Measurements of the correlation function below the electrohydrodynamic instability in a thin layer of a nematic liquid crystal reveal fluctuating convection patches. Their amplitude A¯, correlation length ξ, and correlation time τ can be desribed by a stochastic mean-field model. The amplitude agrees with the expected fluctuations due to thermal noise.

Cavity-QED-enhanced stimulated visible emission was observed in 14-μm-diam rhodamine-6G–ethanol droplets pumped by cw 514.5-nm radiation. Use of droplets provides an excellent test of cavity QED theory for spherical geometries. The mode number and order of the spherical-cavity resonances responsible for the observed emission peaks were identified and their Q values calculated from Lorenz-Mie theory. By equating stimulated gain to calculated/measured cavity losses, it was determined that spherical-cavity Q’s of only ${10}^{3–}$${10}^4$ lead to cavity QED enhancements in excess of 120 in the emission cross section of rhodamine 6G, consistent with theory.

Experiment and theory for surface waves in square containers suggest that the effective symmetry may be larger than the geometric symmetry of the container cross section. The extra symmetries complicate the construction of normal forms and appear to stabilize effects in the experiments that would otherwise be nongeneric. These symmetries may be directly observed if the sidewalls are deformed to a nonsquare cross section that retains square symmetry. The effects of such a deformation are analyzed.

The eddy size and temperature distribution in the inertial subrange of turbulent Rayleigh-Bénard flow at a Rayleigh number Ra≊${10}^{11}$ is calculated from the Boussinesq equations. Velocity and temperature fields are decomposed into Fourier modes with geometrically scaling wave numbers. 1/3 scaling for both velocity u and temperature FTHETA is obtained in agreement with Shraiman and Siggia’s finding, but there is no indication of a new scaling range as claimed recently. We resolve this discrepancy. The isotropization by eddy decay is demonstrated in terms of the ${\mathit{u}}_3$FTHETA scaling, which appreciably differs from 2/3; testing this new quantity experimentally would be of great interest.

We report experimental evidence that the scattering of sound waves by a fluid may be used, as a nonintrusive and nonlocal method, to characterize the space-time structure of the flow. The experiment has been performed using, as a test flow, the von Kármán vortex street behind a cylinder at a low Reynolds number (Re=50). The results are in good qualitative agreement with earlier experiments on the von Kármán vortex street and with recent theoretical developments on sound-vorticity interaction.

A hydrodynamic model for turbulence in dilute polymer solution is used to describe drag reduction. It is shown that flexible polymers lead to an enhancement of molecular viscosity at small length scales while at intermediate length scales the effective viscosity is decreased. The onset of drag reduction is predicted to occur only above a minimum value of the polymer concentration, ${\mathit{c}}_{\mathit{m}}$. A direct calculation of the dependence of ${\mathit{c}}_{\mathit{m}}$ on the energy input per unit mass, ɛ, shows that ${\mathit{c}}_{\mathit{m}}$∼${\mathrm{\varepsilon }}^{\mathrm{-}1}$. Comparing this result with the scaling theory of de Gennes allows us to conclude that the exponent describing the power-law dependence of polymer deformation on spatial scale is 4/5.

The peak pattern of a magnetic fluid, in both a vertical dc and an additional vertical ac magnetic field, behaves as an oscillator. Using the ac-dc field ratio as a control parameter, we study the dynamics of this oscillator. For low values, the peaks oscillate at the ac field frequency, whereas for a large enough value the oscillation is subharmonic (period doubling). The phase diagram is interpreted in terms of a bounded parametric resonance driven by the nonlinearity of the oscillator. In 2D this transition occurs with symmetry breaking from a triangular to a square pattern.

Deformation and breakup of immiscible fluids in deterministic chaotic flows is governed by self-similar distributions of stretching histories and stretching rates and produces populations of droplets of widely distributed sizes. Scaling reveals that distributions of drop sizes collapse into two self-similar families; each family exhibits a different shape, presumably due to changes in the breakup mechanism.

In this paper we report both experimental and theoretical results on a Rayleigh-Bénard convection experiment with a static spatially periodic forcing. For reduced Rayleigh number of order 100, the system undergoes a secondary Hopf bifurcation involving novel and surprising spatially inhomogeneous temporally periodic states. We give a description of these various inhomogeneous states, and develop a simple phenomenological model based on symmetry considerations which seems to capture all the essential qualitative features.

Aggregation in deterministic flows is simulated using a chaotic flow, a regular flow, and a flow with both regular and chaotic regions. Whenever particles of diameter ${\mathit{d}}_0$ touch each other, they form rigid clusters that move as a unit. The model produces fractal aggregates whose morphology can be controlled by tuning flow parameters.

We present results of optical experiments which demonstrate that in a strongly scattering medium containing resonant scatterers the velocity for electromagnetic energy may differ by an order of magnitude from the phase velocity. We derive a microscopic theory that yields an expression for this velocity. Discrepancies are removed, and excellent agreement is found between experiment and theory.

A simple phenomenological model for a passive scalar subject to a mean gradient and undergoing random advection plus molecular mixing yields an exponential distribution as a consequence of general analytic properties of the steady-state solution. The result persists in the presence of a coherent mean flow. Experimental realizations of our model are proposed.

First observations of an evaporative instability in absorptive dye (Nigrosin) doped water droplets heated by a pulsed Nd:YAlG laser (532 nm) are reported. Measurement of the instability thresholds at different dye concentrations shows an approximate inverse linear dependence on droplet absorption index, suggesting that the instability is caused by superheating of the droplet. The instability may trigger subsequent droplet deformation or or disintegration; however, below a well-defined fluence threshold, complete recovery of the droplet occurs following laser excitation. A qualitative model based on Landau instability theory is used to describe the instability.

Numerical solution of two-dimensional incompressible hydrodynamics shows that states of a near-minimal ratio of enstrophy to energy can be attained in times short compared with the flow decay time, confirming the simplest turbulent selective decay conjecture, and suggesting that coherent vortex structures do not terminate nonlinear processes. After all possible vortex mergers occur, the vorticity attains a particlelike character, suggested by the late-time similarity of the streamlines to Ewald potential contours.

Freely evolving two-dimensional turbulence is dominated by coherent vortices. The density of these vortices decays in time as ρ∼${\mathit{t}}^{\mathrm{-}\xi }$ with ξ≊0.75. A new scaling theory is proposed which expresses all statistical properties in terms of ξ. Thus the average circulation of the vortices increases as ${\mathit{t}}^{\xi /2\mathrm{}}$ and their average radius as ${\mathit{t}}^{\xi /4\mathrm{}}$. The total energy is constant, the enstrophy decreases as ${\mathit{t}}^{\mathrm{-}\xi /2\mathrm{}}$, and the vorticity kurtosis increases as ${\mathit{t}}^{\xi /2\mathrm{}}$. These results are supported both by numerical simulations of the fluid equations and by solutions of a modified point-vortex model.

We present the first measurements of an instability in Taylor-Sedov blast waves propagating through a uniform gas. The instability occurred in a gas whose adiabatic index was low. Amplitude perturbations grew as a power of time. Our observations are compared to theory.

It is demonstrated both experimentally and theoretically that broken translational and vertical symmetries of a horizontal convection layer heated from below can lead to a qualitatively new effect, namely the onset of time-dependent convection. In particular, the behavior of a non-Boussinesq fluid in a layer with sinusoidal variation of the horizontal boundaries is studied near onset.

The evolution of the spectral bandwidth in free-electron-laser (FEL) oscillators is studied and found to be different for different saturation characteristics: For weakly saturated FELs in storage rings, the limiting bandwidth is given by that derived in the supermode theory; for linac-based FELs, where the gain reduction due to the high-intensity effect is significant, it is determined by the Fourier transform of the electron pulse length; for the case of a dc beam, it is given by a Schawlow-Townes formula, but the approach to the limit is very slow.

We show that periodic dielectric composite media such as ordered colloidal suspensions exhibit enhanced dispersion forces. In an fcc structure with a full photonic band gap these forces can produce a nearly isotropic pressure on the structure due to the vacuum field fluctuations. This pressure is shown to significantly alter the phase diagram of the Kirkwood-Alder hard-sphere transition for systems with micron-size dimensions. The calculations predict that aqueous solutions of ${\mathrm{TiO}}_2$ particles of the order of 0.35 μm in diameter should be ideal of observing these effects.

The structure and dynamics of both subcritical and supercritical localized traveling-wave (LTW) convective states with different extensions and uniquely selected width are determined by numerical integration of the proper hydrodynamic field equations with realistic horizontal boundary conditions. A large-scale mean concentration current loop influences the LTW significantly. It generates a concentration distribution that hinders propagation of the LTW pulse, so that the group velocity is small but finite.