It is shown that discrete solitons can be navigated in two-dimensional networks of nonlinear waveguide arrays. This can be accomplished via vector interactions between two classes of discrete solitons: signals and blockers. Discrete solitons in such two-dimensional networks can exhibit a rich variety of functional operations, e.g., blocking, routing, logic functions, and time gating.

We have observed the spectrum of electrostrictive stimulated Rayleigh scattering in a liquid and created a transition to stimulated thermal Rayleigh scattering with the addition of an absorbing liquid. With the proper amount of absorption, the electrostrictive and thermal contributions to the scattering exactly cancel, resulting in no stimulated Rayleigh scattering. An absorption coefficient of $0.00012{\mathrm{cm}}^{-1\mathrm{}}$ is sufficient to cancel the electrostrictive Rayleigh scattering in Freon 113.

Recent experimental discovery of extended self-similarity (ESS) was one of the most interesting developments, enabling precise determination of the scaling exponents of fully developed turbulence. A sufficient condition for extended self-similarity in a general dynamical system is derived in this paper. It is also shown that if the pressure-gradient contributions are expressed in terms of velocity differences in the mean-field approximation [V. Yakhot, Phys. Rev. E 63, 026307 (2001)], then the ESS is a consequence of the Navier-Stokes equations.

An extremely long train of highly repetitive pulse (17 THz) is obtained by the rotational four-wave Raman mixing of molecular hydrogen in a resonator using a computer simulation. This highly repetitive pulse can be obtained only when the laser wavelength and the resonator are adjusted to specified values. This pulse train has potential for use in ultrafast data communication because of the accurately determined repetition rate or even as a frequency standard, since the frequencies of the emission lines can be stabilized and locked to the above values.

We report the results of the first experimental study of imperfect gluing bifurcations in an extended fluid flow. It is shown that the central features of the theory are robust and are appropriate to describe the dynamics of a nontrivial physical system. The results include the first experimental evidence for a route to chaos which is an essential part of the theory of imperfect gluing bifurcations.

We address the problem of the microscopic reorganization of a granular medium under a compaction process in the framework of Tetris-like models. We point out the existence of regions of spatial organization which we call domains, and study their time evolution. It turns out that after an initial transient, most of the activity of the system is concentrated on the boundaries between domains. One can then describe the compaction phenomenon as a coarsening process for the domains, and a progressive reduction of domain boundaries. We discuss the link between the coarsening process and the slow dynamics in the framework of a model of active walkers on active substrates.

We evaluate the linear term in the density expansion of the dynamic structure factor for a classical gas using a generalized Enskog theory developed by one of the authors, which enables us to describe the dynamics at small time and length scales where the use of the Boltzmann equation is severely limited. Agreement of the theory with experiment and simulation is very good. We find that the linear term is very sensitive to the shape of the potential so that the dynamic structure factor can serve as a good probe to determine the intermolecular potentials of dilute gases.

We report self-guided propagation of ultrashort IR laser pulses in fused silica over several Rayleigh lengths. Self-guiding is accompanied by pulse splitting and time compression. Numerical simulations involving pulse self-focusing, temporal dispersion, and multiphoton ionization are found to be in good agreement with the experimental results. They show that a quasidynamic equilibrium between multiphoton ionization and self-focusing drives the filamentation process, while temporal dispersion plays a negligible role.

We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particle at a turbulent Reynolds number $R_{\lambda }=740\mathrm{}$, with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentzian form $E^L\left(\omega \right){=u}_{\mathrm{rms}}^2{T}_L/[1+(T_L\omega {)}^2]$, in agreement with a Kolmogorov-like scaling in the inertial range. The probability density functions of the velocity time increments display an intermittency which is more pronounced than that of the corresponding Eulerian spatial increments.

We show experimentally that optical two-dimensional systems such as vectorial lasers can exhibit novel stochastic resonances. All optical noise and modulation of this system allows the isolation of so-called inhibitional and rotational stochastic resonances. In particular, incoherent rotational tunneling is shown to be sensitive enough to be also induced by Faraday noise and by quantum noise, i.e., external spontaneous emission.

Patterns of vortex ripples form when a sand bed is subjected to an oscillatory fluid flow. Here we describe experiments on the response of regular vortex ripple patterns to sudden changes of the driving amplitude $a$ or frequency $f$. A sufficient decrease of $f$ leads to a “freezing” of the pattern, while a sufficient increase of $f$ leads to a supercritical secondary “pearling” instability. Sufficient changes in the amplitude $a$ lead to subcritical secondary “doubling” and “bulging” instabilities. Our findings are summarized in a “stability balloon” for vortex ripple pattern formation.

The nonlinear pulse propagation in photonic crystal fibers without slowly varying envelope approximation is studied using an improved variant of first-order wave equation. Supercontinuum generation is shown to be caused by a novel mechanism of spectral broadening through fission of higher-order solitons into redshifted fundamental solitons and blueshifted nonsolitonic radiation. Good agreement with experimental observations is found, and subcycle pulse compression is studied.

Using a quantum kinetic equation we study the possibility that focused beams at proposed x-ray free electron laser facilities can initiate spontaneous electron-positron pair production from the QED vacuum. Under conditions reckoned achievable at planned facilities, repeated cycles of particle creation and annihilation will take place in tune with the laser frequency. The peak particle number density is insensitive to this frequency, and one can anticipate the production of a few hundred particle pairs per laser period.

We study the statistical properties of the eigenvalues of non-Hermitian operators associated with the dissipative complex systems. By considering the Gaussian ensembles of such operators, a hierarchical relation between the correlators is obtained. Further, the eigenvalues are found to behave like particles moving on a complex plane under two-body (inverse square) and three-body interactions and there seems to underlie a deep connection and universality in the spectral behavior of different complex systems.

For semiconductor lasers subject to a delayed optical feedback, branches of steady states sequentially appear as the feedback rate is increased. But branches of time-periodic solutions are connecting pairs of steady states and provide bridges between stable and unstable modes. All bridges experience a change of stability through a torus bifurcation point. Close to the bifurcation point, the torus remains localized near a specific fixed point in phase space. As the feedback rate increases, the torus envelope suddenly unfolds and its trajectory visits two or more unstable fixed points, anticipating the rich dynamics observed at larger feedback rates.

We report results from a statistical analysis of avalanches of cohesive powders in a slowly rotated drum. Interparticle adhesion, which diminishes the effect of inertia and whose magnitude strongly fluctuates in a local scale, makes avalanches in slightly cohesive powders eligible for displaying self-organized criticality. However, the results show that avalanche sizes, time interval between avalanches, and maximum stable angle do not follow a power-law distribution. Otherwise, these parameters scale with powder cohesiveness.

We consider the curvature driven dynamics of a domain wall separating two equivalent states in systems displaying a modulational instability of a flat front. An amplitude equation for the dynamics of the curvature close to the bifurcation point from growing to shrinking circular droplets is derived. We predict the existence of stable droplets with a radius $R$ that diverges at the bifurcation point, where a curvature driven growth law $R\left(t\right)\approx t^{1/4}$ is obtained. Our general analytical predictions, which are valid for a wide variety of systems including models of nonlinear optical cavities and reaction-diffusion systems, are illustrated in the parametrically driven complex Ginzburg-Landau equation.

We use asymptotic analysis and a near-identity normal form transformation from water wave theory to derive a $1+1$ unidirectional nonlinear wave equation that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation. This equation is one order more accurate in asymptotic approximation beyond KdV, yet it still preserves complete integrability via the inverse scattering transform method. Its traveling wave solutions contain both the KdV solitons and the CH peakons as limiting cases.

We show experimentally and theoretically that cascading due to two-wave parametric frequency conversion in quadratic materials acts as an effective focusing or defocusing nonlinearity, depending not only on mismatch, but also on the selected wave, and the dominant type of process (second-harmonic generation or down-conversion). A dramatic asymmetry of beam spreading and threshold lowering for soliton formation against mismatch is the clear experimental signature of this behavior.

Laser action in the regime of Anderson localization is investigated by coupling Maxwell’s equations in a strongly scattering medium with the rate equations of a four-level atomic system. We find that the localized modes of the passive medium are not modified by the presence of gain and serve as resonant microcavities of the random laser. The spectrum of laser emission is shown to depend on the location of the external pump. These results are similar to the recent experimental observations in semiconductor powder [Cao et al., Phys. Rev. Lett. 82, 2278 (1999)]. We show that local pumping of the system allows selective excitation of individual localized modes.