The excess damping of capillary waves caused by a surfactant monolayer is demonstrated to be present as well for the quadrupole shape mode of an isolated acoustically trapped bubble in water. To facilitate measurements of damping as a function of surface concentration, a method was developed for depositing a known amount of insoluble surfactant (stearic acid) on the surface of the bubble. As the bubble dissolves, the stearic acid concentration increases, and the excess damping has a pronounced local maximum near 0.26 ${\mathrm{nm}}^2$ per molecule specific area in agreement with capillary wave data for a flat surface. The method of depositing insoluble surfactant should be applicable to the characterization of other surface-limited processes in isolated bubbles.

A class of Gledzer-Ohkitani-Yamada shell models for fully developed turbulence is studied numerically in the presence of a hyperviscous damping $\nu k_n^{2+\alpha }$. It is found that the inertial-range scalings ${\zeta }_p$ ( $〈|u_n{|}^p〉\sim k_n^{-{\zeta }_p}$) are not universal, but depend on the hyperviscosity index $\alpha$. A class of anomalous scalings are observed, and remarkably ${\zeta }_p/{\zeta }_3$ are universal. A theoretical explanation is developed based on a recently proposed scaling model of turbulence [She and Leveque, Phys. Rev. Lett. 72, 336 (1994)].

A crisis is a sudden discontinuous change in a chaotic attractor as a system parameter is varied. We investigate phenomena observed when two parameters of a dissipative system are varied simultaneously, following a crisis along a curve in the parameter plane. Two such curves intersect at a point we call a double crisis vertex. The phenomena we study include the double crisis vertex at which an interior and a boundary crisis coincide, and related forms of double crisis. We show how an experimenter can infer a crisis from observations of other related crises at a vertex.

We demonstrate and analyze a bifurcation producing a type of fractal basin boundary which has the strange property that any point that is on the boundary of that basin is also simultaneously on the boundary of at least two other basins. We give rigorous general criteria guaranteeing this phenomenon, present illustrative numerical examples, and discuss the practical significance of the results.

The formation and dynamics of coherent vortices in the Hasegawa-Mima two-dimensional model of drift-wave turbulence is studied numerically. The effect of “vortex shielding” due to the presence of a characteristic length scale (ion Larmor radius ${\rho }_s$) leads to important differences between self-organization in drift-wave and Navier-Stokes fluid turbulence. While it may not be surprising that a finite deformation radius leads to the formation of coherent vortices, we show here that it also results in the appearance of long-range order in the system, i.e., the formation of a vortical “quasicrystal.”

It is shown that a plasma fiber waveguide can provide phase matching over extended interaction lengths for the generation of high-order harmonics and difference frequencies through wave mixing or parametric amplification. An important consideration is that the plasma waveguide mode structure is independent of wavelength. Phase matching may be achieved through either frequency tuning or waveguide structure tuning.

We analyze within a semiclassical approximation the form factor for the fluctuations of quantum matrix elements around their classical average. We find two contributions. One is proportional to the form factor for the density of states, with an amplitude determined by the squared average of the matrix elements. The other is constant and related to the fluctuations of finite time classical trajectory segments around the phase space average. The results are illustrated for an observable in the quadratic Zeemann effect.

We generalize an approach recently introduced to study arbitrary correlators of spectral determinants in quantum chaotic systems with broken T invariance. The utility of this method for obtaining generating functions for a variety of universal correlators is illustrated with several applications.

We present experimental evidence that a complex system of particles suspended by upward-moving gas can exhibit low-dimensional bulk behavior. Specifically, we describe large-scale collective particle motion referred to as slugging in an industrial device known as a fluidized bed. As gas flow increases from zero, the bulk motion evolves from a fixed point to periodic oscillations to oscillations intermittently punctuated by “stutters,” which become more frequent as the flow increases further. At the highest flow tested, the behavior becomes extremely complex (“turbulent”).

We propose a method for finding stationary pulse solutions of the complex Ginzburg-Landau equation, which can be applied to both cubic and quintic models. In particular, we discover previously unknown arbitrary-amplitude pulse solutions for both the cubic and quintic models. Numerical simulations show that these solutions are stable relative to small perturbations.

Using temporally and spectrally resolved diagnostics, we show that the pulse duration of laser-produced soft x rays emitted from solid targets can be controlled, permitting a reduction to as short as a few picoseconds. To enable this control, only a single parameter must be adjusted, namely, the intensity of the high-contrast ultrashort laser pulse (400 fs). These results are found to be in qualitative agreement with a simple model of radiation from a collisionally dominated atomic system.

We present a hydrodynamic model that captures the essence of granular dynamics in a vibrating bed. We carry out the linear stability analysis and uncover the instability mechanism that leads to the appearance of convective rolls via a supercritical bifurcation of a bouncing solution. We also explicitly determine the onset of convection as a function of control parameters and confirm our picture by numerical simulations of the continuum equations.

Numerical calculations have shown that bifurcations of periodic orbits of Hamiltonian systems often occur in organized groups. Normal-form theory provides an explanation.

Recently, biological preparations which are thought to be chaotic have been controlled using algorithms based on the detection and manipulation of periodic unstable points. The dynamics of these systems are, however, contaminated with noise; thus detection becomes a statistical process. Here we show that low dimensional chaos can be reliably detected with large noise contamination and distinguished from noisy limit cycles. We also examine a purely chaotic high dimensional system.

The first experimental evidence of a “negative-viscosity” effect in a magnetic fluid is presented here. In a Poiseuille flow, a constant magnetic field balances vorticity and impedes the rotation of individual magnetic particles. Conversely, an alternating magnetic field helps vorticity and favors this rotation: The magnetic energy is partially transformed into the angular momentum of the particles, which in turn is converted into a hydrodynamic motion of the fluid. It manifests itself in a decrease of the total viscosity: Its rotational part becomes negative. The theory developed here corroborates the experimental results.

We study the viscous fingering instability which results from a competition between capillary and viscous forces. We show that for two different systems the instability is modified drastically by changing the surface tension or viscosity by means of surfactants or polymers. For both systems the width of the finger can increase with increasing velocity before settling at a plateau value larger than half the channel width. A numerical study shows that the large deviations from the classical result can be attributed to a velocity dependence of the dynamic interfacial tension and viscosity.

We examine magnetic surfaces and randomization of field lines with fluctuations transverse to a uniform magnetic field. Analogy with passive scalar transport in inviscid 2D flow provides realizations of magnetic surfaces and motivates a nonperturbative statistical approach. The stochastic wandering of magnetic field lines leads to diffusive perpendicular transport. For two-component fluctuations, appropriate for solar wind turbulence, the diffusion coefficient is a nonadditive combination of slab and 2D coefficients, approaching the latter in the small amplitude limit.

A recent experiment using a 160 MeV stored spin-polarized proton beam found clear evidence for a second-order intrinsic depolarizing resonance. With a 20% partial Siberian snake, we studied a first-order intrinsic depolarizing resonance; we then discovered and studied the second-order depolarizing resonance by changing both the horizontal and vertical betatron tunes. As expected, this second-order resonance is much weaker than the first-order resonance; it is probably due to sextupole fields plus coupling between the horizontal and vertical betatron oscillations caused by the 20% snake.

Using magnetic resonance imaging, we examine the onset and stability of porous media convection (PMC) in packings of solid spheres. Nominally, PMC resembles Rayleigh-Bénard convection, except that there should be no vertical vorticity. We find pinned defects in convection patterns for disordered sphere packings. Roll-like structures form in regularly packed media, with rapid relaxation to stable patterns within the expected stable range. The size of up flow regions decreases relative to down flow regions with increasing Rayleigh number, producing a novel time dependent state for Ra $/$Ra ${}_c>6\mathrm{}$.

Experiments with shadowgraph visualization reveal a subcritical transition to a hexagonal convection pattern in thin liquid layers that have a free upper surface and are heated from below. The measured critical Marangoni number (84) and observation of hysteresis ( $3\%$) agree with theory. In some experiments, imperfect bifurcation is observed and is attributed to deterministic forcing caused in part by the lateral boundaries in the experiment.