We modify the radiation transfer approach, accounting for refraction, and apply this model to the analysis of propagation of spatially incoherent beams in inertial nonlinear media. For double Gaussian beams, an oscillatory regime of nonlinear diffraction is revealed. An explicit analysis of the oscillations was carried out for logarithmic saturating nonlinearity. We show that “big incoherent solitons,” which possess an arbitrary transverse profile of intensity and exist for a wide class of nonlinear media, are steady state solutions of the radiation transfer equation.

From a numerical study of the magnetohydrodynamic (MHD) equations we show, for the first time in three dimensions $(d=3\mathrm{})$, that velocity and magnetic-field structure functions exhibit multiscaling, extended self-similarity (ESS), and generalized extended self-similarity (GESS). We propose a new shell model for homogeneous and isotropic MHD turbulence, which preserves all the invariants of ideal MHD, reduces to a well-known shell model for fluid turbulence for zero magnetic field, has no adjustable parameters apart from Reynolds numbers, and exhibits the same multiscaling, ESS, and GESS as the MHD equations. We also study the inertial- to dissipation-range crossover.

Recent experiments by Kudrolli, Pier, and Gollub [Physica D (to be published)] on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular “superlattice“ pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.

Phase models describing self-synchronization phenomena in populations of globally coupled oscillators are generalized including “inertial” effects. This entails that the oscillator frequencies also vary in time along with their phases. The model can be described by a large set of Langevin equations when noise effects are also included. Also, a description of such systems can be given in the thermodynamic limit of infinitely many oscillators via a suitable Fokker-Planck-type equation. Numerical simulations confirm that simultaneous synchronization of phases and frequencies is possible when the coupling strength goes to infinity.

The Goos-Hänchen shift between a supercritically incident beam and its reflection in a total-internal-reflection mirror comprising a material interface is well established. We experimentally demonstrate that the Goos-Hänchen effect can also occur between the probe beam and the phase-conjugate beam in a phase-conjugate mirror. Controlled lateral displacements of up to $218\mu \mathrm{m}$ were measured using photorefractive four-wave mixing with a frequency-detuned Gaussian probe beam.

We report the pattern formation of degenerate optical parametric mixing—a system with the real-valued order parameter. The phenomena have similarities with and extend those of chemical and hydrodynamic systems described by real order parameter equations, and are different from laser-type pattern formation, where the order parameter is complex. The structure formation is based on a phase bistability. Structures are dominated by fronts separating domains of opposite phase. The domains expand or shrink depending on resonator detuning. Small circular domains, however, are stable and constitute the localized structures of the system. The phenomena are demonstrated experimentally using degenerate four-wave mixing as a prototype process in a resonator of a large Fresnel number.

We investigate the evolution of a thin curtain of heavy gas ( $\mathrm{SF}{}_6$) embedded in a lighter gas (air) and accelerated with a Mach 1.2 planar shock wave. The Richtmyer-Meshkov instability leads to growth of the initial perturbations of the curtain and eventually to transition to turbulence. We visualize a time sequence of images of a section of the flow illuminated with a laser sheet. The $\mathrm{SF}{}_6$ is premixed with tracer (glycol fog), so the intensity of the light scattered off the curtain grows with the local density. As the curtain evolves towards a fully mixed state, real-space correlations of the density, inferred from scattered light intensity, show the emergence of a power-law behavior, indicative of transition to turbulence.

We have performed measurements on forced and decaying 2D turbulence in flowing soap films. Unlike previous experiments, turbulence was excited by grids (arrays of cylinders) lining the walls of the flow channel. The resulting turbulent steady state agrees with the ideas of an inverse energy cascade accompanied by a forward enstrophy cascade. Energy spectra agree, respectively, with $k^{-5\mathrm{}/3}$ and $k^{-3\mathrm{}}$ power laws. Downstream from the forcing section of the channel, the turbulence decays freely, and the energy spectrum scales only as $k^{-3\mathrm{}}$. Our observations unite the results of several theories, and a number of simulations and experiments, into a single self-consistent set of measurements.

A recently developed approach to classical and quantum dynamical entropy involving generalized partitions of unity allows one to use the mathematical formalism typical for quantum statistical mechanics to analyze classical dynamical systems. In particular, density matrices, their von Neumann entropy, and irreversible quantum dynamical maps corresponding to measurement processes appear. To illustrate the power of this new technique we give a simple proof of the Ruelle's inequality between the Kolmogorov-Sinai entropy and the Lyapunov exponents. Continuous time classical dynamical systems are briefly discussed also.

In 1992 Salomons and Mareschal [Phys. Rev. Lett. 69, 269 (1992)] gave evidence that the Burnett equations can provide an important improvement over the Navier-Stokes equations for shock waves at high Mach numbers. In this Letter we solve the Burnett equations and make a comparison with the results from molecular dynamics, the Navier-Stokes equations, and the theory advanced by Holian et al. [Phys. Rev. E 47, R24 (1993)]. A qualitative analysis of the Burnett equations is also done and some open problems are mentioned.

We make a theoretical study of the behavior of a simple fluid displacing a shear thinning fluid confined in a Hele-Shaw cell. To study the Saffman-Taylor instability when the displaced fluid is non-Newtonian we face the problem of having a field which is non-Laplacian. By means of a hodographic transformation we are able to solve the problem in the case of weak shear thinning while taking into account the non-Laplacian character of the equation. Our results predict that the finger width decreases towards zero for small values of the surface tension parameter which is inversely proportional to the finger velocity.

We consider harmonic generation by atoms exposed to an intense laser pulse of a few femtoseconds. Our results, obtained by solving numerically the corresponding three-dimensional time-dependent Schrödinger equation, demonstrate the strong sensitivity of the harmonic spectra to the phase of the laser. These results are explained in terms of both quantum and classical dynamics. We show that this phase sensitivity may be exploited in order to probe the laser phase for ultrashort pulses. Our discussion about this new method of diagnosis takes into account propagation effects.

We consider materials whose mechanical integrity is the result of a jamming process. We argue that such media are generically “fragile,” unable to support certain types of incremental loading without plastic rearrangement. Fragility is linked to the marginal stability of force chain networks within the material. It can lead to novel mechanical responses that may be relevant to (a) jammed colloids and (b) poured sand. The crossover from fragile to elastoplastic behavior is explored.

Cellular automata (CA) and lattice Boltzmann (LB) models are two possible approaches to simulate fluidlike systems. CA models keep track of the many-body correlations and provide a description of the fluctuations. However, they lead to a noisy dynamics and impose a restriction on the possible values of the viscosity. On the other hand, LB models are numerically more efficient and offer much more flexibility to adjust the fluid parameters, but they neglect fluctuations. Here we propose a new multiparticle lattice model which reconciles the two approaches. Our method is tested on the problem of ballistic annihilation in two dimensions for which the fluctuations are known to play an important role.

Clusterlike solutions are reported for volume-averaged equations of motion in fluidized gas-particle suspensions (i.e., fluidized beds). A connection between bubbles and clusters is established through bifurcation analysis and numerical continuation in the mean volume fraction of the suspension. The robustness of this connection is established by varying the model parameters and the closures. The bubbles and clusters are shown to belong to the same family of nonuniform solutions.

Using a very small Nd/YAG pumping laser (0.45 J in 8 nsec), we have demonstrated high gain $(G\approx 14–19\mathrm{cm}{}^{-1\mathrm{}})$ and gain-length product $(\mathrm{GL}\ge 5)$ in hydrogenlike B V ions at a wavelength of 26.2 nm (the 3-2 transition) at a repetition rate of 1 Hz. The preplasma in a ${\mathrm{B}}_2{\mathrm{O}}_3$ microcapillary was created from wall ablation with a 0.2-J (in 20 nsec) KrF laser. The gain was generated in the microcapillary plasma in a traveling wave regime by longitudinal pumping. This very efficient soft x-ray lasing system takes up less space than is available on a $4\mathrm{ft}\times 10\mathrm{ft}$ optical table.

Ultrashort self-guided laser pulses are employed to generate high-order harmonics in noble gases. Interference fringes between fundamental and harmonic waves over several cm reveal a long range longitudinal coherence of the generated harmonics. Quasiphase matching is demonstrated for the third harmonic wave.

We present an experimental realization of an almost noninvasive stabilization and manipulation method of coexisting and underlying states of pattern forming systems. In a photorefractive single feedback system, a ring control path is used to realize amplitude and phase-sensitive Fourier-plane filtering, utilizing only a few percent of the system's intensity. We were able to stabilize desired but not predominantly excited patterns in parameter space regions where several patterns are present as underlying solutions. By positive (in-phase) and negative (out-of-phase) control, rolls could be excited in parameter regions where hexagonal structures are preferably stable.

A nonideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for nonideal gases. The existing lattice Boltzmann models for nonideal gases are analyzed and compared with the model derived here.

We consider the effect of small noise of maximum amplitude $\varepsilon$ on a chaotic system whose noiseless trajectories limit on a fractal strange attractor. For the case of nonhyperbolic attractors of two-dimensional maps the effect of noise can be much stronger than for hyperbolic attractors. In particular, the maximum over all noisy orbit points of the distance between the noisy orbit and the noiseless nonhyperbolic attractor scales like ${\varepsilon }^{{1/D}_1}$ ( $D_1>1\mathrm{}$ is the information dimension of the attractor), rather than like $\varepsilon$ (the hyperbolic case). We also find a phase transition in the scaling of the time averaged moments of the deviations of a noisy orbit from the noiseless attractor.