We show that fractal viscous fingers can be formed in a Hele-Shaw cell with radial symmetry, thereby permitting their study—for the first time—without the complicating effects of boundary conditions such as those present in the conventional linear cell. We find—for a wide range of shear-thinning fluids, flow rates, and plate separations—that radial viscous fingers have a fractal dimension ${\mathrm{d}}_{\mathrm{f}}$=1.70±0.05, the same as diffusion-limited aggregation. We also quantitatively measure the set of growth sites and compare with diffusion-limited aggregation.

We report the first observation of the modulational instability of light waves in dielectric material using a neodymium-doped yttrium aluminum garnet laser operated at 1.319 μm and single-mode optical fibers with anomalous group-velocity dispersion. The observed results are in good agreement with the theoretical predictions. The relationship between the modulation instability and parametric four-wave mixing and the interplay with stimulated Raman and Brillouin scatterings are also presented.

In the process of spontaneous parametric down-conversion a signal and an idler photon are created simultaneously. By use of the photoelectric detection of the signal photon as a gate, a good approximation to the ideal localized one-photon state can be achieved. This has been confirmed by direct photon-counting measurements.

We present the first experimental study of shear-flow–induced behavior in a two-dimensional anisotropic fluid: circular, freely suspended films of smectic-C liquid crystals. Depending on the topology of the in-plane director configuration, we observe either a phase winding state, where Φ, the phase defining the director orientation relative to the velocity field, winds up in the center of the film, or, a flow alignment state, where Φ is constant.

We present the nonlinear phase equations describing the stability of a one-dimensional periodic pattern, with mean flow effect due to Galilean invariance. We show that the phase dynamics is second order in time, and could lead to an oscillatory instability of the pattern.

A novel mechanism capable of efficiently modulating intense relativistic electron beams is reported. This mechanism uses unique properties of slow and fast charge-density waves on an intense beam of a finite transverse dimension. The mechanism was investigated with use of an external microwave energy to excite these waves on a beam. Large-amplitude coherent and monochromatic current oscillations were detected on the electron beam at the same frequency as the external source. With use of this mechanism it becomes possible to construct efficient microwave amplifiers suitable for large rf accelerators.

We demonstrate that a liquid suspension of microparticles can be utilized to generate harmonic phase conjugate waves. This phenomenon involves the formation of higher-order particle gratings via electrostrictive forces generated by the low-frequency pump and probe fields. In turn, such gratings can coherently scatter high-frequency pump radiation, oscillating at a harmonic of the probe wave to form a conjugate wave oscillating at the same frequency.

Near the onset of a period-doubling bifurcation a parametrically modulated NMR laser has been used as a detector of weak input signals with a strongly peaked response curve centered near half the modulation frequency. The maximum sensitivity increases the closer the bifurcation point. A Bloch-Kirchhoff model with realistic parameters has been used for computer simulations. Experiments and theory are in fair agreement. The results suggest that any parametrically modulated laser device could be used as a small-signal detector for selected frequencies.

Infinite pointwise stretching in a finite time for general initial conditions is found in a simulation of the Biot-Savart equation for a slender vortex tube in three dimensions. Viscosity is ineffective in limiting the divergence in the vorticity as long as it remains concentrated in tubes. Stability has not been shown.

An enhancement of ∼100 of stimulated emission over spontaneous emission of the C vi 182-Å line (one-pass gain ∼6.5) was measured in a recombining, magnetically confined plasma column by two independent techniques involving intensity calibrated extreme xuv monochromators. Additional confirmation that the enhancement was due to stimulated emission has been obtained with a soft x-ray mirror; with 12% measured effective reflectivity of the mirror, a 120% increase in intensity of the C vi 182-Å line in the axial direction was observed.

We present measurements of the dynamic behavior of macroscopic structures observed in a periodically excited air jet. The transitional weakly turbulent state is shown to be characterized by a strange attractor with low dimensionality (ν=2.6), whereas motion of the turbulent flow is not restricted to a low-dimensional attractor.

Rayleigh-Bénard convection is studied in alcohol-water mixtures in which the diffusion of concentration opposes convection via the Soret effect. Near onset, the convective rolls are found to move continuously as traveling waves, in contrast to the stationary roll patterns observed in homogeneous fluids. Dependent upon the temperature difference across the fluid layer (i.e., Rayleigh number), these traveling-wave states are either periodic or chaotic. At larger Rayleigh numbers, time-independent flow is observed which is the same as that expected for the homogeneous fluid mixture.

Heat-transport measurements in a normal-fluid ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He mixture contained in a porous medium and heated from below show a bifurcation to steady or oscillatory flow, depending on the mean temperature. With increasing Rayleigh number R the oscillatory state is entered via a forward Hopf bifurcation with frequency ${\mathrm{\omega }}_{\mathrm{c}}$>0. As the stationary bifurcation is approached by change of the mean temperature, ${\mathrm{\omega }}_{\mathrm{c}}$ vanishes. With increasing R, the oscillatory state terminates with vanishing frequency and finite amplitude in a hysteretic bifurcation to a steady state. Those observations agree with recent theoretical predictions.

The finite-amplitude tuning curves of a surface-wave resonator have been determined for various liquid depths. It is found that the direction of the bending of the tuning curve depends on the liquid depth. The free decay rate of the soliton is measured and shows that solitons initially decay much faster than the corresponding transverse mode but have the same rate in the terminal decay.

An experimental study of competing instabilities in a rotating layer of mercury heated from below is reported, and analyzed in the framework of codimension-two bifurcation theory.

We have measured the magnetic field directly inside a thin, circular, parallel-plate capacitor as it is being charged. We find that this field varies linearly with distance from the axis, as is to be expected if a uniform displacement current flows between the plates. The measured slope of B vs r agrees with predictions to within 5%.

Single-mode and multimode self-pulsing instability leading to chaos is reported in the 12.8-μm emission from a homogeneously broadened ${\mathrm{NH}}_3$ laser, near resonantly pumped by ${\mathrm{CO}}_2$ laser radiation. Occurrence of instabilities on two independent emitting transitions over a wide range of operating conditions, including those for optimum lasing, indicate that this behavior is general for near resonantly enhanced two-photon Raman systems of this type.

The radiative decay of the cyclotron motion of a single electron is significantly inhibited when the electron is located within microwave cavity (formed by the electrodes of a Penning trap) rather than in free space. This is the first observation of such inhibited spontaneous emission and the first use of a promising new system for radiative physics. Implications for precision measurements are mentioned.

We present numerical calculations concerning the growth of a large-scale Gaussian spike riding axially over a Gaussian profile intense laser beam. Incorporation of both self-focusing and depletion of the laser beam leads to a criticality with regard to the spike’s initial relative intensity due to the counteracting behavior of these two effects, thereby determining the net power transfer to the spike and its quasistabilization.

A high-gain, high–extraction-efficiency, linearly polarized free-electron laser amplifier has been operated at 34.6 GHz. At low signal levels, exponential gain of 13.4 dB/m has been measured. With a 3-=kW input signal, saturation was observed with an 80-MW output and a 5% extraction efficiency. The results are in good agreement with linear models at small signal levels and nonlinear models at large signal levels.