By eliminating the group-velocity mismatch and enhancing the group-velocity dispersion via pulse-front tilting, we obtained the formation of temporal solitary waves in phase-mismatched second-harmonic generation. Experimental and numerical results match well in a wide range of intensities and $\Delta k$'s. In a 7 mm BBO crystal, 58 fs, 527 nm pulses are obtained starting from 200 fs pump, at the same wavelength.

Faraday, like Chladni, saw fine powder collect in a circular heap at an antinode of a vibrating plate. In each vibration cycle, the heap experiences a free-flight interval during which pressure gradients in the heap's interior drive powder centerward, as Faraday proposed. When heap-floor collision terminates flight, pressure gradients reverse direction; but passage of a compaction front has locked particles against further movement. Before a next flight interval, an increase in porosity will reverse the compaction that accompanied heap-floor collision.

Explicit account is given of the nonlocal dynamics (in a quasistatic approximation) involved in two-phase fluid dynamics quantifying flow through porous media. The results are used to derive the dynamical equation of motion of a Darcy-scale interfacial fluid front. We consider the cases of invasion and imbibition separately, and point out the features responsible for the different depinning exponents observed in the two cases. A Flory-type scaling analysis is also performed on this model, yielding a roughness exponent $\alpha =3/4\mathrm{}$ in a range of intermediate length scales—in good agreement with experimental observations. Possible reasons are outlined for the different universality classes of exponents observed during imbibition experiments.

Phase synchronization transitions in two different coupled chaotic systems (Rössler and Lorentz) are investigated and shown to be well described by a reduced model of an overdamped periodically driven nonlinear oscillator with a time varying coefficient. In both systems, the phase separation increases with $2\pi$ phase jumps below the transition. The scaling rules of the jump near and away from the transition are studied: Near the transition the average interval between two successive jumps follows $\ln 〈l〉\sim -({\epsilon }_c-\epsilon {)}^{1/2}$, while away from the transition $〈l〉\sim ({\epsilon }_t-\epsilon {)}^{-1\mathrm{}/2}$ for both systems.

We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are nonintegrable. As a more sensitive integrability test, we propose the analysis of the complexity (algebraic entropy) of the map using the growth of the degree of its iterates: integrability is associated with polynomial growth while the generic growth is exponential for chaotic systems.

A theoretical analysis of the statistical distributions of the reflected intensities from random media is presented. We use random matrix theory to analytically deduce the probability densities in the localization regime. Numerical calculations of the coupling to backward modes in surface corrugated waveguides are also put forward for comparison. Interestingly, the speckle distributions are found to be independent of the transport regime. Despite the scattering being highly nonisotropic, the predicted probability densities reproduce accurately the numerical results.

A general localization mechanism for waves in dissipative systems is identified that does not require the bistability of the basic state and the nonlinear plane-wave state. We conjecture that the mechanism explains the two-dimensional localized wave structures (“worms”) that recently have been observed in experiments on electroconvection in nematic liquid crystals where the transition to extended waves is supercritical. The mechanism accounts for the shape of the worms, their propagation direction, and certain aspects of their interaction. The dynamics of the localized waves can be steady or irregular.

Steady flows generated by the Rayleigh-Taylor instability (RTI) are considered for incompressible inviscid fluid. There is a family of steady solutions, and for the first time the problem of the solutions' stability is studied theoretically for 2D and 3D flows. The region of stable solutions is found to be very narrow and bounded by Hopf' bifurcations. The influence of flow symmetry and discontinuity of dimensional crossover in RTI are shown; agreement with existing experimental and numerical data is good. Bubbles dynamics is discussed.

Properties of asymmetric square convection in a horizontal fluid layer heated from below are studied numerically with a Galerkin method. Since the Boussinesq approximation is used and symmetric rigid boundaries are assumed, both types of asymmetric square convection—those with rising and those with descending motion in the center—are physically equivalent. It is shown that asymmetric square convection becomes stable with respect to arbitrary three-dimensional infinitesimal disturbances for Rayleigh numbers in excess of 3 to 4 times the critical value.

In an experiment on thin flat strips falling through a fluid in a vertical cell, two fundamental motions are observed: side-to-side oscillation (flutter) and end-over-end rotation (tumble). At high Reynolds number, the dimensionless similarity variable describing the dynamics is the Froude number $\mathrm{Fr}$, being the ratio of characteristic times for downward motion and pendular oscillations. The transition from flutter to tumble occurs at ${\mathrm{Fr}}_c=0.67\mathrm{}\pm 0.05$. We propose a phenomenological model including inertial drag and lift which reproduces this motion, and directly yields the Froude similarity.

A Comment on the Letter by Fred Cooper, et al., Phys. Rev. Lett. 72, 1337 (1994). The authors of the Letter offer a Reply.

A Reply to the Comment by L. Faccioli, et al.

We report on modification of the spontaneous emission of dye molecules embedded in a three-dimensional solid-state photonic crystal exhibiting a stop band in the visible range. Molecules embedded in artificial opal filled with a polymer show a dip in the fluorescence spectrum and nonexponential spontaneous decay kinetics containing both accelerated and inhibited components compared to the dye fluorescence in a reference polymer matrix. Results are interpreted in terms of redistribution of the photon density of states in the photonic crystal.

An order parameter equation is derived for degenerate optical parametric oscillators in the form of a three-dimensional Swift-Hohenberg equation. Three-dimensional Turing structures (lamellae and tetrahedral patterns) and three-dimensional spatial solitons (dark spherical bubbles) are predicted as stable structures.

The stability of optical gap solitons is investigated in the framework of the generalized massive Thirring model. The self-phase modulation can induce either oscillatory or nonoscillatory types of instability, the latter mechanism being described by an explicit criterion, and unfolded geometrically to reveal gap soliton multistability, as well as different nonlinear evolution scenarios.

Observations of parametrically excited surface waves in a magnetic fluid are presented. Under the influence of a magnetic field these waves have a nonmonotonic dispersion relation, which leads to a richer behavior than in ordinary liquids. We report observation of three novel effects, namely, (i) domain structures, (ii) oscillating defects, and (iii) relaxational phase oscillations.

Exact invariant solutions of the spatially uniform Boltzmann equations, the so-called Bobylev-Krook-Wu modes, are presented in the explicit form for an arbitrary $N$-species gas mixture. The corresponding necessary and sufficient conditions imposed on the molecular parameters are formulated. The completeness of the results obtained is supported by the rigorous group analysis of the Boltzmann equations.

We propose a method which can effectively stabilize fixed points in the classical and quantum dynamics of a phase-sensitive chaotic system with feedback. It is based on feeding back a selected quantum subensemble whose phase and amplitude stabilize the otherwise chaotic dynamics. Although the method is rather general, we apply it to realizations of the inherently chaotic Ikeda map. One suggested realization involves the Mach-Zender interferometer with Kerr nonlinearity. Another realization involves a trapped ion interacting with laser fields.

Manifestation of chaotic behavior is found in an intrinsically quantum property. The entanglement process, quantitatively expressed in terms of the reduced density linear entropy, is studied for the $N$-atom Jaynes-Cummings model. For a given energy, initial conditions are prepared as minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. We find for short times a faster increase in decoherence for the chaotic initial conditions as compared to regular ones, which have oscillatory increase.

A nonperturbative renormalization group is derived for chaotic coupled map lattices (CMLs) with diffusive coupling, leading to a natural space-continuous limit of these systems. We show that, under very general conditions, the universal properties of the local map are translated to the spatiotemporal level, demonstrating the self-similarity of the bifurcation diagrams of strongly coupled CMLs and the accompanying divergence of length scales.