We report a new type of optical patterns induced by phase locking of several wave vectors with different lengths and orientations. Wave vector selection is due to the optical nonlinearity provided by a Kerr-like medium. The system displays pattern multistability. We characterize the different configurations by the distribution of wave vector families in Fourier space. Even close to threshold, the strong coupling among families yields a collective behavior without critical slowing down, at variance with the isolated behavior of each separate family.

We present a large scale numerical simulation of three-dimensional Rayleigh-Bénard convection near onset, under free-free boundary conditions for a fluid of Prandtl number $\sigma =0.5\mathrm{}$. We find that a spatiotemporally chaotic state emerges immediately above onset, which we investigate as a function of the reduced control parameter. We conclude that the transition from conduction to spatiotemporal chaos is second order and of “mean field” character. We also present a simple theory for the time-averaged convective current. Finally, we show that the time-averaged structure factor satisfies a scaling behavior with respect to the correlation length near onset.

A Comment on the Letter by Miroslaw Latka and Bruce J. West, Phys. Rev. Lett. 75, 4202 (1995). The authors of the Letter offer a Reply.

A Comment on the Letter by Miroslaw Latka and Bruce J. West. Phys. Rev. Lett. 75, 4202 (1995). The authors of the Letter offer a Reply.

A Reply to the Comment by M. G. Raizen, Bala Sundaram, and Qian Niu. Also S. Meneghini, et al.

We propose a test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via statistical parameters. The approach provides detailed information about episodes with similar dynamics during the measurement period. This allows for a detailed analysis of physically relevant changes in the dynamics.

In this Letter, we report a theoretical and experimental study of the direction of optical energy flow in homogeneous media subject to a transverse magnetic field. For transparent media we verify experimentally for the first time the existence of magnetic deflection of circularly polarized light. In absorbing media the calculated directions of the Poynting vector and of a wave packet do not coincide. Experimentally we demonstrate that the Poynting vector result is not correct.

We investigate experimentally the optical tunneling times associated with frustrated total internal reflection of a light beam. Using as physical clocks the lateral shifts and angular deviations suffered by the transmitted and reflected beams, we measure both components of a complex tunneling time: the phase time and a semiclassical time. The phase time is shown to imply superluminal velocities and to depend strongly on boundary conditions not linked to the tunneling process. By contrast, the semiclassical time yields subluminal velocities and is related solely to tunneling.

We report the first experimental observation of the evolution of an arbitrarily shaped input optical pulse train to the analytic, shape-preserving, Jacobi elliptic pulse-train solutions to the Maxwell-Bloch equations including relaxation.

We derive an exact equation which is nonlocal in time for the linear evolution of the surface of a viscous fluid, and show that this equation becomes local and of second order in an interesting limit. We use our local equation to study Faraday's instability in a strongly dissipative regime and find a new scenario which is the analog of the Rayleigh-Taylor instability. Analytic and numerical calculations are presented for the threshold of the forcing and for the most unstable mode with impressive agreement with experiments and numerical work on the exact Navier-Stokes equations.

From experimental data of a turbulent free jet we calculate the joint probability distribution $p\left(v_1{,L}_1{;v}_2{,L}_2\right)$ for two velocity increments $v_1{,v}_2$ of different length scales $L_1{,L}_2$. We present experimental evidence that the conditional probability distribution $p\left(v_2{,L}_2|v_1{,L}_1\right)$ obeys a Fokker-Planck equation. We calculate the corresponding drift and diffusion coefficients and discuss their relationship to universal behavior in the scaling region and to intermittency of the turbulent cascade. We explicitly present a stochastic process for the log-normal model of Kolmogorov and Oboukhov [A. M. Oboukhov, J. Fluid Mech. 13, 77 (1962); A. N. Kolmogorov, J. Fluid Mech. 13, 82 (1962)].

Spatially coarse-grained (or effective) versions of nonlinear partial differential equations must be closed with a model for the unresolved small scales. For systems that are known to display fractal scaling, we propose a model based on synthetically generating a scale-invariant field at small scales using fractal interpolation, and then analytically evaluating its effects on the large, resolved scales. The procedure is illustrated for the forced Burgers equation, solved numerically on a coarse grid. Detailed comparisons with direct simulation of the full Burgers equation and with an effective viscosity model are presented.

The dynamical evolution of an ultrashort pulse, whose initial temporal envelope is infinitely smooth with compact support, is considered as it propagates through a temporally dispersive, attenuative medium characterized by two resonance lines. As the propagation distance increases, the accuracy of the popular group velocity description decreases monotonically, whereas the accuracy of the mathematically well-defined asymptotic description and its derivative energy velocity description increase.

A theory describing propagation and self-focusing of partially spatially incoherent light beams in nonlinear media is developed. It is shown that this process is effectively governed by an infinite set of coupled nonlinear Schrödinger-like equations, provided they are initially appropriately weighted with respect to the incoherent angular power spectrum of the source. The particular case of spatially incoherent beam propagation in biased photorefractive media is considered in detail. Numerical simulations indicate that spatial compression as well as self-trapped states are possible under appropriate conditions. Our results are in good agreement with recent experimental observations.

We derive local conservation laws for layer-mean quantities in two general settings. When applied to Euler flows, the first of these settings yields well-known local conservation laws for quantities averaged between material surfaces. The second, however, leads to new local conservation laws for quantities involving the vorticity that are averaged between arbitrary surfaces. These produce the crucial vorticity conservation laws in shallow water models that admit nonhydrostatic and noncolumnar motion. Moreover, they seem to lie outside the Hamiltonian paradigm of fluid dynamics. The formalism generalizes to skew-symmetric matrix fields; applications to electromagnetism are suggested.

We experimentally study plane viscous gravity flows starting from triangular prism-shaped configurations with large angles $\alpha$ between the free surface and the substrate ( $15°\le \alpha \le 70°$). We measure the time $t_w$ (waiting time) that the contact line (front) waits before moving and determine the evolution of both the thickness and slope distributions near the front for $t\le t_w$. The waiting time is approximated by the evolution time of the global flow throughout the angular range. An unexpected finite value of $t_w$ for $\alpha >45\mathrm{}°$ is probably due to a surface tension effect.

The generic problem of the spatiotemporal instability of a periodic basic flow (Stuart vortices) is considered in order to interpret the sequence of bifurcations observed in open shear flows. Using a novel numerical technique, we show that the more concentrated the vortices, the smaller the backflow needed to trigger absolute instability. These results allow us to propose an alternative interpretation for the subharmonic resonance observed in forced shear flows, which is classically attributed to an acoustic feedback.

New laboratory and numerical simulation data on turbulent convection have become available. We generalize a recent spectral model of turbulence, which was previously tested on a variety of homogeneous flows, to treat inhomogeneous flows so as to study thermal convection. The model has no adjustable constants. We recover the available data (for large aspect ratios). We further derive an analytic expression for the Nusselt number versus Rayleigh and Prandtl numbers (in the limit of negligible diffusion).

Numerical simulations of rotating turbulence have given rise to “unexpected results”: An increasing $\Omega$ did not lead to the “expected” route to a 2D state. A recent model of turbulence leads to a new number $N=K(\nu \Omega {)}^{-1\mathrm{}}$ (K and ν are turbulent kinetic energy and viscosity) so that DNS (direct numerical simulation) and LES (large eddy simulation) correspond to $N<\mathrm{}1\mathrm{}$ and $N>\mathrm{}1\mathrm{}$. In the first case, the energy cascade is suppressed, while in the second case there exists an inertial spectrum which is an equilibrium of quasi–2D-3D modes. With these ingredients, we reproduce DNS and LES data.

The complexity exhibited by cellular automata is studied using both topological (graph-theoretical) and metric (thermodynamic) techniques. A novel topological classification, based on a hierarchy of languages, is introduced. In particular, it is shown that the elementary rule 22 is able to produce, upon iteration, a deep nesting of grammatical rules and that this asymptotically yields a phase transition when the thermodynamic formalism is applied to the limit spatial configuration.