The time evolution of Couette-Taylor flow has been measured for supercritical, almost tricritical, and subcritical bifurcations. The subcritical transitions near the critical point are dramatically different from the supercritical transitions. A simple relaxational dynamics equation together with a slightly asymmetric sixth-order Landau potential has been shown to fit the experimental data very well. The coefficients of the fit have been compared to the theoretical structure of the coefficients revealed earlier.

We present a new numerical method for calculating interference phenomena for waves propagating through random media. The model is applied to calculate probability distribution functions for the transmission P(T) in one and two dimensions, T being the transmission coefficient. The model reproduces the analytical predictions for one dimension, and yields new results for two-dimensional systems. The distribution function P(T) in two dimensions, in the diffusive regime, is found to be close to a Gaussian with a variance proportional to the mean, in agreement with the results of diagrammatic calculations. A crossover of the distribution to log-normal behavior typical for strong localization is obtained.

A simple optical model to realize a reversible, potentially error-free logic gate—a Fredkin gate—is discussed. The device dissipates no energy and makes use of the Kerr nonlinearity to produce intensity-dependent phase shifts. The analysis shows that quantum mechanics permits the operation of error-free logic gates which dissipate no energy. However, even though the device is nondissipative, error-free performance only occurs under particular operating conditions.

A dynamical theory for the structure functions in convective turbulence at high Rayleigh numbers is presented. A range of scales is identified in which buoyancy forces dominate and the scaling exponents differ significantly from isotropic turbulence. A crossover to Kolmogorov-type scaling is predicted as a function of the Rayleigh number.

The linear-response matrix, L, of a composite made of two isotropic components must obey a number of compatibility relations, involving the response matrices, $L_a$ and $L_b$, of the components, but totally independent of the mixture ratio of the components and the microstructure of the composite: ${\mathrm{LL}}_a^{\mathrm{-}1}$$L_b$-$L_b$$L_a^{\mathrm{-}1}$L=0. For an anisotropic composite, the tensor elements of L must satisfy the same conditions; in this case we obtain relations that the moduli of the composite satisfy among themselves. The mere fact that the composite is made of two isotropic components imposes relations among its moduli.

Shortly after Hawking’s prediction of thermal radiation from black holes, it became apparent that observers in accelerating frames should see a Planck distribution of electromagnetic radiation (Unruh radiation). Since an acceleration g=980 cm/${\sec }^2$ produces a radiation temperature of only ∼4×${10}^{\mathrm{-}20}$ K, the detection of such thermal radiation is a major challenge. A nonlinear optical medium whose index of refraction is changing rapidly with time accelerates zero-point quantum fluctuations. The sudden ionization of a gas or a semiconductor crystal to generate a plasma on a subpicosecond time scale can produce a reference frame accelerating at ∼${10}^{20}$g relative to an inertial frame.

We show that a new class of optical solitons is possible in nonlinear periodic structures. These waves can propagate undistorted even though their power spectra lie well within the frequency band gap of the periodic structure and even though their carrier frequency is very close to the Bragg resonance. Analysis shows that these Bragg solitons can exhibit velocities which are orders of magnitude lower than the speed of light in the unperturbed medium.

We describe a turbulent state characterized by the presence of topological defects. This ‘‘topological turbulence’’ is likely to be experimentally observed in nonequilibrium systems.

The problem of longitudinal mode competition in free-electron lasers is addressed. It is shown that for small enough ratios of the current to output coupling coefficient many single-mode states are possible. However, the time required to reach these states becomes extremely long for typical devices. Before reaching a single-mode state the radiation field becomes relatively constant in amplitude with modulations of its phase. Finally, a simple method for reaching the stable single-mode state with maximum efficiency is suggested.

We have measured the full spectrum of the third-order optical susceptibiltiy, ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$(ω), in polyacetylene using an infrared free-electron laser. The magnitude of ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$(ω) reaches ∼${10}^{\mathrm{-}8}$ esu at 0.6 eV, the largest value of an electronic ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$(ω) inside the gap of a semiconductor. There are two peaks at 0.6 and 0.89 eV in the spectrum of ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$(ω) that are assigned to three- and two-photon resonance enhancements, respectively, implying states of opposite symmetry lie near the 1D band gap at $E_g$∼1.8 eV.

We report on a new hydrodynamic instability which occurs at the spreading edge of a thin wetting film. A drop of aqueous surfactant solution placed on a glass surface moistened with a thin layer of water spreads by propagating fingers, whose velocity and shape depend on the thickness of the ambient water layer and on the surfactant concentration. The two fluids are miscible and show negligible viscosity difference, ruling out a Saffman-Taylor instability. We propose that the Marangoni effect, which is fluid flow induced by gradients in surface tension, drives the instability.

A simple model, in which a boundary layer creates spatial turbulence by emitting ‘‘hog plumes,’’ is introduced. In the turbulent regime we find exponentially decaying fluctuations, a characteristic frequency of time signals, and a power-law scaling between analogs of hydrodynamic quantities.

We study numerically the laminar fully developed region of periodic flows through curved pipes. Under certain conditions the results exhibit period tripling. This striking feature is reminiscent of one of the possible routes to chaos which typical nonlinear dynamical systems take.

We show experimentally the appearance of time-dependent and stationary complex spatial structures in a ${\mathrm{CO}}_2$ laser. A comparison of the data with a theoretical model supports the notion that the observed phenomena result from the nonlinear interaction of transverse cavity modes with the active medium. The simultaneous appearance of spatial and temporal instabilities hints to the interesting prospect that one may be able to study turbulence in a laser system.

We have observed an extremely large second-order susceptibility for second-harmonic generation of 9.6–10.8 μm radiation due to intersubband transitions in electric-field-biased GaAs quantum wells. For 92-Å GaAs wells with 309-Å ${\mathrm{Al}}_{0.48}$${\mathrm{Ga}}_{0.52}$As barriers under a bias of 36 kV/cm, the peak value of the susceptibility was 28 nm/V, 73 times larger than bulk GaAs. The magnitude and sign of the susceptibility depend on the bias field, and are in accord with theoretical predictions.

Statistical properties of solutions of the random-force–driven Burgers equation are investigated by use of the dynamic renormalization group and direct numerical simulations. The agreement between computed and analytical results on both exponents and amplitudes of the correlation functions is good. It is shown that a small-scale noise dominates large-scale, long-time (k→0,ω→0) behavior of the system and, as a consequence, no microscopic system of interacting particles described by Burgers equation in the hydrodynamic limit (k→0,ω→0) exists.

We report experimental observations of traveling-wave convection in a binary fluid mixture in an annular container—a flow which approximates a large, one-dimensional dynamical system. In this geometry, the convective rolls align themselves radially and propagate azimuthally. We observe competition between several non- equilibrium states. This leads to a rich variety of dynamical behavior, including coexisting regions of conduction and convection, sources and sinks of convective rolls, and more complex spatiotemporal defects.

It is shown analytically, in a suitable limit, that a sharp pattern selection mechanism exists in driven explosive crystallization: After the onset of a morphological instability of the steady-state crystallization front, nonlinear effects cause the front to develop a spatial pattern with a definite wavelength. The amplitude, wavelength, and shape of the selected pattern are calculated analytically.

We report a variety of measurements on fluid interface motion through model porous media. The dynamics shares many features with other systems pinned by random fields. Over a range of pressures randomness pins the interface. In this range there are many metastable interface configurations and relaxation is extremely slow. The dc response outside the pinned region is markedly nonlinear. Oscillations in the pressure occur at constant velocity which reflect the pore geometry.

Electron cooling of positrons should make possible a large increase in the luminosity of future high-energy linear colliders, leading to greatly enhanced event rates at these machines. An evaluation of the electron-cooling-time requirement indicates that a positron-source repetition rate of 100 Hz is possible. Final positron-beam normalized emittances of ${10}^{\mathrm{-}7}$ m rad should result, implying a tremendous increase in positron-beam density over that currently obtained.