The transition from a peroidic vortex street to a less ordered state of vortex shedding in the wake of elongated bluff bodies is investigated in the case of a ring. Experimental results characterizing this transition are presented. The complex Ginzburg-Landau model, which is known to accurately describe the periodic regime, is extended to the transition range, and its predictions are compared to the experimental findings. The good agreement allows interpretation of the instability of the periodic vortex shedding in terms of the Benjamin-Feir instability of a one-dimensional system of coupled nonlinear oscillators.

The problem of the existence and of the stability of steady undulating rolls evolving from the zigzag instability of convection rolls in a Rayleigh-Bénard layer are considered. Finite amplitude solutions are given and the onset of a new type of instability leading to a long wavelength domain type pattern is described. Domains of straight rolls with a larger than average wave number and undulating rolls alternate in this pattern. The structure appears to be stable and should be realizable in laboratory experiments.

The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these ‘‘semiquantum’’ dynamics may be derived via the Ehrenfest theorem and recast as an extended classical gradient system with the fluctuation variables coupled to the average variables. An extended potential is constructed for a one-dimensional system. The semiquantal behavior is shown to be chaotic even though the system has regular classical behavior and the quantum behavior had been assumed regular.

A new statistical diagnostic tool for chaotic transport in Hamiltonian systems is proposed. The method, based on the concept of exit times, has an advantage over the calculation of diffusion coefficients in that it remains valid for nondiffusive transport processes. This method is tested on the Chirikov-Taylor standard map: One finds that it is more robust than the usual diffusion coefficient D and conveys the same information as D when the latter is meaningful, for all values of the nonlinearity parameter K.

We report a study on the optical diffraction for light propagation perpendicular to the twist axis in the chiral smectic-C liquid crystal. In this phase grating mode, we find very unusual intensity and polarization features in the diffraction pattern. These observed features can be explained by invoking the theory of anisotropic gratings which takes into account the internal diffractions.

The late time evolution and structure of 2D Rayleigh-Taylor and Richtmyer-Meshkov bubble fronts is calculated, using a new statistical merger model based on the potential flow equations. The merger model dynamics are shown to reach a scale invariant reigme. It is found that the Rayleigh-Taylor front reaches a constant acceleration, growing as 0.05${\mathit{gt}}^2$, while the Richtmyer-Meshkov front grows as ${\mathit{at}}^{0.4}$ where a depends on the initial perturbation. The model results are in good agreement with experiments and simulations.

We have experimentally studied the transition to chaos in a quasi-one-dimensional chain of nonlinear coupled oscillators, with periodic boundary conditions. We show that as long as the dynamics are not chaotic, this transition follows an unusual scenario: the period doubling of a ${\mathit{T}}^2$ torus. During this scenario all oscillators remain in phase. When the chain of oscillators bifurcates to chaos, it loses its spatial homogeneity and localized wave holes randomly propagate along the chain.

Simple kinetic models capture the propagation and evolution of patterns produced by competing autocatalytic processes occurring in chaotic flows. Changes in initial condition of a few percent lead to changes in the final product mix of 100%. This is due to transport and interaction along the intertwining manifolds. Examples include crystallization of chiral substances and bistable enzyme reactions.

Changes in the boundary conditions enforce variations of the eigenvalues of periodic band random matrices. We investigate the statistics of the corresponding curvatures and discuss connections with conductance fluctuations. In particular we show with numerical data that mean curvatures obey a scaling law quite similar to the one expected for mean conductance, and that a distribution law predicted for curvatures of Gaussian orthogonal ensemble matrices also holds for band matrices in the metallic regime.

Self-organized collective behavior in globally coupled multimode lasers is investigated by introducing a new physical quantity, gain cirulation, that characterizes the gain transfer among lasing modes. Numerical simulations indicate that the self-organization is established such that the gain circultions in all the closed interaction paths involving arbitrary multiple lasing modes become neglibibly small as compared with direct mode-to-mode gain circulations. This implies that the nonreciprocal local (i.e., mode-to-mode) gain transfers are self-organized so as to ensure reciprocal average gain flow among modes approximately and that temporal evolutions of individual mode intensities are determined accordingly.

The response of a magnetic fluid microdrop to a rotating magnetic field is studied for the first time. An unexpected shape instability is observed, leading to the formation of a spiny starfish shape that slowly corotates with the field. A simple model accounts for (i) the stability range of an oblate ellipsoidal shape that is a precursor to the starfish, (ii) the rotational frequency which is substantially lower than that of the applied magnetic field, and (iii) a lateral peak instability that is responsible for growth of the spiny arms of the starfish.

The topology of minimal orbits of the energy functional of a complex 2D vector field depends on the sign of nonlinear terms breaking the SU(2) symmetry, giving rise to either linearly or circularly polarized states (LP and CP) which possess different sets of defects. The CP vortices have two alternative core structures, with either vanishing amplitude or reversed polarization in the inner core. In the LP state, there are two distinct topological charges. Vortices carrying two half-unit charges have a circularly polarized core. Unit-charged vortices have a core with a vanishing amplitude, and may suffer a core instability splitting into a pair of half-unit-charged vortices.

A method for controlling spatiotemporal chaos in certain classes of spatially extended systems is proposed. In these systems, unstable defects emit convectively unstable waves which subsequently break and may nucleate new defects. Control is achieved via the stabilization of one such active wave source, which then sweeps all of the chaotic fluctuations to the system boundaries. This method is applied to the one- and two-dimensional complex Ginzburg-Landau equation, and to a recent model of spiral breakup in excitable media.

A spatial instability is observed when a laser beam at 795 nm is transmitted through a rubidium cell with single plane feedback mirror. The emitted beams have patterns looking like flowers. The dependence of the number of petals in the pattern with the distance between the cell and the mirror is studied and interpreted using an expansion of the instability in Laguerre-Gauss modes. This experiment shows the influence of the saturation of the nonlinearity in the pattern selection.

Using tools for the analysis of nonlinear chaotic observations, we have determined the embedding dimension required for data from measurements of wall pressure fluctuations in high Reynolds number boundary layer flow around an axisymmetric body. The Reynolds number based on the boundary layer size is as large as ${10}^5$, and the number of degrees of freedom excited in the fluid is certainly very large. Yet the active degrees of freedom seen by the pressure sensors in the transitional and turbulent parts of the flow are as low as 8 to 10. We discuss the source of these results in terms of sensor size and the known coherent structures in these shear flows.

We present an experimental test of the theorem of isospectral domains which states that certain pairs of planar domains have identical spectra for eigenvalues of the Laplacian operator or the Helmholtz wave equation. The experiments employ thin microwave cavities shaped in the form of two different domains known to be isospectral. We verify the equality of at least 54 of the measured low-lying eigenvalues to a few parts in ${10}^4$. We also obtain the eigenfunctions experimentally, and confirm that two nonisometric transformations connect isospectral eigenfunction pairs. An analysis in terms of periodic orbits using the trace formula is also carried out, and shown to be an alternative confirmation of isospectrality.

We report the measurement of what we believe to be the narrowest known optical resonance in a solid. This was made on the ${}_{}{}^7{}_{}{}^{}$${\mathit{F}}_0$${\to }^5$${\mathit{D}}_0$ transition of ${\mathrm{Eu}}^{3+}$:${\mathrm{Y}}_2$${\mathrm{SiO}}_5$ at 1.4 K using photon echoes with sufficiently low laser power to almost eliminate contributions from instantaneous diffusion. The optical resonance widths measured for ${\mathrm{Eu}}^{3+}$ ions in the two crystallographic sites of ${\mathrm{Y}}_2$${\mathrm{SiO}}_5$ and in a magnetic field of 100 G are 122 Hz (site 1) and 167 Hz (site 2). These widths are dominated by population decay, but up to 20 Hz is attributed to ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ spin fluctuations which have been reduced by the applied magnetic field.

Second- and third-harmonic generation are observed in a semiconductor heterostructure which approximates a two-state system with an 11-meV level spacing. A resonance in the second- (third-) harmonic generation is found when the depolarization-shifted infrared absorption peak is Stark tuned through 2 (3) times the pump frequency. These resonances are thus associated with the depolarization-shifted, and not the bare, intersubband energy. Data are analyzed with a theory of second-harmonic generation including dynamic screening. Saturation is observed at pump intensities >10 kW/${\mathrm{cm}}^2$.

Relaxation of 2D turbulence has been measured in magnetized electron columns, which follow the same (r,θ) dynamics as 2D incompressible fluids. The turbulence arises from shear instabilities on initially hollow columns, then relaxes to long-lasting, axisymmetric metaequilibria. The measured metaequilibrium vorticity profiles are in close agreement with the minimum enstrophy vortices predicted by the ‘‘selective decay’’ hypothesis.

We present experimental results on the dynamics of concentric roll and textured patterns in a convecting fluid of Prandtl number about 1 and with radius-to-height ratio near 40 and for ε==ΔT/Δ${\mathit{T}}_{\mathit{c}}$-1≤0.8. At ε=0.21, the concentric-roll state was lost by the pattern center moving to the wall while nucleating new rolls which traveled outward. The textured pattern contained sidewall foci which also emitted traveling waves. The average frequency of the emission increased linearly with ε, but then increased rapidly by about 40% at ε≊0.65 where spiral defects appeared.