High frequency capillary waves on the surface of dilute aqueous solutions of cetyltrimethylammonium bromide have been studied by quasielastic light scattering. The wave propagation deviates significantly from classical expectation, due to enhanced coupling between the capillary and dilational modes of the surface. At a concentration of 0.04mM the capillary wave behavior clearly demonstrates mixing of these two surface modes. The effects appear to derive from a reduction in the stability of the dilational waves.

We discuss two-point correlations of the actions of classical periodic orbits in chaotic systems. For systems where the semiclassical trace formula is exact and the spectral statistics follow random matrix theory, there exist nontrivial correlations between actions, which we express in a universal form. We illustrate this result with the analogous problem of the pair correlations between prime numbers. We also report on numerical studies of three chaotic systems where the semiclassical trace formula is only approximate, but nevertheless these unexpected action correlations are observed.

Single beam holographic grating recording, based on the photogalvanic coupling between orthogonal birefringent modes, is demonstrated in a photorefractive ${\mathrm{BaTiO}}_3$ crystal.

Recently it has been shown that there are chaotic attractors whose basins are such that every point in the attractor’s basin has pieces of another attractor’s basin arbitrarily nearby (the basin is ‘‘riddled’’ with holes). Here we report quantitative theoretical results for such basins and compare with numerical experiments on a simple physical model.

Proofs that Fredholm determinants of transfer operators for hyperbolic flows are entire can be extended to a large new class of multiplicative evolution operators. We construct such operators both for the Gutzwiller semiclassical quantum mechanics and for classical thermodynamic formalism, and introduce a new functional determinant which is expected to be entire for Axiom A flows, and whose zeros coincide with the zeros of the Gutzwiller-Voros zeta function.

We consider fluid flow through a layer of adsorbed homopolymer, which we decompose into an equivalent set of polymeric loops, each tethered to the adsorbing wall and obeying Zimm dynamics. Using a multiple scattering analysis, we obtain an integral equation for the velocity profile. New results are presented for flow profiles in steady and oscillatory weak shear past an adsorbed layer at the theta temperature. Near the wall we find a universal behavior under steady shear for the fluid velocity u(z)∼${\mathit{z}}^{\mathit{y}}$ at height z, with an exponent y≃2.0.

We present theoretical and experimental results of the leading order angular correlations of second harmonic light generated inside random media, for both the transmission and reflection geometries. We find the striking result that correlations in reflection of the second harmonic light scales with the sample thickness L, in sharp contrast to the corresponding short-range correlation function in reflection of the fundamental light in the linear scattering regime, which scales with mean free path ${\mathit{l}}^{\mathrm{*}}$.

Measurements based on balanced detection demonstrate more than 3 dB photon-number squeezing from a quantum well laser injection locked to a coherent signal. We show that injection locking significantly reduces the photon-number fluctuation by suppressing weak side modes that feature intensity noise far above the standard quantum limit. The measurements also reveal that the photon statistics vary qualitatively with the polarization of the laser field.

Self-phase modulation resulting from radiation influence on material parameters of a medium can, like the Doppler and gravitational redshifts, result in a nearly uniform frequency shift. This is confirmed experimentally by the use of the orientational mechanism of the interaction of a laser beam with a nematic liquid crystal. The self-induced frequency shift is proportional to light intensity and the distance light travels in the medium.

Optical bistability in a two-dimensional nonlinear superlattice, resulting from the index-modulation mechanism, was observed in experiment for the first time. The two-dimensional nonlinear superlattice was constructed by recording a two-dimensional refractive index grating into a photorefractive material, a Fe-doped ${\mathrm{LiNbO}}_3$ single crystal. Optical instability was also observed in this experiment.

The static as well as the dynamic behavior of granular material are determined by dynamic and static friction. There are well known methods to inlcude static friction in molecular dynamics simulations using scarcely understood forces. We propose an ansatz based on the geometrical shape of nonspherical particles which does not involve an explicit expression for static friction. It is shown that the simulations based on this model are close to experimental results.

Direct numerical simulations with up to ${4096}^2$ resolution are performed to address the question of universality of statistical properties of the enstrophy cascade in homogeneous two-dimensional turbulence driven by large-scale Gaussian white-in-time noise. Data with different Reynolds numbers are compared with each other. The energy spectrum is found to be very close to 1/${\mathit{k}}^3$. It is shown that the primary contribution to the enstrophy transfer function comes from wave-number triads with one small leg and two long ones, corresponding to wave numbers in the inertial range.

A rare exact solution to the nonlinear Boltzmann equation describing rheological phenomena far from equilibrium is reconsidered. We show the existence of a critical shear rate beyond which the solution fails to exist. The implication of this exact result is a singular transition from simple uniform shear flow to a more complex state, perhaps involving spatial ordering.

Chaotic transport in a laminar fluid flow in a rotating annulus is studied experimentally by tracking large numbers of tracer particles for long times. Sticking and unsticking of particles to remnants of invariant surfaces (Cantori) around vortices results in superdiffusion: The variance of the displacement grows with time as ${\mathit{t}}_{\mathrm{\delta }}$ with γ=1.65±0.15. Sticking and flight time probability distribution functions exhibit power-law decays with exponents 1.6±0.3 and 2.3±0.2, respectively. The exponents are consistent with theoretical predictions relating Lévy flights and anomalous diffusion.

The Maass operator for automorphic forms is interpreted as the Hamiltonian of a charged particle moving in a constant magnetic field on a Riemann surface of constant negative curvature. A careful analysis of the classical trajectories in the presence of the magnetic field shows that the action on a periodic orbit is related to the action on a free periodic geodesic. This identification provides a semiclassical interpretation of the Selberg-Maass trace formula for automorphic forms.

The exponential decay of correlations in chaotic systems is often modulated and shows up as broad peaks in the power spectrum. For a particle sliding freely on a compact surface of constant negative curvature, we show that these classical resonances are directly related to the quantal eigenenergies of the system. We use this as the basis for proposing a quantization scheme which requires the knowledge of a single arbitrary ergodic classical trajectory. Our results are substantiated numerically.

A model one-dimensional drift-wave equation driven by a sinusoidal wave is used to study controlling chaos in partial differential equations. By injecting negative feedback through a monochromatic wave or pinning at a certain x-space point we can successfully stabilize unstable steady states and control chaos. In the case of bistability, an unstable steady state in the middle branch can be also stabilized by these controlling approaches. The methods used in this Letter can be applied to general continuous spatiotemporal systems.

We present a solution to the direct determination of the statistical parameters (correlation length and root mean square deviation), characterizing the profile of a random rough surface with large slopes, thus producing multiple scattering. This is done from the specular, coherent, component of the mean intensity of waves scattered from the surface, and, today, is the only reliable, realistic procedure which uses an analytical expression of this component. The method is applicable whenever this specular component may be measured, and is valid for a wide variety of physical problems involving surface scattering.

We report on time-delayed wave-mixing experiments which allowed, for the first time, the observation of ultrafast modulation due to the interference between third- and fifth-order optical polarizations. The new effect was observed in semiconductor doped glasses by controlling the relative phase of the optical fields which induce distinct wave-mixing processes. The experiments allowed us to measure the relative phase between the nonlinear susceptibilities ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ and ${\mathrm{\chi }}^{\mathrm{}\left(5\right)\mathrm{}}$ as well as their relative magnitude. In principle the interference effect may be observed in a large variety of materials and the exploitation of this phenomenon to develop a new technique for nonlinear spectroscopy is also discussed.

The whole needle-crystal solution for three-dimensional (3D) dendritic growth is described analytically. Its construction involves the existing 3D selection theory for the tip of the dendrite (M. Ben Amar and E. A. Brener [Phys. Rev. Lett. 71, 589 (1993]) plus matching of the tail to this tip. This is exhibited here. Both intermediate and final asymptotics of the tail shape are given. This shape, which deviates strongly from an Ivantsov paraboloid, is in qualitative agreement with experiental observations.