical conditions for onset of elastic instabilities in two-dimensional, single-phase isothermal viscoelastic flows. The new dimensionless group is analogous to classical Taylor and Görtler numbers characterizing inertial instabilities of Newtonian fluids and quantifies both the curvature of the streamlines and the dynamics of the non-Newtonian fluid motion.

The stationary condition (Hopf equation) for the $(n+1\mathrm{})$-point correlation function of a passive scalar advected by turbulent flow is argued to have an approximate $\mathrm{SL}\left(n,R\right)$ symmetry which provides a starting point for our phenomenological theory in which less symmetric terms are treated perturbatively. The large scale anisotropy is found to be a relevant field, in contradiction with Kolmogorov phenomenology, but in agreement with the large scalar skewness observed in shear flows. Exponents are not universal, yet quantitative predictions for experiments to test the $\mathrm{SL}\left(n,R\right)$ symmetry can be formulated in terms of the correlation functions.

Forced rotating turbulence is simulated within a periodic box of small aspect ratio. Critical parameter values are found for the stability of a 2D inverse cascade of energy in the presence of 3D motions at small scales. There is a critical rotation rate below which 2D forcing leads to an equilibrated 3D state, while for a slightly larger rotation rate, 3D forcing drives a 2D inverse cascade. It is shown that inverse and forward cascades of energy can coexist. This study is relevant to geophysical flows, and contains physics beyond the scope of quasigeostrophic models.

Experiments on the explosively driven compression and reexpansion of metal cylinders are reported. Analysis of radiography data taken with a pulsed x-ray source reveals scale invariant density fluctuations. The marginal density spectra are consistent with a $k^{-8\mathrm{}/3}$ power law, where $k$ is wave number, corresponding to scalar density spectra varying as $k^{-5\mathrm{}/3}$. Remarkably, the same scaling behavior is observed for a variety of metals with widely different mechanical properties. The relation of these results to fully developed turbulence in both incompressible fluids and compressible fluids with large density variations is discussed.

We report on chaotic localized traveling-wave states (pulses) near the onset of electroconvection in a nematic liquid crystal. They coexist with the conduction state, are long lived, appear and die at irregular locations and times, have unique small widths, and vary irregularly in length. In this system there are only four linearly unstable modes. Thus it should be possible to reproduce the dynamics of the pulses by four coupled complex Ginzburg-Landau equations once their coefficients are derived from the equations of motion (the weak-electrolyte model).

The synchronization of spatiotemporal chaos of two arrays of coupled nonlinear oscillators is achieved by discrete time coupling of individual cells of the arrays. This synchronization method is based on the knowledge of the local dynamics and can be applied to any type of arrays where the synchronization properties of the cells are known. Furthermore, we discuss possible applications of synchronizing spatiotemporal chaos in communication and anticontrol of chaos.

The modified asymptotic description of dispersive Gaussian pulse propagation, which is uniformly valid in the initial pulse envelope width, is shown to reduce to the energy velocity description when the propagation distance becomes sufficiently large in a Lorentz model dielectric. This then resolves the apparent controversy between the modern asymptotic description upon which the energy velocity description is based and the classical group velocity description of Gaussian pulse propagation and related experimental results.

We present a physical explanation of turbulent bursts in the flow between concentric, rotating cylinders (Couette-Taylor flow), based on fully resolved direct numerical calculations. The bursts are a temporal oscillation between a spatially laminar flow and turbulence, discovered experimentally by Hamill et al. The onset of turbulence is shown to be due to a linear instability of the spiral flow, discovered in our calculations and since confirmed experimentally.

For turbulent velocity data measured in high-Reynolds-number atmospheric surface layer, we show that the observed dependence of the inertial range statistics on large scale fluctuations is a manifestation of the mixed averaging of regions of different local Reynolds number. This dependence can be subsumed by the Obukhov conditional averaging and the second refined similarity hypothesis of Kolmogorov. We identify a subset of velocity increments which seem to possess no large-scale dependence.

For isotropic turbulence, the pressure structure function $D_p$ can be simply related to $D_{1111}$, the fourth-order longitudinal velocity structure function. Using measurements of $D_{1111}$ in different flows and Reynolds numbers, plausible distributions of $D_p$ are obtained for separations in both the viscous and inertial ranges.

Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior with regions that obey the Wigner-Dyson statistics and localized and quasi-ideal states distributed according to Poisson statistics. Although the averaged spatial extension of the eigenstates in the present model scales with the size of the system as in the Gaussian orthogonal ensemble, the fluctuations are much larger.

Positive and negative Lyapunov exponents for a dilute, random, two-dimensional Lorentz gas in an applied field, $\overrightarrow{E}$, in a steady state at constant energy are computed to order $E^2$. The results are ${\lambda }_{\pm }={\lambda }_{\pm }^0{-a}_{\pm }(\mathrm{qE}/\mathrm{mv}{)}^2{t}_0$ where ${\lambda }_{\pm }^0$ are the exponents for the field-free Lorentz gas, $a_{+}=11\mathrm{}/48$, $a_{-}=7\mathrm{}/48$, $t_0$ is the mean free time between collisions, $q$ is the charge, $m$ is the mass, and $v$ is the speed of the particle. The calculation is based on an extended Boltzmann equation in which a radius of curvature, characterizing the separation of two nearby trajectories, is one of the variables in the distribution function. The analytical results are in excellent agreement with computer simulations.

We have experimentally demonstrated antimonotonicity, the concurrent creation and destruction of periodic orbits in a driven nonlinear electronic resonator. A manifestation of antimonotonicity in one-dimensional systems is the formation of dimples in high iterate return maps. Our maps computed from 16-bit resolution time domain data unequivocally exhibit the formation of such dimples.

We observe incomplete synchronization of coupled chaotic oscillators over a wide range of coupling strengths and coupling schemes for which high-quality synchronization is expected. Long intervals of high-quality synchronization are interrupted at irregular times by large, brief desynchronization events that can be attributed to "attractor bubbling," clearly demonstrating that the standard synchronization criterion is not always useful in experiments. We suggest a simple method for rapidly selecting the coupling schemes that are most likely to produce high-quality synchronization.

Topological invariants which control the organization and the evolution of ensembles of singularities may be evidenced in optical caustics. Our physical model is the optical pattern produced by light deflected through a nematic liquid crystal. We determine experimentally the Euler number of the critical set associated with the caustic and we identify the umbilics. We develop a method that enables us to determine the index of the umbilics and to distinguish between the two types of hyperbolic umbilics. We are then able to check, for the first time, the value of the topological invariant predicted by the recent Chekanov theory.

We derive new nonlinear evolution equations for long internal waves in a two-fluid system, when the thickness of the lower layer is effectively infinite, by making the only assumption that the thickness of the upper layer is small compared with the characteristic wavelength. The resulting equations have the full nonlinearity of the original problem and retain the leading-order dispersive effects. For large amplitude internal solitary waves, we show that our model captures the scaling relation between the amplitude and the characteristic wavelength observed experimentally by Koop and Butler.

We calculate the 2-point spectral correlation function for classically chaotic systems in the semiclassical limit using Gutzwiller's trace formula. The off-diagonal contributions from pairs of nonidentical periodic orbits are evaluated by relating them to the diagonal terms. The behavior we find is similar to that recently discovered to hold for disordered systems using nonperturbative supersymmetric methods. Our analysis generalizes immediately to include parametric statistics and higher-order correlations and to the study of the semiclassical distribution of matrix elements.

We report the generation of laser pulse energies up to $30\mu \mathrm{J}$ at 46.9 nm in the plasma column of a fast compressional capillary discharge. Double pass experiments using an iridium mirror achieved a gain-length product greater than 25. The results provide the first clear evidence of saturated operation of a table-top soft x-ray amplifier.