We propose that cycle expansions be ordered with respect to stability rather than orbit length for many chaotic systems, particularly those exhibiting crises. This is illustrated with the strong-field Lorentz gas, where we obtain significant improvements over traditional approaches.

Within the framework of a 1D model we study systems which are extended in certain directions but are restricted in size and open in other directions. Besides the coefficient $D$ characterizing diffusion on the chaotic repeller, a coefficient $\hat{D}$ is introduced to measure the broadening of the distribution of trajectories during the transiently chaotic motion and is expressed in terms of the correlation function suitably defined for transient chaos. It is shown that there is a situation where two smooth conditionally invariant measures exist resulting in nonuniqueness of both diffusion coefficients.

We deduce the equation describing the refractive index perturbation in photovoltaic photorefractive crystals produced by the incidence of a focused laser beam and an incoherent uniform illumination. Under short-circuit conditions the equation shows a saturable Kerr-type nonlinearity that can be controlled by the intensity of the uniform background illumination. Z-scan experiments in an iron doped lithium niobate crystal are carried out using a 532 nm wavelength laser line to evaluate its self-lensing properties and to measure its photovoltaic field.

Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter range with parameter-dependent exponents of singularity, and is insensitive to the specific nature of the dynamical units involved. Whether or not the units are coupled with their neighborhood is also unimportant. It is discovered numerically that the derivative of the original amplitude field exhibits strong spatial intermittency with multifractal structure.

A cascade of surface wave patterns with increasing rotational symmetry ranging from simple square to tenfold quasiperiodic is observed for Faraday waves. The experiment concerns the excitation of subharmonic standing surface waves by oscillating vertical acceleration. Our observation agrees with the prediction of a recent theory. By presenting these predictions in a dimensionless form, we illustrate the genericity of this phenomenon and emphasize the very favorable agreement with experiment.

We report the first demonstration of saturation in a Ni-like x-ray laser, specifically Ni-like Ag x-ray laser at 14 nm. Using high-resolution spatial imaging and angularly resolved streaking techniques, the output source size as well as the time history, divergence, energy, and spatial profile of the output beam have been fully characterized. The output intensity of the Ag laser was measured to be about $70\mathrm{GW}{\mathrm{cm}}^{-2\mathrm{}}$. The narrow divergence, short pulse duration, high efficiency, and high brightness of the Ag laser make it an ideal candidate for many x-ray laser applications.

Monodisperse, highly charged colloidal particles in low ionic strength solutions self-assemble into bcc or fcc crystalline colloidal arrays (CCAs) due to interparticle repulsive interactions. We demonstrate that a CCA of dyed particles embedded in a poly acrylamide hydrogel acts as a nanosecond optical Bragg diffraction switching device. Under low light intensities the CCA is refractive index matched to the medium and does not diffract. However, high intensity excitation within the dye absorption band heats the spheres within nanoseconds to decrease their refractive index. The array “pops up” to diffract light within 2.5 ns. These intelligent CCA hydrogels may have applications in optical limiting, computing, and nanosecond fast optical switching devices, etc.

We investigate the Lévy flights observed experimentally in the transport of tracers in a temporally irregular flow that has no Kolmogorov-Arnold-Moser surfaces, and show that the Lévy flights are due to the sticking of the tracers near the walls. The tracer is found to spread superdiffusively with an exponent $\nu =3\mathrm{}/2$, in reasonable agreement with the experiments.

Two-dimensional lattice models of crack branching give rise to fragmentation if disorder is introduced in the model. The resulting fragment-size distribution is analyzed within a simple analytical model and by numerical simulations. The analytical model gives, under rather general conditions, a power-law distribution over the entire size range. In the specific case studied, the exponent ranges from $-\infty$ to $-0.5\mathrm{}$, depending on the stopping probability of cracks. The analytical results are consistent with the numerical simulations.

A circularly polarized laser beam propagating through sodium vapor is shown to be deflected by the inhomogeneous magnetic field from a nearby electric current-carrying thin wire aligned parallel to the beam. The effect arises from the refractive index gradient induced by magnetic-field-modified optical pumping. The experimentally observed beam deflection is in good agreement with predictions from a $J=1\mathrm{}/2\leftrightarrow J=1\mathrm{}/2$ model for the full four-dimensional spatialtemporal evolution of the interaction between radiation field and atoms. The time of order 100 ns needed for the beam to switch between undeflected and deflected positions is determined by the average Larmor precession period and is 2 orders of magnitude shorter than the optical pumping time.

A numerical model of three-dimensional impact fragmentation produces a power-law cumulative fragment mass distribution followed by a flat tail. The result is consistent with an experimental result in a recent paper by Meibom and Balslev [Phys. Rev. Lett. 76, 2492 (1996)]. Our numerical simulation also implies that the fragment mass distribution changes from a power law with a flat tail to a power law with a sudden cutoff, depending on the aspect ratio of the fractured object.

The anomalous scaling phenomena of three-dimensional passive scalar turbulence are studied using high resolution direct numerical simulation. The inertial range scaling exponents of the passive scalar increment and the scalar dissipation are obtained. The connection between the intermittency structure and the scaling exponent is examined and the structure instability of the high amplitude scalar dissipation is used to clarify previous experimental results for the scaling exponents.

A dissipative quantum system is treated here by coupling it with a heat bath of harmonic oscillators. Through quantum Langevin equations and Ehrenfest's theorem, we establish explicitly the quantum Duffing equations with a double-well potential chosen. A quantum noise term appears the only driving force in dynamics. Numerical studies show that the chaotic attractor exists in this system while chaos is certainly forbidden in the classical counterpart.

A general three-dimensional wave equation first order in the propagation coordinate is derived covering a broad range of phenomena in nonlinear optics. This equation provides an accurate description of the evolution of the wave packet envelope down to pulse durations as short as one carrier oscillation cycle. The concept of envelope equations is found to be applicable to the single-cycle regime of nonlinear optics.

We reveal that three-wave parametric mixing in a diffractive quadratic (or ${\chi }^{\left(2\right)}$) medium can lead to multistability of self-guided beams. Switching between different stable states of these multivalued spatial solitary waves is also demonstrated.

Ultrashort optical solitons with different states of polarization are used to map the polarization evolution in a fixed section of a weakly birefringent fiber. Soliton polarization evolution was compared to linear propagation. A significant change in the polarization behavior between the solitons and linear regime is observed. Although solitons contain a continuum of instantaneous intensities, they transform their polarization as a unit, demonstrating the particlelike nature of solitons.

A thin slab of two-dimensional photonic crystal is shown to alter drastically the radiation pattern of spontaneous emission. More specifically, by eliminating all guided modes at the transition frequencies, spontaneous emission can be coupled entirely to free space modes, resulting in a greatly enhanced extraction efficiency. Such structures might provide a solution to the long-standing problem of poor light extraction from high refractive-index semiconductors in light-emitting diodes.

We propose a mechanism to explain what occurs when a mixture of grains of different sizes and different shapes (i.e., different repose angles) is poured into a quasi-two-dimensional cell. Specifically, we develop a model that displays spontaneous stratification of the large and small grains in alternating layers. We find that the key requirement for stratification is a difference in the repose angles of the two pure species, a prediction confirmed by experimental findings. We also identify a kink mechanism that appears to describe essential aspects of the dynamics of stratification.

We propose a model of turbulent viscosity which preserves all the known conservation laws of the two-dimensional incompressible Euler equation, and is invariant by changes of reference frames. This model is derived by a systematic procedure, using a principle of maximum entropy production.

A theory of the cross-field turbulent transport of a passive scalar in a magnetized, two dimensional, electrically conducting fluid is presented. Both a renormalized quasilinear calculation and analyses of an exactly solvable simple model demonstrate that weak magnetic fields in a highly conducting medium are capable of strongly suppressing the turbulent cross-field transport by alteration of the Lagrangian correlation time of a scalar fluid element, without effect on the turbulence intensity. Passive scalar transport along the magnetic field is unchanged. An explicit expression for the effective cross-field diffusivity is given.