We report a new mechanism of intrinsic bistability, operative in excited atomic systems with substantial atom-atom coupling. Predictions and observations of bistable luminescence from ${\mathrm{Yb}}^{3+}$ pairs in crystalline ${\mathrm{Cs}}_3$${\mathrm{Y}}_2$${\mathrm{Br}}_9$: ${\mathrm{Yb}}^{3+}$ are in good agreement and have interesting implications for local field effects in solids and dense, ultracold gases.

Boundary-layer instability waves are studied using the Orr-Sommerfield model. A spatial analysis has been performed using complex frequencies to model modulated waves. The use of complex frequency has led to the discovery of a pair of modes satisfying a 2:1 resonance condition. Wind-tunnel experiments have been carried out and show that the rapid nonlinear breakdown process is strongly enhanced for parameter values near the resonance condition. The breakdown is characterized by a quadratic nonlinearity. The approach may have applicability to many nonlinear wave systems.

The dynamic structure factor $G(\mathbf{k},\omega )$ is studied in a time-dependent Ginzburg-Landau model for microemulsions in thermal equilibrium by field-theoretic perturbation methods. For small viscosities, the structure factor develops a peak at a nonzero frequency $\omega$, for fixed wavelengths of the order of the typical domain size of oil and water regions. This implies that the intermediate scattering function oscillates in time. We give a simple explanation for these temporal oscillations by considering the flow through a tube with a radius-dependent tension.

We propose an extension to multivariate time series of the phase-randomized Fourier-transform algorithm for generating surrogate data. Such surrogate data sets must mimic not only the autocorrelations of each of the variables in the original data set, they must mimic the cross correlations between all the variables as well. The method is applied both to a simulated example (the three components of the Lorentz equations) and to data from a multichannel electroencephalogram.

We study the threshold in systems which exhibit a symmetry breaking instability, described, e.g., by Ginzburg-Landau or Swift-Hohenberg equations, with the control parameter fluctuating in space and time. Because of the long-tail property of the probability distributions all the moments of the linearized equations have different thresholds and none of them coincides with the threshold of the nonlinear equations, where the long tails are suppressed. We introduce a method to obtain the threshold of the full nonlinear system from the stability exponents of the first and second moments of the linearized equation.

Some properties of a model of intermittency in fully developed turbulence due to She and Lévêque [Phys. Rev. Lett. 72, 336 (1994)] are explored. The probability functions solution of the model is shown to be simply related to the log-Poisson statistics of local nondimensional energy dissipation. It is also shown that the intermittency obtained by She and Lévêque can be interpreted as the consequence of the scale covariance of the energy dissipation. Based on these observations, a new picture of turbulence is presented, in which scale covariance plays a central role.

We have measured the viscosity $\eta$ and the frequency-dependent shear modulus of the glass-forming liquid di-$\eta$-butylphthalate. Both $\eta$ and the shear relaxation time $\tau$ have non-Arrhenius dependence on temperature $T$. The ratio $\frac{\eta }{{\tau }^T}$ is weakly $T$ dependent implying a slight deviation from the Einstein-Debye equation. This is fully explained by a smooth evolution of the relaxation spectrum and is not accompanied by growth of the elastic shear modulus or a correlation length, as had been suggested.

The parametric sensitivity of complex quantum systems is characterized by the distribution of eigenvalue curvatures k, defined as the second derivative of the eigenvalues with respect to a perturbation parameter. For systems without time-reversal symmetry (unitary ensemble), the exact distribution is found to be P(k)=(2/π)[1 +${\mathit{k}}^2$${]}^{\mathrm{-}2}$. This proves a recent conjecture by Zakrzewski and Delande [Phys. Rev. E 47, 1650 (1993)].

We study the interplay between tunneling and chaos in a quantum system which classically would be weakly chaotic. We show that the tunneling rate between two stable islands is exponential and regular when the characteristic size of the chaotic region separating the islands is much larger or much smaller than Planck's constant. When the chaotic region and Planck's constant are of the same size the tunneling rate is shown to be irregular. This result is obtained by means of a numerical analysis of the quantum kicked Harper model, but we argue this to be a generic effect of classical chaos on tunneling.

A semiclassical criterion for the existence of scars, formulated in terms of a finite number of classical periodic orbits, is shown to be useful in order to predict scarring of specific wave functions of chaotic systems, and to partly disentangle their structure. This is demonstrated by a numerical study of wave functions of a chaotic billiard that are of sufficiently high energy to be considered semiclassical.

The asymptotically exact expressions for all statistical moments of the transmission coefficient are obtained for a 1D disordered lossy system by mapping the Fokker-Planck problem onto a Schrödinger equation with imaginary time. It is shown that even arbitrary small absorption leads to the quantization of the spectrum of the initial Fokker-Planck equation. The quantization reveals itself as the appearance of a new scale: the disorder-induced absorption length.

We study the statistics of an ensemble of images taken in the woods. Distributions of local quantities such as contrast are scale invariant and have nearly exponential tails. Power spectra exhibit scaling with a nontrivial exponent. These data limit the information content of natural images and point to the importance of gain-control strategies in visual processing.

We investigate propagation of light beams in photorefractive media by direct numerical simulation. The two dimensional model is based on solution of nonlinear material equations and parabolic equations for the electromagnetic field. We show that this set of equations describes the wealth of complicated spatial structures observed in these media. We present results on fanning of a single beam and on formation of various four-wave-mixing geometries including self-conjugation of a light beam via total internal reflection, mutual phase conjugation, and self-bending of two counterpropagating beams.

We study numerically a Swift-Hohenberg equation describing, in the weak dispersion limit, nascent optical bistability with transverse effects. We predict that stable localized structures, and organized clusters of them, may form in the transverse plane. These structures consist of either kinks or dips. The number and spatial distribution of these localized structures are determined by the initial conditions while their peak (bottom) intensity remains essentially constant for fixed values of the system’s parameters.

We have studied segregation in binary mixtures of different granular media subjected to rotation in horizontal tubes. Mixtures separate into bands of different relative concentrations arranged along the axis of the tubes. Axial modulations of the tube radius lock bands in space and induce segregation in otherwise nonsegregating mixtures of glass beads. The segregation results from an instability analogous to spinodal decomposition, and we present a model which describes this instability.

Motivated by recent experiments on Rayleigh-Bénard convection, where spiral defect chaos was discovered, we have simulated the Boussinesq equations for the appropriate Rayleigh numbers not far from threshold for large aspect ratio systems using a Galerkin method. A detailed analysis of the results reproduces the experimental findings almost quantitatively. A critical comparison with recent model calculations is also presented. Our investigations show that the new spatiotemporal pattern must be considered generic for Rayleigh-Bénard convection.

It has been known that if the local Poincaré map is quadratic and there are no external noises, the characteristic relation of type-I intermittency is of the form ${\epsilon }^{\frac{-1\mathrm{}}{2}}$. However, we here show that various characteristic relations such as $-\ln \epsilon$ and ${\epsilon }^{-\nu }\left(0\mathrm{}\le \nu \le \frac{1}{2}\right)$ appear according to reinjection probability distributions.

A time series analysis of transient chaos has been carried out in a laboratory experiment. The process is based on the construction of a long artifical time series obtained by gluing pieces of many transiently chaotic signals together. The strange saddle responsible for the transient chaotic behavior of an NMR laser has been reconstructed. Characteristics like dimension, Lyapunov exponent, and correlation function are determined showing that the motion on this set is more unstable than on the coexisting chaotic attractor.

It is shown that a coupled map model for open flow may exhibit spatial chaos and spatial quasiperiodicity with temporal periodicity. The locations of these patterns, which cover a substantial part of parameter space, are indicated in a comprehensive phase diagram. In order to analyze the encountered phenomena, a novel class of spatial maps is introduced which is very efficient in accurately reproducing the original spatial patterns. It is found that temporally period one spatial chaos is convectively unstable, and that it is possible to predict an essential aspect of the bifurcation behavior of the coupled system solely by considering its corresponding spatial map.

When grains are added to a large sandpile, quasiperiodic large avalanches maintain the steady state mass. The buildup periods between the large avalanches contain many small avalanches. The size distribution of the small events does not vary during a buildup period but their mean rate of occurrence does. The qualitative behavior of the real sandpile avalanches is identical to the behavior of earthquakes on a model fault proposed by Carlson and Langer. As that model suggests, the running total number of small avalanches can in principle predict the occurrence of the large avalanches.