In the chaotic region the spectra of hydrogen are shown to display universality in the response of the energy levels to magnetic field. Several autocorrelation functions are measured and shown to be in close agreement with recent theoretical predictions. These results represent the first experimental verification of universality beyond distributions of level spacings.

We have found several cases in our numerical simulations where Richtmyer’s prescription fails to give the correct growth rate for the Richtmyer-Meshkov instability in the linear regime. Another expression, due to Fraley [Phys. Fluids 29, 376 (1986)], agrees with our simulations. We discuss recent experiments and report two new types of perturbation freeze-out, single-shock and double-interface, which are quite distinct from the previously reported double-shock freeze-out.

A theory is presented for the electrohydrodynamic deformation of a thin fluid stream and applied to the experiments of Rhodes, Synder, and Roberts on colloidal dispersions. The resulting transverse velocity field has a symmetric four-lobe structure and, when the conductivity of the sample is greater than that of the surrounding fluid, the sample deforms into a ribbon whose axis is parallel to the incident field. The ribbon axis is perpendicular to the field if the conductivities are reversed. Electrohydrodynamic velocities are of the order of microns per second and the theory agrees with the qualitative and quantitative features of existing experimental data.

A continuous time dynamic model of a d-dimensional lattice of coupled localized m-component chaotic elements is solved exactly in the limit m→∞. A self-consistent nonlinear partial differential equation for the correlations in space and time is derived. Near the onset of spatiotemporal disorder there are solutions that exhibit a novel space-time symmetry: the corresponding correlations are invariant to rotations in the d+1 space-time variables. For d<3 the correlations decay exponentially at large distances or long times. For d≥3 the correlations exhibit a power law decay as the inverse of the distance or time.

We derive here an expression for the length spectrum, Σδ(l-${\mathit{l}}_{\mathit{j}}$) of periodic orbits in chaotic billiards. Our analysis yields the average exponential proliferation of lengths superimposed by fluctuations which arise as a sum over contributions from ‘‘quantal energies.’’ We further show that these fluctuations are non-Poisson. Long-orbits, however, mimic the Poisson result for the spectral rigidity, Δ(L).

The balance of one-point and two-point statistical characterics of vorticity, is considered on the basis of the Navier-Stokes equations. It is shown that within the inertial range of scales (L ${\mathrm{Re}}^{\mathrm{-}3/4}$≪r≪L, L external scale, Re Reynolds number) there is a physically distinguished scale ${\mathit{l}}_{\mathit{s}}$∼L ${\mathrm{Re}}^{\mathrm{-}3/10}$. The balance of vortical correlations with scales r≥${\mathit{l}}_{\mathit{s}}$ is directly affected by the large-scale motion. ${\mathit{l}}_{\mathit{s}}$ is a natural length scale for the ‘‘vortex strings,’’ observed experimentally and numerically in three-dimensional turbulent flows. The twist of vortex lines in the internal structure of vortex strings is also briefly discussed.

We report on observations of turbulent behavior made without requiring the use of Taylor’s ‘‘frozen turbulence’’ hypothesis. Initially, a towed grid generates homogeneous turbulence of grid Reynolds number of order ${10}^5$ within a stationary channel filled with helium II. The subsequent decay in time t of the line density of quantum vortices is measured by second sound attenuation, and the associated rms vorticity ω follows the behavior expected of a classical fluid with ω∼${\mathit{t}}^{\mathrm{-}3/2}$, consistent with the notion of a coupled turbulent state of helium II. This technique also yields the time dependence of the Kolmogorov microscale.

We propose a new definition of natural invariant measure for trajectory segments of finite duration for a many-particle system. On this basis we give an expression for the probability of fluctuations in the shear stress of a fluid in a nonequilibrium steady state far from equilibrium. In particular we obtain a formula for the ratio that, for a finite time, the shear stress reverse sign, violating the second law of thermodynamics. Computer simulations support this formula.

Partial dynamical symmetry is a situation in which the Hamiltonian does not have a certain symmetry yet a subset of its eigenstates does. It is shown that partial dynamical symmetry may cause suppression of chaos even in cases where the fraction of states which has the symmetry vanishes in the classical limit. The average entropy associated with the symmetry is a sensitive quantum measure of the partial symmetry and its effect on the chaotic dynamics.

We show that in a chaotic scattering system the stable and unstable foliations of isolated chaotic invariant sets can become heteroclinically tangent to each other at an uncountably infinite number of parameter values. The first tangency, which is a crisis in chaotic scattering, provides the link between the chaotic sets. A striking consequence is that the fractal dimension of the set of singularities in the scattering function increases in the parameter range determined by the first and the last tangencies. This leads to a proliferation of singularities in the scattering function and, consequently, to an enhancement of chaotic scattering.

We show that spatiotemporally complex patterns in the presence of a symmetry imposed by the container geometry can have ordered spatial and temporal averages. The system studied was the Küppers-Lortz unstable state in rotating thermal convection. As the control parameter ΔT was increased above onset, fluctuations about the ordered averaged state increased and the correlation of individual patterns with the averaged state decreased. The pattern fluctuations about the averaged state were highly correlated with the instantaneous heat transport fluctuations.

We introduce models incorporating an adaptive self-regulatory feedback mechanism on an extended chaotic lattice. Numerical experiments show that our system gives rise to a host of novel spatiotemporal phenomena characterized by a rich variety of ‘‘phases’’ in parameter space. Moreover, interestingly, certain phases exhibit distinct scaling properties and 1/f noise.

A self-consistent many-body approach to quantum noise is presented. Many-photon polarization effects produce system-size scaling in quantum dissipative systems. The role of system-size quantum noise on the dynamics near the bifurcation point in an optical parametric oscillator is investigated, and nonlinear spectra are presented in the nonadiabatic limit.

Experimental results of the first efficient operation of a long pulse cyclotron autoresonance maser oscillator are presented. Output power of 1.9 MW for a beam energy of 450 keV and current of 80 A, corresponding to an efficiency of 5.2%, has been measured at 27.8 GHz in the ${\mathrm{TE}}_{11}$ mode of a Bragg resonator. The observed frequency of the cyclotron autoresonance maser emission corresponds to a Doppler unshifted frequency of 2.9 times the relativistic cyclotron frequency. A significant mode competition between the ${\mathrm{TE}}_{11}$ and a ${\mathrm{TM}}_{01}$ mode is present.

We present the first full band-structure calculations for periodic, elastic composites. For transverse polarization of the vibrations we obtain a ‘‘phononic’’ band gap which extends throughout the Brillouin zone. A complete acoustic gap or a low density of states should have important consequences for the suppression of zero-point motion and for the localization of phonons, and may lead to improvements in transducers and in the creation of a vibrationless environment.

We report experiments on convection patterns in a cylindrical cell with a large aspect ratio. The fluid had a Prandtl number σ≊1. We observed a chaotic pattern consisting of many rotating spirals and other defects in the parameter range where theory predicts that steady straight rolls should be stable. The correlation length of the pattern decreased rapidly with increasing control parameter so that the size of a correlated area became much smaller than the area of the cell. This suggests that the chaotic behavior is intrinsic to large aspect ratio geometries.

A numerical solution of a generalized Swift-Hohenberg equation in two dimensions reveals the existence of a spatiotemporal chaotic state comprised of a large number of rotating spirals. This state is observed for a reduced Rayleigh number ε=0.25. The power spectrum of the state is isotropic, and the spatial correlation function decays exponentially, with an estimated decay length ξ≊2.5${\lambda }_{\mathit{c}}$, where ${\lambda }_{\mathit{c}}$ is the critical wavelength near the onset of convection. Our study suggests that this spiral defect state occurs for low Prandtl numbers and large aspect ratios.

Chaotic spatiotemporal patterns can have highly ordered time averages. This fact is demonstrated for Faraday waves by averaging shadowgraph images. The averages exhibit box quantization effects, and their spatial form is similar to that predicted for patterns near onset, despite the large fluctuations. Patches of the disordered instantaneous patterns retain significant phase coherence with the ordered averages.

The nonlinear dynamics of two ions in a Paul trap is known to show chaos or condensation into a regular ‘‘crystal.’’ We present the first observations of frequency locking of two microspheres (diameter 10 μm) in a Paul trap, in close agreement with theoretical predictions. This system reproduces the main features of our earlier work on two-ion chaos. The phase space is fragmented, and chaotic transients can converge to several regular attractors. Damping, including laser cooling, can extinguish frequency-locked attractors, explaining their absence in ion trap experiments. Study of two weakly coupled circle maps shows that this is a general phenomenon when three frequencies are present.

Noncohesive granular materials driven by a vertically vibrated horizontal surface become unstable when the acceleration exceeds g. Then there is internal convective transport of materials balanced by continuous surface avalanches leading to an inclined surface. We describe studies above the onset to flow where new surface wave motions occur. The surface waves travel upward against gravity on the free surface. They occur only above minimum accelerations and dimensionless energies, and only with large vibration amplitude.