Velocity measurements made in the wake of a circular cylinder near the onset of turbulence have been analyzed to determine various scaling exponents. One conclusion is the apparent divergence of a correlation length as one approaches a “critical” Reynolds number. Other aspects analyzed are the scaling of turbulent energy and energy dissipation rate, as well as the circulation around square boxes of various sizes.

A new type of classical billiard—the Andreev billiard—is investigated using the tangent map technique. Andreev billiards consist of a normal region surrounded by a superconducting region. In contrast with previously studied billiards, Andreev billiards are integrable in zero magnetic field, regardless of their shape. A magnetic field renders chaotic motion in a generically shaped billiard, which is demonstrated for the Bunimovich stadium by examination of both Poincaré sections and Lyapunov exponents. The issue of the feasibility of certain experimental realizations is addressed.

We report on coherent backscattering measurements from amplifying random media using optically pumped Ti:sapphire powders. The top of the backscattering cone sharpens with increasing gain, reflecting a change in the relative contributions to the intensity from paths of different lengths. A calculation based on diffusion theory is performed on coherent backscattering from amplifying random media, which is in good agreement with the data.

We report quantitative experimental results for the intensity of noise-induced fluctuations below the critical temperature difference $\Delta T_c$ for Rayleigh-Bénard convection. The structure factor of the fluctuating convection rolls is consistent with the expected rotational invariance of the system. In agreement with predictions based on stochastic hydrodynamic equations, the fluctuation intensity is found to be proportional to $1/\sqrt{-\epsilon }$, where $\epsilon \equiv \Delta T/\Delta T_c-1\mathrm{}$. The noise power necessary to explain the measurements agrees with the prediction for thermal noise.

Solitary pulses in an active medium, like those for the Kuramoto-Sivashinsky equation for thin falling films, are often destroyed by growing and expanding wave packets from localized disturbances. The stability of a solitary pulse is then determined by whether is can escape the expanding wave packets. We show that this pulse-packet interaction is determined by the essential spectrum of the pulse and a pulse stability theory can be derived from a simple extension of the classical convective instability theory for a wave packet on the trivial state.

An eikonal-type description for the evolution of $k$ spectra of passive scalars convected in a Lagrangian chaotic fluid flow is shown to accurately reproduce results from orders of magnitude more time consuming computations based on the full passive scalar partial differential equation. Furthermore, the validity of the reduced description, combined with concepts from chaotic dynamics, allows new theoretical results on passive scalar $k$ spectra to be obtained. Illustrative applications are presented to long-time passive scalar decay, and to Batchelor's law $k$ spectrum and its diffusive cutoff.

A comment on the Letter by Sergey V. Nazarenko, Phys. Rev. Lett. 73, 1793, (1994). The authors of the Letter offer a Reply.

A Reply to the Comment by E. B. Sonin.

The transition between rotating spirals and spatiotemporal chaos (“spiral turbulence”) in an excitable reaction-diffusion system is investigated by means of statistics of topological defects of the concentration field. The ratio of the variance and the mean value of the number of defects show a significant deviation from unity at this point. A change of the defect dynamics within the turbulent regime reveals a strong similarity to a liquid-to-gas transition, while a liquid-solid-like transition occurs upon a jumplike return to the region of spiral stability.

We study the photonic “acoustic band” for both square arrays of dielectric and infinite refractive index cylinders. We show that the effective refractive index defined by this band does not have a continuous limit as the cylinder refractive index approaches infinity, and we explain this physically.

The nonlinear Goos-Hänchen effect is experimentally isolated for the total reflection of a Gaussian beam at an interface between a linear medium and a negative Kerr-type nonlinear medium. The evolution of this nonlinear spatial shift versus light intensity is measured for both TE and TM polarizations. The results are in good agreement with a simple model based on nonlinear Artmann's formulas.

We have measured the ac-Stark effect on single terrylene molecules in $p$-terphenyl crystals at superfluid helium temperatures. With the pump beam far enough from resonance, the molecular transition shifts as expected, i.e., proportional to the pump intensity and to the inverse pump detuning. Experiments closer to resonance with stronger beams show Autler-Townes-like structures that can be well reproduced by means of Bloch equations with two intense laser fields. These experiments are a demonstration of nonlinear optical effects with the localized electronic states of a single molecule trapped in a solid.

We have observed the stable coexistence of target and spiral patterns in thick freely suspended films of a smectic- $C$ liquid crystal in a rotating electric field. In this system, patterns arise from a competition between boundary effects and bulk electric field torques and show a simple connection between spiral and target dynamics. We compare our observations in this driven system with experimental reports of spirals and targets in nonequilibrium systems such as large aspect ratio Bénard convection.

The ratio $R_1$ between the average magnetic energy and the square-averaged flux plays an important role in the study of nonlinear dynamos, as a measure of the efficiency of a dynamo at generating flux. For large values of $R_m$, $R_1$ displays a scaling behavior of the type $R_1\sim R_m^n$, where $R_m$ is the magnetic Reynolds number. We show by direct numerical evaluation that $n$ depends sensitively on the flow complexity for small-scale dynamos. Furthermore, by relating $n$ to the cancellation exponent and the correlation dimension of the magnetic field, we argue that $n$ is not likely to be close to zero in general.

Direct numerical simulation is used to study the periodic generation and evolution of streamwise vortical structures in the near wake of a circular cylinder. It is observed that streamwise structures are formed due to stretching of core vorticity which escapes out of the core and due to stretching of small scale streamwise vorticity already present outside the core. Distinct hairpin structures are observed which play a central role in transferring vorticity out of the core. Furthermore, the hairpin structures are associated with a spanwise subharmonic mode and are thus manifestations of a period-doubling mechanism.

A Comment on the Letter by Yoshihiro Tanabe and Kunihiko Kaneko, Phys. Rev. Lett. 73, 1372 (1994). The authors of the Letter offer a Reply.

A Reply to the Comment by L. Mahadevan, H. Aref, and S. W. Jones.

We present results of an exact computation of the properties of the development of the wave function in the presence of a potential barrier in a bounded well. We find that the complex behavior of this evolution, associated with tunneling, is very similar to that expected from a chaotic dynamical system.

We report the demonstration of efficient soft x-ray lasing in nickel-like lanthanide elements (Nd, Sm, Gd, Tb, and Dy) covering the spectral range between 6 and 8 nm. A curved slab target was pumped by 1.053- $\mu$m-wavelength multiple laser pulses: two or three 100-ps-duration pulses separated by 400 ps. A gain coefficient of 3.1 ${\mathrm{cm}}^{-1\mathrm{}}$ and a gain-length product of 7.8 have been achieved at 7.97 nm in the Nd ions with 250 J pumping energy on a 2.5-cm-length target. The result represents close to an order of magnitude reduction in the energy required to pump these soft x-ray lasers.

Wave functions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wave functions display universal density distributions and density autocorrelations in agreement with expressions derived from a 0D nonlinear σ model of supersymmetry, which coincides with random matrix theory. In contrast, disordered wave functions show deviations from this universal behavior due to Anderson localization. A systematic behavior of the distribution function is studied as a function of the localization length, and can be understood in the framework of a 1D version of the nonlinear σ model.