The spectral fluctuations of random capillary wave fields appear to be intermittent. This intermittency is related to local creation and annihilation of coherent structures: ordered regions that have definite symmetry. Both the occurrence of non-Gaussian fluctuations and the existence of (quasi) long-range order question the applicability of a thermodynamic description of spatiotemporal chaos in two dimensions.

The motion of the bubble radius and of the air trapped inside the bubble during sonoluminescence are determined self-consistently by coupling the solution of the Rayleigh-Plesset equation governing the bubble radius to the solution of Euler’s equations for the motion of air in the bubble. Results are presented for three slightly different conditions of excitation, in two of which shocks are formed during the collapse of the bubble, and in which such high temperatures are attained that the air is ionized. Estimates are made of the duration and intensity of the light then radiated by the plasma.

We have measured the crystal-angle dependence and the intensity of the parametric x radiation from a Si single crystal impinged upon by an electron beam with the energy ranging from 200 to 1100 MeV. It has been found that the x-ray intensity is higher and the angular spread is less broad than the predictions of the theoretical model due to Feranchuk and Ivashin. This calls for a more elaborate theoretical treatment of multiple scattering, and encourages research aiming at a new type of x-ray source based on the parametric x-radiation mechanism.

Reynolds number dependence of turbulence energy spectra and higher-order moments of velocity differences is explored by means of numerical integrations of the incompressible Navier-Stokes equation. The simulations have spatial resolutions up to ${512}^3$ and cover the range 15≤${\mathit{R}}_{\lambda }$≤200, where ${\mathit{R}}_{\lambda }$ is the Taylor microscale Reynolds number. Over this range, the energy spectra collapse when scaled by the wave number ${\mathit{k}}_{\mathit{p}}$ of peak dissipation and also by the spectrum level at ${\mathit{k}}_{\mathit{p}}$. It is found that ${\mathit{k}}_{\mathit{p}}$ varies with ${\mathit{R}}_{\lambda }$ in accord with the 1941 Kolmogorov theory. High-order normalized moments of velocity differences over inertial-range distances exhibit an ${\mathit{R}}_{\lambda }$-independent variation with separation distance. Implications of these observations are discussed.

The use of chaos to transmit information is described. Chaotic dynamical systems, such as electrical oscillators with very simple structures, naturally produce complex wave forms. We show that the symbolic dynamics of a chaotic oscillator can be made to follow a desired symbol sequence by using small perturbations, thus allowing us to encode a message in the wave form. We illustrate this using a simple numerical electrical oscillator model.

Helicity production in a homogeneous fluid is numerically demonstrated by using steady and unsteady forced Navier-Stokes equations: Even if all Fourier components of the force do not have helicity, nonlinear interactions of the zero-helicity components can generate helicity in the flow. When the Reynolds number increases, the flow nature changes from steady to temporally periodic to chaotic. The produced helicity has the largest time-averaged value in the periodic motion.

We report the first positive experimental observation of the optical activity effect on normal reflection. The experiment was performed along the optic axis in a gyrotropic semiconductor crystal of α-HgS, cinnabar, in a spectral region of strong absorption. Reflected light polarization azimuth rotation resulting from the reflection is in the order of ${10}^{\mathrm{-}4}$ rad and has pronounced dependence on ħω-${\mathit{E}}_{\mathit{g}}$.

Topological reconfigurations of the boundaries of thin fluid layers in Hele-Shaw flow are studied. A systematic treatment of the dynamics of the bounding interfaces is developed through an expansion in the aspect ratio of the layer, yielding nonlinear partial differential equations for the local thickness. For both density-stratified fluid layers and gravity-driven jets, numerical study of the dynamics at second order suggests strrongly the collision of the interfaces in finite time. There are associated singularities both in the fluid velocity and in geometric properties of the interfaces.

Viscous fingering in a linear channel is investigated in the presence of anisotropy, when the directions of easy growth are at 45° to the direction of the cell axis. Experimentally, when the velocity is increased, the stable fingers and the averaged unstable ones tend to occupy an increasing fraction of the cell width, in contrast with the standard situation. The numerical simulation and the analytical investigation reveal the existence of a new solution for the Saffman-Taylor finger which does not belong to the standard manifold.

Navier-Stokes turbulence at low Reynolds number (${\mathit{scrR}}_{\lambda }$≊15) is studied by high-resolution computer simulation. The energy spectrum in the range 5${\mathit{k}}_{\mathit{d}}$<k<10${\mathit{k}}_{\mathit{d}}$ is well fitted by ${\mathit{k}}^{\mathrm{\alpha }}$exp(-ck/${\mathit{k}}_{\mathit{d}}$), where ${\mathit{k}}_{\mathit{d}}$ is the Kolmogorov dissipation wave number, α≊3.3 and c≊7.1. High-order spatial derivatives of the velocity field exhibit strong intermittency, associated with gentle spatial variation of large-scale structure rather than with sparse, intense small-scale structures. Analysis by the direct-interaction approximation, which ignores intermittency, gives α=3, c≊11.

It is shown that in nonlinear discrete systems localized modes may exist in the form of self-induced gap solitons. Such structures appear due to a nonlinearity-induced gap in the cw spectrum, when one group of particles in the lattice plays a role of an effective periodic potential to other particles supporting a spatially localized oscillation. Two examples are considered and exact soliton solutions describing this type of localized modes are presented.

We study the motion of advected particles in the Kuramoto-Sivashinsky equation. We give numerical evidence as well as analytical arguments for anomalous diffusion in which the particle displacement Δr satisfies 〈[Δr(t)${]}^2$〉∼${\mathit{t}}^{\mathrm{\eta }}$ where η>1. We show that if the flow is initially seeded with many particles, they will coalesce in time and that a passive scalar density tends to an asymptotic (time dependent) distribution, which, for given initial conditions on the velocity field, is independent of the initial distribution of the passive scalar.

The parameter space of the Hénon map is reported to contain a regular structure-parallel-to-structure sequence of shrimp-shaped robust isoperiodic domains. They appear densely concentrated on a neighborhood along a main α direction, extending across both orientation-preserving and -reversing domains. There is also a secondary β direction, roughly perpendicular to a very dense ‘‘foliation of legs’’ emanating from the isoperiodic domains. Familiar bifurcation phenomena observed in unimodal maps correspond to particular cuts along the β direction. The α direction is rich in new phenomena. The topology along α is conjectured to be typical of bimodal maps.

The first infrared vibrational photon echo experiments conducted in a liquid and a glass are reported. The experiments were performed on the CO stretching mode of tungsten hexacarbonyl at 5.1 μm (1960 ${\mathrm{cm}}^{\mathrm{-}1}$) in 2-methyltetrahydrofuran over the temperature range 300 to 16 K using picosecond pulses from the free electron laser at Stanford University. In addition, the first vibrational population relaxation measurements spanning a temperature range that takes a system from a liquid to a supercooled liquid to a glass are reported.

The temporal evolution of global modes is studied, which are time-harmonic solutions of the linear disturbance equations, subject to homogeneous boundary conditions in all space directions. As basic flow we consider weakly nonparallel three-dimensional shear flows. A necessary condition for the existence of a global mode is the presence of at least two branches of the local dispersion relation and a location where they coalesce. It leads to a mode coupling in a neighborhood of that point. To analyze the mode coupling the uniform asymptotic description of Kravtsov and Ludwig is employed which also yields a general formula for the global eigenfrequency.

A phenomenological description of the dynamical correlations in a fluid confined between two parallel solid walls, using a generalization of Onsager’s theory of fluctuations, is presented. Besides the bulk viscosity, this description involves parameters characterizing the boundary conditions. Correlations functions obtained in equilibrium molecular dynamics simulations are very well described within this framework. Featureless walls yield perfect slip boundary conditions, while corrugated walls in most cases correspond to stick boundary conditions. Only for very small corrugation amplitudes is it necessary to introduce a finite slipping length.

A variational principle for thermostated nonequilibrium steady states recently proposed by Evans and Baranyai [Phys. Rev. Lett. 67, 2597 (1991)] is analyzed by means of a model kinetic equation for dilute gases. It is shown that the principle does not apply exactly, although deviations from it are small, especially when the gradients are not very large.

The nonlinear resonant response of a bound electron to a time-varying spatially inhomogeneous electric field was studied experimentally. By use of the artificial atom ‘‘geonium’’ (an electron bound in a Penning trap), we observed up to ninth-order multipole (pentacosiododecapole) coherent excitation of the electron’s magnetron motion, and up to third-order (octupole) excitation of the cyclotron motion. Also, by applying two fields simultaneously, we have observed coherent stimulated Raman excitation of the electron’s motion.

Quasiregularity of Hamiltonian chaos is approached using the concept of the type of a chaotic orbit, i.e., the sequence of resonances visited by the orbit. A simple method is introduced for determining the type in the case of kicked-rotor Hamiltonians. First applications of this method are given in the calculation and study of quantities characterizing ‘‘vague tori’’ within resonances, namely, survival probabilities and average dwelling times. Results concerning a newly defined disorder parameter, characterizing quasiregularity, are briefly reported.

We show that a dynamical system of N phase oscillators with global cosine coupling is completely integrable. In particular, we prove that the N-dimensional phase space is foliated by invariant two-dimensional tori, for all N≥3. Explicit expressions are given for the constants of motion, and for the solitary waves that occur in the continuum limit. Our analysis elucidates the origin of the remarkable phase space structure detected in recent numerical studies of globally coupled arrays of Josephson junctions, lasers, and Ginzburg-Landau oscillators.