Failing to satisfy Liouville's theorem, the dynamics of granular materials is affected by the attractors in their phase spaces. Motion of inelastic hard disks in a thin pipe with energy sources at both ends of the pipe is simulated and the statistical steady state is studied. We investigate the probability distribution function of the spacing $l$ between neighboring particles, and find that the attractors can lead to a phase of the cluster of particles with structures different from that of an ideal gas.

Convection patterns in ethanol-water mixtures with negative $\psi$ are studied when the fluid is heated from above. Although the linear analysis predicts that the instability occurs at zero wave number, a large wave number pattern is observed. The onset is supercritical with a threshold that is experimentally indistinguishable from zero. The convection amplitude exhibits damped oscillations for sudden change in the forcing parameter. At the constant Rayleigh number the patterns first coarsen, then exhibit growth of narrow plumes. The instability appears to be related to salt fingering.

We have performed Rayleigh-Taylor instability and feedthrough growth experiments in a 2D cylindrically convergent geometry by imploding gelatin cylinders with high-pressure gases. Instability growth was seeded by fabricating sinusoidal undulations on the outer surfaces of the cylinders, which were then observed during implosion with high-speed framing cameras. These experiments are the first to study feedthrough perturbation growth in an incompressible, convergent geometry. We compare the results to small-amplitude perturbation analysis and to a recent radiation-drive feedthrough experiment.

A Comment on the Letter by Iwao Hosokawa, Shin-ichi Oide, and Kiyoshi Yamamoto Phys. Rev. Lett. 77, 4548 (1996).

This paper examines the consequences of the interaction between temporal period doubling and spatial pattern formation. We propose a simple discrete time, spatially continuous system, where the discrete time dynamics incorporates period doubling and the spatial operator imposes patterning at a preferred length scale. We find that this model displays a variety of bifurcations between different spatiotemporal states, and these bifurcations are generic in that they do not depend on the details of the model. The results from our simple model bear remarkable similarities with recent experiments on a vertically vibrated granular layer.

We report on selection and stabilization of transverse optical patterns in a feedback mirror experiment. Amplitude filtering in the Fourier plane is used to select otherwise unstable spatial patterns. Optical turbulence observed for nonlinearities far above the pattern formation threshold is stabilized by low-pass filtering of the optical power spectrum. Experimental observations obtained with a photorefractive nonlinearity are consistent with calculations based on a generic, cubic nonlinearity.

Acoustic wave propagation in liquid media containing many air-filled bubbles is ab initio considered. A self-consistent method is used to derive a set of coupled equations describing rigorously the multiple scattering of waves in such media. The wave transmission and backscattering are then solved exactly. The numerical results indicate localization of acoustic waves in a range of frequency.

Laser-induced fluorescence is used to image the central plane of the mix region of two immiscible liquids subject to the Rayleigh-Taylor instability at an acceleration of 70 times Earth's gravity. The size of the mixing zone grows with coefficient ${\alpha }_b\gtrsim 0.054$. Individual bubbles are clearly resolved and their structure is measured. The widths of the bubbles are narrower than recent models predict. An internal structure in the bubbles appears after the mixing zone is established. This structure suggests a cascade to small wavelengths. The cascade is required for molecular mix.

The results of the first nonequilibrium molecular dynamics simulation of transport of a gas mixture through a carbon nanopore, in the presence of an external chemical potential gradient, are reported. While the structure of the pore walls and the composition of the mixture have essentially no effect on the separation factor, the temperature of the system and the pore size strongly influence it. The results are in qualitative agreement with the new experimental data that are presented in this Letter.

The dynamic structure factor, $S(Q,E)$, of neon has been studied by inelastic x-ray scattering and by molecular dynamic simulation in the momentum transfer region $Q=1\mathrm{}–25{\mathrm{nm}}^{-1\mathrm{}}$ at $T=295\mathrm{}\mathrm{K}$ and $P=3\mathrm{}\mathrm{kbar}$. At this density, comparable to that of the liquid at ambient pressure, the shape of $S(Q,E)$ evolves from a Brillouin triplet towards a complex single line shape, which precurs the shape expected for single-particle behavior. The data, analyzed using the three mode model of the molecular hydrodynamics, show the absence of positive dispersion in the sound velocity and a minimum in the dispersion curve.

We analyze experimental data from Rayleigh-Bénard convection in a large aspect ratio cell using a new, efficient method applicable to disordered striped patterns from biological, chemical, optical, and fluid systems. We present statistics of various local pattern properties such as the local wave-vector magnitude, local pattern orientation, and defect densities. Using these statistics, we provide quantitative evidence demonstrating that the stability boundaries derived for infinite systems are applicable to local patches within disordered patterns. We also present the first experimental observation of multiple length scales within spiral defect chaos.

The transmission of microwaves through an array of 100 scatterers inserted into a waveguide is studied. The length of each scatterer could be varied individually, thus allowing the realization of arbitrary scattering arrangements. For periodic sequences with varying period length the found transmission bands reproduced the Hofstadter butterfly, originally predicted for the spectra of conduction electrons in strong magnetic fields. In the experiment it was used that the same transfer matrix formalism is applicable to both the microwave and the electronic systems.

Helium atoms ionized by intense few-cycle light pulses in the barrier suppression regime emit spatially coherent extreme ultraviolet continuum extending to photon energies greater than $E_{\mathrm{ph}}=0.5\mathrm{}\mathrm{keV}$ ( $\lambda <2.5\mathrm{}\mathrm{nm}$). The high-energy end of the continuum in the range of $E_{\mathrm{ph}}\ge 0.2\mathrm{keV}$ ( $\lambda \le 6\mathrm{nm}$) was characterized spectrally over a considerable dynamic range using energy-dispersive detection. The sub-10-fs laser pulse duration was found to be crucial for generating radiation with the highest photon energies at the low ( $<0.5\mathrm{}\mathrm{mJ}$) pump energy levels used in the experiments. The single-atom quantum theory of high-order harmonic generation combined with Maxwell's wave equation provides a satisfactory account for the experimental observations.

We investigate the interaction of mutually incoherent spatial solitons in photorefractive media with anisotropic nonlocal nonlinear response. We show that the photorefractive nonlinearity leads to an anomalous interaction between solitons. Theoretical and experimental results reveal that an incoherent soliton pair may experience both attractive and repulsive forces, depending on their mutual separation.

Multiscale correlation functions in high Reynolds number experimental turbulence and synthetic signals are investigated. Fusion rule predictions as they arise from multiplicative, almost uncorrelated, random processes for the energy cascade are tested. Leading and subleading contributions, in both the inertial and viscous ranges, are well captured by assuming a simple multiplicative random process for the energy transfer mechanisms.

We propose a novel model of two-phase flow in porous media in which both fluids act as the invaders as well as the defenders. Monte Carlo simulations show that the structure of the fluids' clusters is volatile and changes with the time $t$ and length scale. Moreover, $n_s$, the number of clusters of size $s$, and $〈s〉$, the mean cluster size, both oscillate with $t$, indicating the constant breakup and recoalescence of the clusters. New dynamical scaling laws for the cluster size distribution are also obtained.

Practical applications of chaos require the chaotic orbit to be robust, defined by the absence of periodic windows and coexisting attractors in some neighborhood of the parameter space. We show that robust chaos can occur in piecewise smooth systems and obtain the conditions of its occurrence. We illustrate this phenomenon with a practical example from electrical engineering.

Synchronization between coupled chaotic systems can be described in terms of invariant manifolds. If such manifolds possess the additional property of normal $k-\mathrm{hyperbolicity}$, it can be deduced that synchronization will persist under perturbations. This suggests a mathematical framework within which the different aspects of synchronization can be discussed and analyzed. Using these techniques, it can be shown that unidirectionally and bidirectionally coupled synchronized systems are locally equivalent.

We present a novel extension of the concept of scars for the wave functions of classically chaotic few-body systems of identical particles with rotation and permutation symmetry. Generically there exist manifolds in classical phase space which are invariant under the action of a common subgroup of these two symmetries. Such manifolds are associated with highly symmetric configurations. If sufficiently stable, the quantum motion on such manifolds displays a notable enhancement of the revival in the autocorrelation function which is not directly associated with individual periodic orbits. Rather, it indicates some degree of localization around an invariant manifold which has collective characteristics that should be experimentally observable.

Measurements of the mean-square amplitude $〈{\theta }^2〉$ of thermally induced fluctuations of a thin layer of the nematic liquid crystal I52 subjected to a voltage $V$ are reported. They yield the limit of stability $V_c$ of the spatially uniform conduction state to infinitesimal perturbations. Localized long-lived convecting structures known as worms form spontaneously from the fluctuations for $V$ well below $V_c$. This, as well as measurements of the lifetime of the conduction state for $V<\mathrm{}{V}_c$, suggests a thermally activated mechanism of worm formation.