In this Letter, we present a theoretical analysis of the acoustic transmission through two-dimensional arrays of straight rigid cylinders placed parallel in the air. Both periodic and completely random arrangements of the cylinders are considered. The results for the sound attenuation through the periodic arrays are shown to be in remarkable agreement with the reported experimental data. As the arrangement of the cylinders is randomized, the transmission is significantly reduced for a wider range of frequencies. For the periodic arrays, the acoustic band structures are computed by the plane-wave expansion method and are also shown to agree with previous results.

We demonstrate alignment control in high density vapors of $\mathrm{CS}{}_2$, hexane, and $\mathrm{N}{}_2$ $(\sim {10}^{17}$ molecules $\mathrm{cm}{}^{-3\mathrm{}})$ using the electric field of a 300 ps duration laser pulse. This was sufficient to study for the first time the molecular orientation dependence of high-order harmonic generation using a second, 70 fs duration laser pulse of intensity $\sim 5\times {10}^{14}\mathrm{W}\mathrm{cm}{}^{-2\mathrm{}}$. We were able to modulate and significantly enhance the harmonic intensity in aligned molecules compared to the randomly oriented case. Our results are consistent with the existence of an anisotropic dipole phase.

Temperature and vertical velocity fluctuations are measured in turbulent Rayleigh-Bénard convection for Rayleigh numbers $2\times {10}^8<R<\mathrm{}4\mathrm{}\times {10}^9$ in cells with cylindrical and square geometries with approximately unit-aspect ratios. The geometries are constructed such that they have the same height and cross sectional area. We find, very unexpectedly, that both the magnitudes and scalings of fluctuations as a function of $R$ depend strongly on the geometry. This latter result implies a possible nonuniversality in internal fluctuations and poses significant difficulties for existing model descriptions of turbulent convection.

We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Péclet numbers, in contrast to finite mean-field predictions. We develop a new master equation description of the fluid mechanics that incorporates the physically relevant fluctuations, and we treat those fluctuations by a renormalization group procedure. We find a finite dispersion coefficient at low volume fraction of disorder and high Péclet numbers.

We model friction acting on the tip of an atomic force microscope as it is dragged across a surface at nonzero temperatures. We find that stick-slip motion occurs and that the average frictional force follows $|\ln v{|}^{2/3}$, where $v$ is the tip velocity. This compares well to recent experimental work, permitting the quantitative extraction of all microscopic parameters. We calculate the scaled form of the average frictional force’s dependence on both temperature and tip speed as well as the form of the friction-force distribution function.

In a Ginzburg-Landau model for parametrically driven waves, a transition between a state of ordered and one of disordered spatiotemporal defect chaos is found. To get insight into the breakdown of the order, the defect trajectories are tracked in detail. Since the defects are created and annihilated in pairs, the trajectories form loops in space-time. The probability distribution functions for the size of the loops and the number of defects involved in them undergo a transition from exponential decay in the ordered regime to a power-law decay in the disordered regime. These power laws are also found in a simple lattice model of randomly created defect pairs that diffuse and annihilate upon collision.

Motivated by turbulent drag reduction by minute concentrations of polymers we study the effects of minor viscosity contrasts on the stability of hydrodynamic flows. The key player is a localized region where fluctuations are produced by interactions with the mean flow (the “critical layer”). We show that a layer of weakly space-dependent viscosity placed near the critical layer has a very large stabilizing effect on hydrodynamic fluctuations, retarding significantly the onset of turbulence. The effect is not due to a modified dissipation (as is assumed in theories of drag reduction) but is due to reduced energy intake from the mean flow to the fluctuations. Similar physics may act in turbulent drag reduction.

We study the nature of the phase transition in the multifractal formalism of the harmonic measure of diffusion limited aggregates. Contrary to previous work that relied on random walk simulations or ad hoc models to estimate the low probability events of deep fjord penetration, we employ the method of iterated conformal maps to obtain an accurate computation of the probability of the rarest events. We resolve probabilities as small as ${10}^{-35\mathrm{}}$. We show that the generalized dimensions $D_q$ are infinite for $q<\mathrm{}{q}^{*}$, where $q^{*}=-0.18\mathrm{}\pm 0.04$. In the language of $f\left(\alpha \right)$ this means that ${\alpha }_{\max }$ is finite. We present a converged $f\left(\alpha \right)$ curve.

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. With very few provisos on the transporting velocity field, correlation functions of the transported field in the forced case are dominated by statistically preserved structures. In decaying experiments we identify infinitely many statistical constants of the motion, which are obtained by projecting the decaying correlation functions on the statistically preserved functions. We exemplify these ideas and provide numerical evidence using a simple model of turbulent transport. This example is chosen for its lack of Lagrangian structure, to stress the generality of the ideas.

The method for extracting symbolic cycles from the fluctuation data is presented. For the example of the Lorenz model we demonstrate that approximately the same complex structure of cycles can be computed using time records of different variables. Our method has been applied to the analysis of turbulent fluctuations measured in water flow in a pipe. Even though the fluctuations in the bulk of the water and near the wall of the pipe appear to be very different, the majority of the most stable cycles extracted from the data are identical.

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Bénard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power law is found to arise from quasidiscontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.

We report the experimental observation of revival structures in the alignment of a ground-state rotational wave packet following nonresonant excitation of $I_2$ molecules by an intense picosecond laser pulse. The revivals appear at characteristic time delays following the excitation by the pump laser pulse, and show a significant narrowing of the angular distribution during a few picoseconds. The interaction with the pump laser also leads to a steady-state alignment of the molecule, due to rotational pumping.

We report the first experimental observation of anticipating chaotic synchronization in an optical system using two diode lasers as transmitter and receiver. The transmitter laser is rendered chaotic by application of an optical feedback in an external-cavity configuration. It is found that the anticipation time does not depend on the external-cavity round trip time of the transmitter.

We report measurements of microwave transmission over the first five Mie resonances of alumina spheres randomly positioned in a waveguide. Though precipitous drops in transmission and sharp peaks in the photon transit time are found near all resonances, measurements of transmission fluctuations show that localization occurs only in a narrow frequency window above the first resonance. There the drop in the photon density of states is found to be more pronounced than the fall in the photon transit time above the resonance, leading to a minimum in the Thouless number.

We demonstrate experimentally and theoretically (both analytically and numerically) a new type of spatial soliton: a rotating “propeller” soliton. This is a composite soliton made of a rotating dipole component jointly trapped with a bell-shaped component. We observe as much as 239° of rotation over 13 mm of propagation (6.5 diffraction lengths).

The falling water drop is a simple model for studying phenomena related to chemical extraction, where two immiscible phases are dynamically blended to promote the transport of solute molecules from one phase to the other. Convective motion inside the drop significantly influences the extraction efficiency. Whereas optical and tracer methods are model bound or invasive, NMR imaging is noninvasive, direct, and applicable to nontransparent media. The first NMR measurements of a water drop falling through air are reported. It is shown that, in drops from pure water, large-scale convection rolls are observed in contrast to drops with the surface tension lowered by surfactants.

We present simple hydrodynamic equations of supercritical fluids close to the gas-liquid critical point. We numerically solve them to examine plume generation and convection under gravity. These results are in good agreement with the experiment [A. B. Kogan and H. Meyer, Phys. Rev. E 63, 056310 (2001)]. This Letter is a first study of transient behavior of convection, which is unique in compressible fluids due to the piston effect.

Relatively weak counterpropagating light is shown to disrupt the emission of laser high-harmonic generation. Harmonic orders ranging from the teens to the low thirties produced by a 30-femtosecond pulse in a narrow argon jet are “shut down” with a contrast as high as 2 orders of magnitude by a chirped 1-picosecond counterpropagating laser pulse (60 times less intense). Alternatively, under poor phase-matching conditions, the counterpropagating light boosts harmonic production by similar contrast through quasiphase matching where out-of-phase emission is suppressed.

A new instability in the combined flow of fine grains and gas is investigated by means of experiments, simulations, and analytic techniques. When a bubble of air rises through a granular packing in a tube, a sequence of smaller bubbles spontaneously forms in front of it. The existence of this instability is shown from the experiments, simulations, and theoretical considerations. Moreover, the simulations and experiments agree on the quantitative level. In particular, when the tube is tilted away from the vertical the experiments and the simulations show the same increase in the speed of the rising bubble.

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.