The spectrum of coherent scattering induced by electrostriction in gases has been analyzed in the previously unexplored, free-molecule limit by solving Boltzmann's equation with a periodic force due to the optical fields. Calculated and measured spectra of several gases at rarefied conditions are nearly Gaussian with widths approximately 10% wider than the spontaneous Rayleigh widths. Our results are the first spectrally resolved measurements of coherent Rayleigh scattering in the free-molecule limit, where the hydrodynamic analysis of stimulated Rayleigh-Brillouin scattering does not apply.

High-order stimulated Raman scattering for pumping by ps and sub-ps pulses is studied in the frame of a time-domain approach without the slowly varying envelope approximation. Formation of pulse trains with sub-fs durations in the ps-pump regime is demonstrated using external phase compensation. For sub-ps excitation a novel broadening mechanism of Raman lines is predicted that leads to a quasicontinuous spectrum and permits one to generate single sub-fs pulses. We predict also essential shortening of a delayed fs-probe pulse by the Raman oscillations without phase control.

Thermal convection is observed in molecular dynamic simulations of a fluidized granular system of nearly elastic hard disks moving under gravity, inside a square box. Boundaries introduce no shearing or time dependence, but the energy injection comes from a slip (shear-free) thermalizing base. The top wall is perfectly elastic and lateral boundaries are either elastic or periodic. The spontaneous temperature gradient appearing in the system due to the inelastic collisions, combined with gravity, produces a buoyancy force that, when dissipation is large enough, triggers convection.

When one applies a sufficiently large electrical field normal to the surface of a conducting liquid the fluid rises in a spout to form a jet leaving the surface. Using high-speed photography, we have studied the development of this electrohydrodynamical spout and found that its curvature and height can be scaled with respect to a critical time indicating the presence of a critical point in the dynamics underlying the instability.

We present a numerical study on the dynamics of imbibition fronts in porous media using a pipe network model. This model quantitatively reproduces the anomalous scaling behavior found in imbibition experiments [Phys. Rev. E 52, 5166 (1995)]. Using simple scaling arguments, we derive a new identity among the scaling exponents in agreement with the experimental results.

Quantized, compact graphs are excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity, we show that they display all the features which characterize quantum chaotic scattering. We derive exact expressions for the scattering matrix, and an exact trace formula for the density of resonances, in terms of classical orbits, analogous to the semiclassical theory of chaotic scattering. A statistical analysis of the cross sections and resonance parameters compares well with the predictions of random matrix theory. Hence, this system is proposed as a convenient tool to study the generic behavior of chaotic scattering systems and their semiclassical description.

Three-tori solutions of the Navier-Stokes equations and their dynamics are elucidated by use of a global Poincaré map. The flow is contained in a finite annular gap between two concentric cylinders, driven by the steady rotation and axial harmonic oscillations of the inner cylinder. The three-tori solutions undergo global bifurcations, including a new gluing bifurcation, associated with homoclinic and heteroclinic connections to unstable solutions (two-tori). These unstable two-tori act as organizing centers for the three-tori dynamics. A discrete space-time symmetry influences the dynamics.

Turbulence in a freely suspended soap film is created by electromagnetic forcing and measured by particle tracking. The velocity fluctuations are shown to be adequately described by the forced Navier-Stokes equation for an incompressible two-dimensional fluid with a linear drag term to model the frictional coupling to the surrounding air. Using this equation, the energy dissipation rates due to air friction and the film's internal viscosity are measured, as is the rate of energy injection from the electromagnetic forcing. Comparison of these rates demonstrates that the air friction is a significant energy dissipation mechanism in the system.

The boundary condition for the flow velocity of a Newtonian fluid near a solid wall has been probed experimentally with a novel setup using total internal reflection–fluorescence recovery after photobleaching leading to a resolution from the wall of the order of 80 nm. For hexadecane flowing on a hydrocarbon/lyophobic smooth surface, we give what we think to be the first direct experimental evidence of noticeable slip at the wall. We show that the surface roughness and the strength of the fluid-surface interactions both act on wall slip, in antagonist ways.

We develop a self-consistent theory of temporal fluctuations of a speckle pattern resulting from the multiple scattering of a coherent wave in a weakly nonlinear disordered medium. The speckle pattern is shown to become unstable if the nonlinearity exceeds a threshold value. The instability is due to a feedback provided by the multiple scattering and manifests itself in spontaneous fluctuations of the scattered intensity. The development of instability is independent of the sign of nonlinearity.

Using a coherent nonlinear optical technique, slipping of the carrier through the envelope of 6-fs light wave packets emitted from a mode-locked-oscillator/pulse-compressor system has been measured, permitting the generation of intense, few-cycle light with precisely reproducible electric and magnetic fields. These pulses open the way to controlling the evolution of strong-field interactions on the time scale of the light oscillation cycle and are indispensable to reproducible attosecond x-ray pulse generation.

Dynamical properties of topological defects in a two dimensional complex vector field are considered. These objects naturally arise in the study of polarized transverse light waves. Dynamics is modeled by a vector complex Ginzburg-Landau equation with parameter values appropriate for linearly polarized laser emission. Creation and annihilation processes, and self-organization of defects in lattice structures, are described. We find “glassy" configurations dominated by vectorial defects and a melting process associated with topological-charge unbinding.

We report on the observation and interaction of dissipative localized structures in an optical pattern-forming system. Single localized structures are found to have oscillatory decaying tails originating from diffraction. We observe bound states of two or more constituents. These clusters contain several preferred mutual distances. Numerical simulations show that the corresponding interactions are mediated by the oscillatory tails.

The evolution of vortex statistics for decaying two-dimensional turbulence in a square container with rigid no-slip walls is compared with a few available experimental results and with the scaling theory of two-dimensional turbulent decay as proposed by Carnevale et al. Power-law exponents, computed from an ensemble average of several numerical runs, coincide with some experimentally obtained values, but not with data obtained from numerical simulations of decaying two-dimensional turbulence with periodic boundary conditions.

Stationary, highly localized (oscillon) structures are observed in a Newtonian fluid when nonlinear surface waves are parametrically excited with two frequencies. Oscillons have a characteristic structure, that of periodically self-focusing jets. In contrast to previously observed oscillons in highly non-Newtonian media, these states are temporally harmonic with the forcing. For wave amplitudes greater than a critical value, they nucleate from an initial pattern via a hysteretic bifurcation, and can therefore be localized on a background of patterns with a variety of different spatial symmetries.

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers $Q\ne 0$, $\pi$. Incommensurate analytic SWs with $|Q|>\pi /2$ may however appear as “quasistable,” as their instability growth rate is of higher order.

A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data point and short range couplings are introduced. The stationary regime of the system corresponds to a macroscopic attractor independent of the initial conditions. The mutual information between pairs of maps serves to partition the data set in clusters, without prior assumptions about the structure of the underlying distribution of the data. Experiments on simulated and real data sets show the effectiveness of the proposed algorithm.

The phase evolution of light in an optical waveguide structure has for the first time been visualized with subwavelength resolution using a novel heterodyne interferometric photon scanning tunneling microscope. Phase singularities in the optical field of the waveguide have been observed. The phase singularities of charge one appear at locations where the modal field amplitude vanishes, due to the interference of various modes in the waveguide. Excellent agreement of the data with calculations has been obtained.

Fast NMR imaging was used to measure the density profile of a three-dimensional granular medium fluidized by vertical vibrations of the container. For container acceleration much larger than gravity, the rise in center of mass of the granular medium is found to scale as $v_0^{\alpha }/N_{\ell }^{\beta }$ with $\alpha =1.0\mathrm{}\pm 0.2$ and $\beta =0.5\mathrm{}\pm 0.1$, where $v_0$ is the vibration velocity, and $N_{\ell }$ is the number of layers of grains in the container. This value for $\alpha$ is significantly less than found previously for experiments and simulations in one dimension ( $\alpha =2\mathrm{}$) and two dimensions ( $\alpha =1.3\mathrm{}–1.5$).

We study the dynamics of an incommensurate chain sliding on a periodic lattice, modeled by the Frenkel-Kontorova Hamiltonian with initial kinetic energy, without damping and driving terms. We show that the onset of friction is due to a novel type of dissipative parametric resonances, involving several resonant phonons which are driven by the (dissipationless) coupling of the center of mass motion to the phonons with the wave vector related to the modulating potential. We establish quantitative estimates for their existence in finite systems and point out the analogy with the induction phenomenon in Fermi-Ulam-Pasta lattices.