Black or reflective particles can be trapped in the dark central minimum of a doughnut laser beam produced using a high efficiency computer generated hologram. Such beams carry angular momentum due to the helical wave-front structure associated with the central phase singularity even when linearly polarized. Trapped absorptive particles spin due to absorption of this angular momentum transferred from the singularity beam. The direction of spin can be reversed by changing the sign of the singularity.

A lattice Boltzmann scheme able to model the hydrodynamics of phase separation and two-phase flow is described. Thermodynamic consistency is ensured by introducing a nonideal pressure tensor directly into the collision operator. We also show how an external chemical potential can be used to supplement standard boundary conditions in order to investigate the effect of wetting on phase separation and fluid flow in confined geometries. The approach has the additional advantage of reducing many of the unphysical discetrization problems common to previous lattice Boltzmann methods.

A theory of the novel spiral chaos state recently observed in Rayleigh-Bénard convection is proposed in terms of the importance of invasive defects, i.e., defects that through their intrinsic dynamics expand to take over the system. The motion of well developed spiral defects is dominated by wave vector frustration, rather than a rotational motion driven by a vertical vorticity field. This leads to a continuum of spiral frequencies, and a spiral may rotate in either sense depending on the wave vector of its local environment. Results of extensive numerical work on equations modeling the convection system provide confirmation of these ideas.

We introduce a method of characterizing the complexity of the minima of a given function, of $N$ variables, by means of the entropy, $S\left(N\right)$, of a measure selected as follows: One chooses an algorithm which computes the minima, and assigns to a single minimum a probability equal to the (relative) measure of its basin of attraction. The behavior of $S\left(N\right)$, for large $N$, gives a well defined entropy density $\sigma$ for the minima, with respect to the chosen minima-generating law. $\sigma$ characterizes the complexity of the minima in a rather natural way in the framework of information theory, i.e., the number of bits one uses to transmit one (typical) minimum configuration is $\simeq N\sigma /\ln 2$.

A new effect is considered in multiple scattering of light in a disordered dielectric medium exposed to an external magnetic field: a transverse diffusive current. This current is proportional to the imaginary, antisymmetric part of the dielectric function of the effective medium.

The interplay between the polarization state of light and transverse effects in lasers is analyzed through an amplitude equation description of an atomic transition between spin sublevels. Linearly polarized traveling waves are found, whose stability is restricted by a phase instability associated with the direction of polarization. The instability persists for polarization stabilized lasers. Novel states of laser light such as standing waves with a spatially periodic linear polarization or coexisting traveling waves with different wave numbers and circular polarizations are also found.

We show that the second-order nonlinear optical material in a waveguide can be used to achieve transversely pumped counterpropagating optical parametric oscillation and amplification based on our proposed novel interaction configuration. By changing the incident angle of the pump beam, one can tune the output frequency through a large range. Although the vertical and horizontal cavities are not required to establish the oscillation, they can be used to reduce the threshold pump power by several orders of magnitude. For the optimum semiconductor structure, the threshold pump power for the oscillation can be as low as $\sim$100 μW.

Circulation around closed contours (square boxes) of various sizes is computed from two-dimensional spatial velocity data, acquired by the particle image velocimetry technique in the turbulent wake behind a circular cylinder. Scaling is observed for an intermediate range of box sizes even at the low and moderate Reynolds numbers of measurement. The scaling exponents are determined at various Reynolds numbers and presented with a plausible interpretation.

Turbulent Rayleigh-Bénard convection in water has been studied using a newly developed technique of incoherent cross-correlation spectroscopy. At high Rayleigh number Ra (hard turbulence), local velocity fluctuations are isotropic, and their probability density functions in the center region have an invariant Gaussian form, with the rms velocity ${\upsilon }_0\sim {\mathrm{Ra}}^{0.44}$. At low Ra in the soft turbulence regime, the probability density functions for the vertical velocity fluctuations do not have a universal form and appear to depend on the coherence of thermal plumes emitted from the boundary layers.

A Comment on the Letter by R. Blümel, Phys. Rev. Lett. 73, 428 (1994). The authors of the Letter offer a Reply.

A Reply to the Comment by Rüdiger Schack.

An interphase boundary may be immobilized due to nonlinear diffractional interactions in a feedback optical device. This effect reminds one of the Turing mechanism, with the optical field playing the role of a diffusive inhibitor. Two examples of pattern formation are considered in detail: arrays of kinks in 1D and solitary spots in 2D. In both cases, a large number of equilibrium solutions are possible due to the oscillatory character of diffractional interaction.

The translational and rotational motion of a sphere in a bulk viscous Lennard-Jones fluid and in the vicinity of a wall is studied using molecular-dynamics simulations. The results of continuum hydrodynamics are reproduced for the motion in an unbounded fluid even for spheres comparable in size to that of the fluid molecules. Our work addresses the issue of the divergences arising from the continuum analysis when the sphere moves in a fluid in the vicinity of a solid wall.

A two-dimensional Couette cell is formed by drawing a soap film over the annular region between an inner rotating disk and a fixed circular hole. When the inner disk is concentric, a smooth laminar flow is observed for all rotation rates. However, when the inner disk is eccentric, the film thickness $H(x,y,t)$ fluctuates in space and time. Spectral analysis of $H(x,y,t)$ reveals a power-law dependence on spatial scales that is consistent with Batchelor's calculation for turbulent dispersion of a passive scalar.

A recent ansatz for dissipation terms gave anomalous inertial-range scaling exponents ( $\propto n^{1/2},n\to \infty$) for the $n$th-order structure functions of a passive scalar field advected by a random velocity field. Analysis of a series expansion for the conditional mean of a dissipation term suggests that the ansatz gives the only possible anomalous scaling. Anomaly of inertial-range scaling is supported by realizability inequalities on the dissipation field. Predictions for conditional means and structure functions are compared with simulations.

The large deformations and breakup of circular 2D liquid patches in a high Reynolds number ( $\mathrm{Re}=1000\mathrm{}$) gas flow are investigated numerically. The 2D, plane flow Navier-Stokes equations are directly solved with explicit tracking of the interface between the two phases and a new algorithm for surface tension. The numerical method is able to pursue the simulation beyond the breaking or coalescence of droplets. The simulations are able to unveil the intriguing details of the nonlinear interplay between the deforming droplets and the vortical structures in the droplet's wake.

The distributed approximating functional-path integral is formulated as an iterated sequence of $d$-dimensional integrals, where $d$ is the intrinsic number of degrees of freedom for the system under consideration. This is made practical for larger values of $d$ by evaluating these integrals using average-case complexity integration techniques, based on deterministic “low discrepancy sequences,” as opposed to products of one-dimensional quadratures or basis functions. The integration converges as $(\log P{)}^{d-1\mathrm{}}/P,$ where P is the number of sample points used, and the dimensionality of the integral does not increase with the number of time slices required.

In a microwave transmission measurement the Green function $G({r,r}^{\prime },k)$ of a stadium billiard was determined as a function of $r^{\prime }$ and $k$ for fixed $r$. From this billiard wave functions were obtained including the sign, which was not available earlier. The propagator $K({r,r}^{\prime },t)$ was obtained by Fourier transform of $G({r,r}^{\prime },k)$. It is shown that $K({r,r}^{\prime },t)$ supplies a very suggestive picture of pulse propagation including pulse reconstruction by focusing effects. This can be considered as an experimental verification of a work of Tomsovic and Heller, who found that semiclassical dynamics can account for the quantum mechanical behavior of billiards over surprisingly long times.

For a chaotic billiard, we calculate the quantum spectral functions associated with the position operator $\hat{X}$ and the momentum operator ${\hat{P}}_x$. Semiclassical analysis shows that the quantum spectral function is determined to a large extent by classical ergodic autocorrelations inherent in the Weyl part. For the first time, we calculate periodic orbit corrections to the spectral function.

We study diffractive effects in two-dimensional polygonal billiards. We derive an analytical trace formula accounting for the role of the nonclassical diffractive orbits in the quantum spectrum. As an illustration, the method is applied to a triangular billiard.