We report the first observation of intrinsic optical bistability in ${\mathrm{CsCdBr}}_3:1\%$ ${\mathrm{Yb}}^{3+}$ and show, using site-selective spectroscopy, that only the asymmetric, strongly coupled ${\mathrm{Yb}}^{3+}$ ion-pair minority site gives rise to hysteresis of near-infrared and cooperative up-conversion luminescence as a function of incident laser intensity below 15 K.

The existence of surface states for sonic propagation in elastic band gap finite periodic systems is shown in this Letter. These surface states slide and propagate the sound along the surface edges as whispering galleries. We also experimentally observe such surface modes as well as localization phenomena in linear and point defects.

The signal generated by a weak impulse propagates dispersively in a gravitationally compacted granular chain. For a power-law-type contact force, we show analytically that the type of dispersion follows power laws in depth. The power law for a grain displacement signal is given by $h^{-(1/4)[1-(1/p\left)\right]}$ where $h$ and $p$ denote depth and the exponent of the contact force, respectively, and the power law for the grain velocity is $h^{-(1/4)\left[\right(1/3)+(1/p\left)\right]}$. Other depth-dependent power laws for oscillation frequency, wavelength, and period are given by combining the above two expressions and the phase velocity power law $h^{(1/2)[1-(1/p\left)\right]}$. We verify these power laws by comparing with the data obtained by numerical simulations.

Parametrically excited surface waves (Faraday waves) are studied near the threshold for breaking. The breaking state ejects droplets from wave peaks when the applied forcing exceeds an acceleration threshold. The rate of breaking events approaches zero gradually with decreasing acceleration. Two properties of these ejections were studied around the ejection threshold. Analysis of the ejection rate dependence on acceleration allows a determination of the ejection threshold and an inference about the wave height distribution. A Poisson distribution is found for the times between ejections.

We report the first experimental study of the dispersion of pairs of passive particles, performed in a controlled two-dimensional turbulent flow, in which Kolmogorov-Kraichnan scaling $E\left(k\right)\sim k^{-5\mathrm{}/3}$ holds. The Richardson $t^3$ law is observed, and strongly non-Gaussian behavior is obtained for the Lagrangian distributions of separations. The process is shown to be isotropic, and self-similar in time. The observations, which fit well in the Kolmogorov framework, jeopardize the relevance of the Lévy walk approach.

We have found a new class of exact solutions for multicomponent partially coherent solitons in photorefractive media with a drift mechanism of nonlinear response. Their novel feature is that the composite $M$-component sech-shaped soliton is located on a constant-background plane wave. The solutions are characterized by two free parameters and these are related to the maximum intensity of the composite soliton and to the amplitude of the background.

We apply the discrete parametric control (Ott-Brebogi-York method) to stabilize the high-order $(k=34\mathrm{})$ unstable periodic orbit of a 2D chaotic map. The map describes a complex reversible system, the phase space of which contains elements typical for both Hamiltonian and dissipative dynamics. Stabilization was achieved (even with external noise) for the unstable orbit where the amplitude of chaotic oscillations shows variations by 4 orders of magnitude.

A periodically driven nonlinear electric resonance circuit with a ferroelectric inside the capacitance shows the recently discovered effect of noise induced attractor deformations. By exposing the system to dynamical noise we observe and quantitatively characterize the effect of attractor elongation due to perturbations at homoclinic tangencies. The analysis of the experimental observations fits perfectly with theoretical predictions.

We report the first observation of random laser action with coherent feedback in semiconductor powder. Since the scattering mean free path is less than the emission wavelength, recurrent light scattering arises and provides coherent feedback for lasing. Discrete lasing modes have been observed above the threshold. The dependence of the lasing threshold intensity on the excitation volume agrees with the random laser theory. Laser emission from the powder could be observed in all directions. This observation also provides direct evidence for the existence of recurrent scattering of light.

Reduction of a large system of equations to a lower-dimensional system of similar essential dynamics is investigated. For dynamical systems with disparate time scales, a criterion for determining redundant dimensions and a general reduction method based on the minimization of evolution rate are proposed.

A Comment on the Letter by Peng-Ye Wang, et al., Phys. Rev. Lett. 80, 4669 (1998). The authors of the Letter offer a Reply.

A Reply to the Comment by G. K. Harkness, et al.

We show how the resolution of an experimental spectrum influences the standard statistical tests of random matrix theory such as the nearest neighbor distribution, the Fourier transform, or the number variance. A new experiment on very highly excited vibrational states of ${\mathrm{CS}}_2$ is analyzed in light of these new results. The resolution problem in the published results concerning the molecular vibrational chaos is then examined.

We show theoretically that patterns with concentric rings of bright or dark spots made up by modes with coprime azimuthal indexes may arise in codimension one bifurcations in optical systems with a metallic diffractor, a polarizer, and a nonlinear medium. These patterns are a consequence of diffraction-induced polarization in systems without polarization dynamics. As an example of this type of system, we investigate numerically the symmetry-breaking bifurcations of a ring laser with a metallic duct and a polarizer inside the optical cavity.

We have studied the transition to chaos in the ferroelectric ${\mathrm{KH}}_2{\mathrm{PO}}_4$ crystal near the phase transition temperature. An unusual scenario has been found: the transition from a fixed point to a quasiperiodic motion on a torus ( $T$) through Hopf bifurcation to a quasiperiodic motion on a two-torus ( $T^2$) through a cascade of torus doublings, and then directly to chaos. These results point to the essential role of the polarization fluctuations near the phase transition and the electromechanical couplings between the soft-mode polarization $P$ and the elastic shear strain $X$ of the crystal, whose dynamics are described by a Duffing's anharmonic oscillator coupled by a piezoelectric oscillator.

We report the effect of light-induced sliding of the nematic director over an isotropic boundary surface in an azo-dye doped liquid-crystal cell. We show that illumination of the cell with polarized laser light induces transient dynamic sliding followed by permanent reorientation of the director. The two effects are in competition and tend to orient the director along mutually orthogonal directions. The sliding can be controlled and even completely quenched by the amount of induced anchoring energy. A physical model is proposed which accounts for the experimental results.

We present a series of numerical and analytical computations on heat conduction for a strongly chaotic system—the Lorentz gas. Heat conduction is characterized by nontrivial features: While the heat conductivity is well defined in the thermodynamic limit, a linear gradient appears only for quite small temperature differences. The key dynamical feature inducing such a behavior is recognized as deterministic diffusion (along transport direction) which is usually associated to full hyperbolicity.

Experimental observations of pulsed ultrasonic transmission through granular glass beads under oedometric loading are presented. We observe in the transmitted signals the coexistence of a coherent ballistic pulse traveling through an “effective contact medium” and a specklelike multiply scattered signal. The relative amplitudes of these signals strongly depend on the ratios of the bead size to the wavelength and to the detector size. Experimental data support recent descriptions of the inhomogeneous stress field within granular media.

A Comment on the Letter by H. P. Schriemer et al. Phys. Rev. Lett. 79, 3166 (1997). The authors of the Letter offer a Reply.