We study the dynamics of localized perturbations in plane Couette flow with periodic lateral boundary conditions. For small Reynolds numbers and small amplitude of the initial state the perturbation decays on a viscous time scale $t\propto \mathrm{Re}$. For Reynolds number larger than about 200, chaotic transients appear with lifetimes longer than the viscous one. Depending on the type of the perturbation, isolated initial conditions with infinite lifetime appear for Reynolds numbers larger than about 270–305. In this third regime, the lifetime as a function of Reynolds number and amplitude is fractal. These results suggest that in the transition region the turbulent dynamics is characterized by a chaotic repeller rather than an attractor.

We study the downward miscible displacement of a fluid by a lighter and less viscous one in the gap of a Hele-Shaw cell. For sufficiently large velocities, a well-defined interface separates the two fluids. As long as the velocity or the viscosity ratio are below a critical value, the interface has the shape of a tongue symmetric across the gap. For viscosity ratios larger than a critical value, estimated at 1.5, there exists a critical velocity, above which the interface becomes unstable, leading to a new 3D pattern involving regularly spaced fingers of wavelength about 5 times the cell thickness. We delineate the stability diagram.

We present a modal theory of self-trapping spatially incoherent light beams in any general nonlinear media. We find that a self-trapped incoherent beam induces a multimode waveguide which guides the beam itself by multiply populating the guided modes. The self-trapping process alters the statistics of the incoherent beam, rendering it localized. We find the conditions for self-trapping (“existence region” in parameter space) and the correlation function of the incoherent self-trapped beam.

The segregation phenomena of a mixture of two types of particles with different frictional properties in a rotating drum are studied by simulations which mimic the granular flow by a surface flow and a bulk solid rotation. The surface flow is modeled by rules similar to sandpile models. Radial segregation is clearly observed but will occur only if the rotational transport rate is less than some critical value. Furthermore, linear growth in segregation is also observed in the early stage of demixing, similar to observations of real experiments.

The multiple-precision time series solution of the incompressible inviscid flow equations with the initial velocity field $u(x,y,z)=v(y,z,x)=w(z,x,y)=\sin x(\cos 3y\cos z-\cos y\cos 3z)$, has been computed to 32 terms and maximum wave number 99. Ratio test and Padé analyses indicate a real-time singularity in enstrophy $\Omega \left(t\right)$ with the form $(t_{\mathrm{crit}}^2{-t}^2{)}^{-1\mathrm{}}$ where $t_{\mathrm{crit}}\sqrt{\Omega \left(0\right)}\cong 4$.

Intermittency in the Gledzer-Okhitani-Yamada model of turbulence is explained in terms of collisions of coherent solitonlike structures with a random background issuing from the disintegration of their predecessors. This two-fluid picture is substantiated by the elucidation of local dynamical mechanisms leading to anomalous growth of coherent structures, their detection in true signals involving forcing and dissipation, and an investigation of their statistics.

We present an experimental study of turbulent convection in a cell with staggered fingers on its sidewall using water as the convecting fluid. Our measurements reveal that $\mathrm{Nu}\sim {\mathrm{Ra}}^{-0.27\mathrm{}}$, and that the temperature probability density function (PDF) at the cell center is a double-peaked function which can be fitted by the superposition of two Gaussians. Moreover, it is found that the size of the local temperature fluctuations scales with Ra and that the scaled PDFs for different Ra have an invariant form. Visualization studies show that the mean flow pattern in the cell is a twisted asymmetric four-roll circulation, which helped to explain the observed PDF.

The symmetry of standing wave patterns on the surface of a vertically oscillated fluid layer depends on the depth of the layer. In a large experiment we trace out the stability diagram. The dependency can be understood on the basis of the oscillatory character of the waves and the dispersion relation. A simple amplitude equation can be constructed with the variation with depth of the dispersion relation and a general quadratic nonlinearity as its only ingredients. The predictions of this model agree well with the experiment.

We show that the viscosity of a dilute emulsion exhibits oscillations and hysteresis as a function of the shear rate. This results from breaking up of droplets in response to the shear flow. The new phenomena we describe are generic and do not depend on a specific choice of model. The interesting dependence of the basic properties of a dilute emulsion on the shear rate results from the fact that the immersed droplets must break when the shear rate applied to the system is large enough.

We propose an experimental configuration, within an ion trap, by which a quantum mechanical delta-kicked harmonic oscillator could be realized, and investigated. We show how to directly measure the sensitivity of the ion motion to small variations in the external parameters.

We quantize graphs (networks) which consist of a finite number of bonds and nodes. We show that their spectral statistics is well reproduced by random matrix theory. We also define a classical phase space for the graph, where the dynamics is mixing and the periodic orbits (loops on the graph) proliferate exponentially. An exact trace formula for the quantum spectrum is developed and used to investigate the origin of the connection between random matrix theory and the underlying chaotic classical dynamics. Being an exact theory, and due to its relative simplicity, it offers new insights into this problem which is at the forefront of the research in quantum chaos and related fields.

Molecular dynamic simulations for a Xe film sliding on an Ag(111) substrate are performed from the submonolayer through the bilayer regime, which, when compared to both friction and surface resistivity measurements, demonstrate that the friction in this system is dominated by phonon excitations. Slip times are found both by direct calculation of the decay of the center-of-mass velocity, as well as from the decay of the velocity correlation function. Agreement of the slip times from the two methods supports the occurrence of a friction force linear in velocity over a wide velocity range.

We study interfacial instabilities between two spatially periodically sheared ideal fluids. Bloch wave function decompositions of the surface deformation and fluid velocities result in a non-Hermitian secular matrix with an associated band structure that yields both linear oscillating and nonoscillating instabilities, enhanced near Bragg planes corresponding to the periodicity determined by converging or diverging surface flows. The instabilities persist even when the dynamical effects of the upper fluid are neglected, in contrast to the uniform shear Kelvin-Helmholtz (KH) instability. Periodic flows can also couple with uniform shear and suppress standard KH instabilities.

Coherent resonant tunneling peaks are observed in the conductance of a quantum point contact coupled to an open resonator in a two-dimensional electron gas as we tune the resonator's dimensions. A wavelet based boundary wall method is used to compute both the electronic wave function and probability current in and around the resonator. We find excellent agreement between the calculated and measured conductance resonances, and identify fine structure associated with the lemon billiard cavity modes.

Spatial-correlation properties of the wave functions (eigenvectors) of a spin-one eigenproblem for dipole interaction is studied for random geometries of the underlying system. This problem describes, in particular, polar excitations (“plasmons”) of large clusters. In contrast to Berry's conjecture of quantum chaos for massive particles, we have found long-range spatial correlations for wave functions (eigenvectors). For fractal systems, not only individual eigenvectors are chaotic, but also the amplitude-correlation function exhibits an unusual chaotic, “turbulent” behavior that is preserved by ensemble averaging. For disordered nonfractal systems, the eigenvectors show a mesoscopic delocalization transition different from the Anderson transition.

We report the first experimental demonstration of the optical pushbroom—a novel type of all-optical pulse compression. In the optical pushbroom high intensity pump pulses, tuned well away from the resonance of a Bragg grating, modify the transmission of a weak probe tuned near to the grating's photonic band gap. The clarity of the experimental results and their close agreement with numerical simulations highlight the tremendous potential of the fiber environment for the detailed study and practical application of nonlinear Bragg grating effects.

Parametric waves arise spontaneously when a thin layer of granular material is oscillated vertically. A dynamical model of these waves accounting for the observed instability threshold and appearance of square patterns is presented. The proposed instability mechanism is due to two competing processes: a focusing effect that concentrates particles in space, and a diffusion effect that relaxes large thickness gradients in the layer. When the layer is in a liquid-type state, close to a solid-liquid transition, the model correctly predicts the presence of oscillons recently reported by P. Umbanhowar et al. [Nature (London) 382, 793 (1996)].

Vibrated horizontally, granular material has different convection patterns from those observed for the equivalent vertical vibration. Among the patterns that develop, above the onset of bulk motion, is a four roll convection pattern. Surface sloshing produces two smaller convective rolls above two lower interior rolls. Horizontal vibration creates intermittent gaps between the sidewalls and the heap of material. Avalanches of material into these gaps drives the lower convection rolls. This is a different physical mechanism from that observed in convection driven by vertical vibration. As is well known, convection patterns can drive size segregation, and we illustrate some of these effects.

This Letter presents some quantitative predictions for the small-scale statistics for a passive scalar mixed in a fully turbulent flow. Our method uses an equation [S. Vaienti et al. Physica (Amsterdam) 73D, 99 (1994)] which controls the evolution through the scales of the probability density function of temperature increments. This equation, which needs some closure as well as initial data, uses results from direct numerical simulations or from experiments. For the dissipative and small inertial range scales, our predictions are in excellent agreement with the measured or numerically calculated probability density functions. The associated Yaglom equation is also well verified for the same range of scales.

Using concepts of invasion percolation in a gradient, we develop a phase diagram of fully developed drainage in porous media. The transition between stabilized displacement (where the conventional continuum applies) and fingering is controlled by the change of the sign of the gradient of the percolation probability (from stabilizing to destabilizing). The transition boundary is described by scaling laws.