Consider the situation where two individuals observe the same chaotic physical process but through time series of different measured variables (e.g., one individual measures a temperature and the other measures a voltage). If the two individuals now use their data to reconstruct (e.g., via delay coordinates) a map, the maps they obtain may appear quite different. In the case where the resulting maps appear one dimensional, we introduce a method to test consistency with the hypothesis that they represent the same physical process. We illustrate this method using experimental data from an electric circuit.

Coherent backscattering is a multiple scattering interference effect which enhances the diffuse reflection off a disordered sample in the backward direction. Classically, the enhanced intensity is twice the average background under well chosen experimental conditions. We show how the quantum internal structure of atomic scatterers leads to a significantly smaller enhancement. Theoretical results for double scattering in the weak localization regime are presented which confirm recent experimental observations.

Surface flows are excited by steadily adding spherical glass beads to the top of a heap. To simultaneously characterize the fast single-grain dynamics and the much slower collective intermittency of the flow, we extend photon-correlation spectroscopy via fourth-order temporal correlations in the scattered light intensity. We find that microscopic grain dynamics during an avalanche are similar to those in the continuous flow just above the transition. We also find that there is a minimum jamming time, even arbitrarily close to the transition.

In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic Poincaré equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behavior of the eigenmodes and eigenspectrum in the physically relevant régime of very low viscosities which are out of reach numerically. This problem offers a canonical ill-posed Cauchy problem which has applications in other fields.

We report the first observations of superlattices in thermal convection. The superlattices are selected by a four-mode resonance mechanism that is qualitatively different from the three-mode resonance responsible for complex-ordered patterns observed previously in other nonequilibrium systems. Numerical simulations quantitatively describe both the pattern structure and the stability boundaries of superlattices observed in laboratory experiments. In the presence of the inversion symmetry, superlattices are found numerically to bifurcate supercritically directly from conduction or from a striped base state.

It is shown, for the first time, that the transmittivity of wave guides created as rectilinear defects in periodic elastic band-gap materials oscillates as a function of frequency. The results are obtained using the finite difference time domain method for elastic waves propagating in two-dimensional inhomogeneous media. The oscillations of the transmittivity are due to the richness of modes in the elastic systems and, mainly, due to the periodicity of the potential in the direction of the wave propagation. Results are presented for a periodic array of Pb and Ag cylinders inserted in an epoxy host, as well as for Hg cylinders in an Al host.

By an inversion symmetry, we show that in the Abelian sandpile model the probability distribution of dissipating waves of topplings that touch the boundary of the system shows a power-law relationship with critical exponent $5/8$ and the probability distribution of those dissipating waves that are also last in an avalanche has an exponent of 1. Our extensive numerical simulations not only support these predictions, but also show that inversion symmetry is useful for the analysis of the two-wave probability distributions.

We report the experimental dynamics of a new two-dimensional (2D) fluid phenomenon that occurs when an intense, pointlike vortex is placed within a diffuse, circular vortex. Our observations, made using strongly magnetized electron columns to model the 2D fluid, support the analysis performed by Jin and Dubin.

Starting from stationary bifurcations in Couette-Dean flow, we compute nontrivial stationary solutions in inertialess viscoelastic circular Couette flow. These solutions are strongly localized vortex pairs, exist at arbitrarily large wavelengths, and show hysteresis in the Weissenberg number, similar to experimentally observed “diwhirl” patterns. Based on the computed velocity and stress fields, we elucidate a heuristic, fully nonlinear mechanism for these flows. We propose that these localized, fully nonlinear structures comprise fundamental building blocks for complex spatiotemporal dynamics in the flow of elastic liquids.

Quantum effects in $N$-bound solitons can be drastically enhanced compared to the fundamental soliton. In particular, the spectral photon-number correlations are much stronger. The formation of spectral domains of almost perfect positive and negative correlations is predicted. Criteria that are based on the Cauchy-Schwarz inequality are used for studying nonclassical correlations. Interferences between different soliton components of the $N$-bound solution being responsible for the strong changes in the coherent amplitude may also be a mechanism for the strong correlations. The results offer novel possibilities of producing light with highly nonclassical properties.

We study the dynamics of bubbles in the one dimensional Cahn-Hilliard equation. For a gas of diluted bubbles we find ordinary differential equations describing their interaction which permits us to describe the ulterior dynamics of the system in very good agreement with numerical simulations.

Synchronization due to a weak global coupling with time delay in a semiconductor laser array is investigated both in the cw and self-pulsing regimes. A generalized form of the Kuramoto phase equations is derived and discussed analytically. The time delay is shown to induce in-phase synchronization in all dynamical regimes. Another form of synchronization is found which leads to local extinction of self-pulsing in the array.

Bicritical points at wave numbers $k_b$ larger than the critical wave numbers $k_c$ are found in parametric surface waves (Faraday waves) using both numerical simulations and nonlinear analysis. Because $k_b-k_c$ is small, it is argued that subcritical bifurcations at $k>\mathrm{}{k}_b$ can be easily observed in experiments. In the second part we present a generic argument predicting the existence of nonlinear states resembling a balloon outside the instability region. The prediction is confirmed in simulations and it is argued to apply to other systems with similar instability curves.

In a dielectric-barrier discharge between diametrically opposite sides of a narrow tube, discharge filaments stabilize at regular intervals along the tube's length. Three types of periodic patterns are observed, as is a disordered state in which filaments fire at apparently random positions and times. Time-resolved current measurements indicate that for each spatial pattern, a particular number of discharge stages occur during the voltage half-cycle. A preliminary model of the pattern-formation dynamics is described, motivating further work on time-resolved imaging and investigations of surface charge distributions.

A Comment on the Letter by Janna Levin, Phys. Rev. Lett. 84, 3515 (2000).

We consider a conformal theory of fractal growth patterns in two dimensions, including diffusion limited aggregation (DLA) as a particular case. In this theory the fractal dimension of the asymptotic cluster manifests itself as a dynamical exponent observable already at very early growth stages. Using a renormalization relation we show from early stage dynamics that the dimension $D$ of DLA can be estimated, $1.69<D<\mathrm{}1.72\mathrm{}$. We explain why traditional numerical estimates converged so slowly. We discuss similar computations for other fractal growth processes in two dimensions.

We introduce a stochastic partial differential equation capable of reproducing the main features of spatiotemporal intermittency (STI). The model also displays a noise-induced transition from STI to laminarity as the noise intensity increases. Simulations and mean-field analysis are used to characterize this transition and to give a quantitative prescription of its loci in the relevant parameter space.

We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a Hamiltonian system (a Fermi-Pasta-Ulam chain of oscillators); (ii) a general model for spatiotemporal chaos (the complex Ginzburg-Landau equation); (iii) experimental data taken from a ${\mathrm{CO}}_2$ laser with delayed feedback. In the last case, the convective Lyapunov exponent is determined directly from the experimental data.

Resonances of the time evolution (Frobenius-Perron) operator $P$ for phase space densities have recently been shown to play a key role for the interrelations of classical, semiclassical, and quantum dynamics. Efficient methods to determine resonances are thus in demand, in particular, for Hamiltonian systems displaying a mix of chaotic and regular behavior. We present a powerful method based on truncating $P$ to a finite matrix which not only allows us to identify resonances but also the associated phase space structures. It is demonstrated to work well for a prototypical dynamical system.