Spatial dark-soliton (SDS) stripes are experimentally found in the transverse plane of a laser beam that passes through a rectilinear diffraction screen before propagating in a self-defocusing nonlinear material. Materials with different mechanisms of nonlinearity manifest the same qualitative results. The SDS nature of the observed phenomenon is verified by numerical simulations of the (2+1)-D nonlinear Schrödinger equation, analytical solutions for the (1+1)-D case, and their comparison with experimental data.

Harmonic operation of a free-electron-laser amplifier is studied. The key issue investigated here is suppression of the fundamental. For a tapered amplifier with the right choice of parameters, it is found that the presence of the harmonic mode greatly reduces the growth rate of the fundamental. A limit on the reflection coefficient of the fundamental mode that will ensure stable operation is derived. The relative merits of tripling the frequency by operating at the third harmonic versus decreasing the wiggler period by a factor of 3 are discussed.

Using a simple mean-field model of the electron-electron interaction, we have studied the effect of space charge in a planar diode. Our results show, in particular, that the classical value for the limiting current in such a diode can be exceeded by a large factor due to the effect of tunneling. The smooth transition of the solutions from the quantum to the classical (nonquantum) regime is demonstrated.

The wavelet-transformed Navier-Stokes equations are used to define quantities such as the transfer and flux of kinetic energy through position x and scale r. Analysis of pseudospectral direct numerical simulations of turbulent flows reveals that although the mean spatial values of these quantities agree with their traditional counterparts in Fourier space, their spatial variability is very large, exhibiting non-Gaussian statistics. The local flux of energy involving scales smaller than some r also exhibits large spatial intermittency and it is negative quite often, indicative of local inverse cascades.

Nonstationary stimulated Brillouin backscattering in a large gain optical-fiber ring cavity laser exhibits superluminous Stokes pulses of quasisoliton type and partial self-induced transparency for the pump. Experimental evidences, comforted by numerical simulation of the three-wave coherent model taking the acoustic-wave dynamics into account, show that this class of long transients occurs even with a cw-coupled pump wave.

The propagation of target waves in the presence of walls and windows is considered. It is shown that in a finite system, for sufficiently small passages no target waves are triggered. Propagation through a large opening can inhibit the onset of waves from smaller windows.

We use Floquet theory, fully resolved numerical simulation, and laboratory experiment to study two quasiperiodic modes in the Couette-Taylor system which have the same symmetry but different spatial structure. Although each mode has been observed in previous experiments, their coexistence in the same region of parameter space is a new numerical prediction. Because they have the same symmetry, the modes are strongly coupled, which results in chaotic behavior.

I describe experiments on ‘‘pulses’’ of convective traveling waves in an ethanol water mixture contained in an extremely uniform annular cell. In contrast to previous observations, I find that pulses drift continuously, with no long-term change in velocity. The drift velocity vanishes at onset, increases with the distance above onset, and agrees with the results of numerical integrations of the Navier-Stokes equations.

We develop a general model for flow suspended particles in a porous medium. The model can take into account the effects of the morphology of the porous medium (including pore surface roughness and fractality), the chemistry of the flowing fluid, and all important forces between the particles and the pore surface. If surface deposition and pore plugging by size exclusion take place, the process is a percolation phenomenon which may belong to a different universality class than that of random percolation. The model is applied to two classes of problems, flow of solid, electrically charged colloidal particles, and that of stable emulsion droplets in a porous medium.

A generalized class of Cantor-set models are introduced in a deductive way to explain the intermittent and multifractal structure in the inertial range of isotropic turbulence. All such Cantor-set models are produced by taking the probability density of the stochastic ratio of averaged disspations in the basic breakdown process with scale ratio ${\mathit{A}}^{\mathrm{-}1}$, ${\mathrm{\varepsilon }}_{\mathit{r}}$/${\mathrm{\varepsilon }}_{\mathit{A}\mathit{r}}$, as a polynomial δ function, and it is proved that only some can guarantee the f-α spectra with a non-negative f. The whole statistics of the dissipation density, its square root, and the scaling index α which these models should imply are revealed, and typical models are compared with a recent direct numerical simulation to indicate promising applications.

We present a phase diagram for fluid invasion of porous media as a function of pressure P and the contact angle θ of the invading fluid. Increasing P leads to perculation above a critical ${\mathrm{\theta }}_{\mathit{c}}$, and depinning below ${\mathrm{\theta }}_{\mathit{c}}$. Depinning is characterized by a diverging coherence length and the power-law distribution of events typical of self-organized critical phenomena. At the transition from percolation to depinning another correlation length diverges and an order parameter, an effective macroscopic surface tension, becomes nonzero. The fluid interface changes from self-similar to self-affine. Results are compared to experiments.

Combining methods and ideas of dynamical systems theory with the usual stability analysis for extended hydrodynamic systems we show that defect-mediated turbulence is a generic consequence of a set of physical properties which are shared by many systems. We show how the interplay between broken continuous symmetries and the dynamics of patterns leads to a universal scenario for the onset of this type of turbulence.

We report the observation of coherent emission from a Cherenkov free-electron laser driven by a 5-MeV radio-frequency microtron. Power up to 50 W in pulses of 4-μs duration has been generated at the wavelengths of 1.6 and 0.9 mm using two different dielectric-loaded waveguides.

The kinetic fluctuations of a stable interface driven by the gradient of a Laplacian field are investigated. In three and more dimensions the interface width is finite. In two dimensions the width diverges logarithmically with time and system size. Its scaling form is derived in agreement with simulations of diffusion-limited erosion (anti diffusion-limited aggregation). A crossover to algebraic roughness with an extended intermediate scaling regime is predicted for diffusion with a drift towards the interface. Capillary effects are discussed in relation to recent experiments on fluid displacement in porous media.

We show that dc-electric-field coupling of the 2s and 2p states in atomic hydrogen leads to resonantly enhanced second-order susceptibility with reduced absorption at the second-harmonic wavelength, and exact phase matching at the center of the Stark-split components.

We present a physical model constructed from the Navier-Stokes equation to describe the evolution of the probability distribution function of transverse velocity gradients in 3D isotropic turbulence. Quanitative agreement with data from direct numerical simulations of isotropic turbulence for a wide range of Reynolds number is obtained. The model is based on a concrete physical picture of self-distortion of structures and interaction between random eddies and structures; the dynamical balance explains the non-Gaussian equilibrium probability distributions.

We consider the behavior of solitons described by the nonlinear Schrödinger equation with periodic perturbation (not necessarily small) whose period ${\mathit{Z}}_{\mathit{a}}$ is much shorter than the characteristic period of the solitons, ${\mathit{Z}}_0$. The soliton behaves like the guiding-center motion of a charged particle in a magnetic field, smooth and adiabatic. However, when ${\mathit{Z}}_{\mathit{a}}$ approaches ${\mathit{Z}}_0$, resonances appear between the periodic perturbations and the characteristic frequencies of the solitons which induce the generation of dispersive waves and/or splitting of solitons.

Narrow-bandwidth operation of a quasicontinuous free-electron laser by seed injection has been demonstrated. The pulse-to-pulse frequency bandwidth has been reduced from 1.6 to 0.16 GHz. An order-of-magnitude reduction of the sideband-mode beating in a single pulse and a 30% reduction in laser start-up time has been obtained. Numerical simulations of the multimode free-electron laser show that the sideband-mode suppression and the buildup of coherence are rather slow, underlining the importance of seeding to obtain single-mode operation for the available pulse length.

A multifrequency model is developed for a Compton free-electron laser and is solved to investigate the continuous-electron-beam limit. Both numerical simulations and perturbation expansions allow us to exhibit a mechanism leading to the broadening of the spectrum. Then, the nonlinear asymptotic behavior of the spectrum is analyzed.

We have observed directional pattern growth in a lipid monolayer near the three-phase contact line of the Langmuir-Blodgett meniscus. This growth results from the receding flow of the meniscus due to the change in fluid surface tension upon monolayer compression. A gradient in surface tension forms near the three phase contact line and relaxes as the meniscus recedes to its equilibrium height. This pattern formation may be caused by either directional solidification of the monolayer or the coupling between fluid flow and surface tension of the meniscus.