We report the results of essentially ab initio simulations of creeping flow through large three-dimensional random fiber webs that closely resemble fibrous sheets such as paper and nonwoven fabrics. The computational scheme used in this Letter is that of the lattice-Boltzmann method and contains no free parameters concerning the properties of the porous medium or the dynamics of the flow. The computed permeability of the web is found to be in good agreement with experimental data, and confirms that permeability depends exponentially on porosity over a large range of porosity.

We investigate chaos synchronization in coupled chaotic oscillators by local feedback injections (pinnings). A novel approach to count the dimension of unstable manifold of coupled systems and to characterize the controllability condition of chaos synchronization is suggested. The relation between pinning density and the diffusive and gradient couplings is investigated in detail, and it is shown that high control efficiency can be achieved at strong gradient coupling.

We investigate the evolution of active particle ensembles in open chaotic flows. The active processes of the type $A+B\to 2B$ and $A+B\to 2C$ are considered in the limit of weak diffusion. As an illustrative advection dynamics, we choose a model of the von Kármán vortex street, and show that the backbone of the active processes is the fractal structure associated with the passive dynamics' chaotic saddle. This fractal dynamics leads to singularly enhanced concentrations, resulting in a distribution of products that differs entirely from the one in conventional active processes. This may account for the observed filamental intensification of activity in environmental flows.

Experiments of four-photon frequency conversion in a birefringent optical fiber reveal, besides the usual small-signal parametric modulational instability, a novel large-signal instability. The main observed physical signatures of this instability are the peak stimulated conversion at signal detunings outside the parametric gain bandwidth and a signal power threshold. The transition between the two instability domains is controlled by the wavelength separation between pump and probe beams.

We present analytic formulas for the nonlinear evolution of the bubble amplitude in Rayleigh-Taylor and Richtmyer-Meshkov instabilities in two and three dimensions. Direct numerical simulations of He/Xe shock tube experiments are also presented and the results are found to agree well with the analytic formulas which are based on an extension of Layzer's theory [Astrophys. J. 122, 1 (1955)].

A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending on the dimensionality $d$ of space and the degree of compressibility of the smooth advecting velocity field, the cascade of the scalar is direct or inverse. If $d>\mathrm{}4\mathrm{}$ the cascade is always direct. For a small enough degree of compressibility, the cascade is direct again. Otherwise it is inverse; i.e., very large scales are excited. The dynamical hint for the direction of the cascade is the sign of the Lyapunov exponent for particles separation. Positive Lyapunov exponents are associated to direct cascade and Gaussianity at small scales. Negative Lyapunov exponents lead to inverse cascade, Gaussianity at large scales, and strong intermittency at small scales.

A Comment on the Letter by Alexander Altland and Martin R. Zirnbauer, Phys. Rev. Lett. 77, 4536 (1996). The authors of the Letter offer a Reply.

A Reply to the Comment by Giulio Casati, F. M. Izrailev, and V. V. Sokolov.

The surface-wave scattering processes responsible, in part, for the optical glory have never been compared with theoretical predictions. Here, THz impulse ranging is used to measure the time domain impulse response of spherical targets with sufficiently high temporal resolution to permit the surface-wave contribution to the total impulse response to be isolated. The first direct experimental comparison for the surface wave with Mie theory as well as the surface-wave approximation of van de Hulst is performed. Interference of the surface waves from a dielectric sphere is shown to lead to the frequency and angular intensity dependence of the THz glory.

Measurements of the force required by a bidimensional piling to be compressed are reported. This force is shown to exhibit sudden fluctuations of large amplitude which strongly deviate from the mean value. We determine the scaling laws followed by the mean force and by the fluctuations as a function of the grain diameter, the grain mass, the aspect ratio, and the container filling. The mechanism of fluctuations is identified, and the passage to the Mohr-Coulomb plasticity behavior is recognized in the limit of very large systems.

Measurements of vorticity fluctuations are carried out in rapidly flowing turbulent soap films driven by gravity. Isotropic turbulence is generated by inserting one-dimensional grids through the film. The vorticity fluctuations are measured using two optical-fiber velocimeters capable of measuring the fluctuations of both the longitudinal and transverse components of the velocity simultaneously. Our results indicate scaling of the vorticity spectrum, yet this scaling is different from what is predicted theoretically.

Using a turbulence model, we derive two scaling regimes for rapidly rotating Rayleigh-Bénard turbulent convection. For $\mathrm{Ra}{}_{*}<\mathrm{Ra}<\mathrm{Ra}{}_{**}$, where $\mathrm{Ra}{}_{*}$ and ${\mathrm{Ra}}_{**}$ are functions of $\Omega$, the Nusselt number Nu is a function only of the scaling variable $\mathrm{Ra}/\mathrm{Ra}{}_{*}$; this corresponds to the first regime. For $\mathrm{Ra}>{\mathrm{Ra}}_{**}$, $\mathrm{Nu}$ is almost unaffected by rotation and satisfies the nonrotating scaling law $\mathrm{Nu}\sim \mathrm{Ra}{}^{\gamma }$, $\gamma \sim 1/3$. The two scaling laws are confirmed by existing data.

A new class of microscopic jet flows is here reported: for a certain range of physical parameters and geometrical configurations, a perfectly steady microscopic liquid thread can be formed by a laminar accelerating gas stream, eventually giving rise to a nearly monodisperse fine spray. Some interesting characteristics for many applications of this robust and versatile flow and related atomization technique are highlighted. Concentric multicomponent liquid threads can also be produced. A theoretical model is presented that shows agreement with experiments.

The anomalously strong scarring of the electronic wave functions of quantum wells in a tilted magnetic field is shown to be due to special properties of the classical dynamics of this system. A certain subset of periodic orbits is identified which is nearly stable over a very large interval of variation of the system parameters; hence this subset exhibits strong scarring. Semiclassical arguments shed further light on why these orbits dominate the experimentally observed tunneling spectra.

Power-law sensitivity to the initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity within the generalized statistics recently introduced by one of the authors (C.T.) and characterized by the entropic index $q$. We show that general scaling arguments imply that $1/(1-q)=1\mathrm{}/{\alpha }_{\min }-1\mathrm{}/{\alpha }_{\max }$, where ${\alpha }_{\min }$ and ${\alpha }_{\max }$ are the extremes of the multifractal singularity spectrum $f\left(\alpha \right)$ of the attractor. This relation is numerically verified in standard $D=1\mathrm{}$ dissipative maps.

Numerical simulations and laboratory experiments are conducted for thin layers of particles in a vertically oscillated container as a function of the frequency $f$, amplitude $A$, and depth $H$. The same standing wave patterns (stripes, squares, or hexagons oscillating at $f/2$ or $f/4$) and wavelengths are obtained in the simulations and experiments for a wide range of $(f,A)$ and two layer depths. Two model parameters are determined by fits at just two points $(f,A,H)$. Simulation results lead to heuristic arguments for the onset of patterns and the crossover from squares to stripes.

The correlation between contact forces and the texture of a packing of rigid particles subject to biaxial compression is analyzed by means of numerical simulations. Four different aspects are investigated: stress tensor, dissipation due to friction, angular distribution of forces, and fabric tensor characterizing the anisotropy of the texture. All of them provide evidence that the contact network can be decomposed unambiguously into two subnetworks with complementary mechanical properties.

We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite polynomial expansion. Discretizing the Boltzmann equation with a Bhatnagar-Gross-Krook collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers.

Strong modification of turbulent transport in fluid flows with chemical reactions or heterogeneous phase transitions is analyzed. It is shown that turbulent diffusion may be strongly depleted in chemically reacting flows or in flows with phase transitions. In addition, the existence of nondiffusive heat and mass fluxes of the components in the systems with chemical reactions or heterogeneous phase transitions is demonstrated. These fluxes can be interpreted as “turbulent” analogs of the known cross-effects in irreversible thermodynamics. The mechanism of turbulent cross-effects is completely different and is associated with turbulent transport in reacting flows. The analyzed effects may result in the excitation of a large-scale instability which causes formation of large-scale inhomogeneities in the spatial distributions of temperatures and number densities of admixtures.

In many nonequilibrium dynamical situations delays are crucial in inducing chaotic scenarios. In particular, a delayed feedback in an oscillator can break the regular oscillation into trains mutually uncorrelated in phase, whereby the phase jumps are localized as defects in an extended system. We show that an adaptive control procedure is effective in suppressing these defects and stabilizing the regular oscillations. The analysis of the transient times for achieving control demonstrates that stabilization is obtained within an amplitude turbulent regime, analogous to what is present in spatially distributed systems. The control technique is robust against the presence of large amounts of noise.