High order correlation tensors for the spatial derivatives of the velocity field are studied with an emphasis on angular dependencies and sensitivity of these correlations to the effect of intermittency. In particular, it is found that the sum of longitudinal and transverse correlations of the deformation rates is proportional to the intermittency deviation from the classical scale similarity of velocity field.

The Kolmogorov equation with a forcing term is compared to experimental measurements, in low temperature helium gas, in a range of microscale Reynolds numbers $R_{\lambda }$ between 120 and 1200. We show that the relation is accurately verified by the experiment (i.e., within $\pm 3\%$ relative error, over ranges of scales extending up to three decades). Two scales are extracted from the analysis, and revealed experimentally, one characterizing the external forcing and the other, varying as $R_{\lambda }^{-3\mathrm{}/5}$, defining the position of the maximum of the function ${-S}_3\left(r\right)/r$, and for which a physical interpretation is offered.

The influence of the boundary layer properties on the heat transport in turbulent thermal convection is experimentally investigated in a cell with a rough bottom plate. It is shown that the standard 2/7 exponent of the convective heat flow dependence on the Rayleigh number, usually observed in a cell with smooth boundaries, increases if the roughness has power law distributed asperity heights and the thermal boundary layer thickness is smaller than the maximum asperity size. In contrast a periodic roughness does not influence the heat transport law exponent.

A Comment on the Letter by Gregory L. Baker, James A. Blackburn, and H. J. T. Smith, Phys. Rev. Lett. 81, 554 (1998).

A Reply to the Comment by Peter Grassberger.

We report a visible laser with a subhertz linewidth for use in precision spectroscopy and as a local oscillator for an optical frequency standard. The laser derives its stability from a well-isolated, high-finesse, Fabry-Pérot cavity. For a 563 nm laser beam locked to our stable cavity, we measure a linewidth of 0.6 Hz for averaging times up to 32 s. The fractional frequency instability for the light locked to the cavity is typically $3\times {10}^{-16\mathrm{}}$ at 1 s. Both the linewidth and fractional frequency instability are approximately an order of magnitude less than previously published results for stabilized lasers.

The stationary lasing of the modes in a microdisk is formulated as a nonlinear eigenvalue problem for a nonlinear Maxwell equation. It is shown that whispering gallery modes can be obtained as stationary lasing solutions with finite pumping thresholds. Further, it is discovered that whispering gallery lasing modes can exist even though the angle of incidence to the disk boundary is smaller than the critical angle for total internal reflection.

We demonstrate a new type of basin boundary for typical chaotic dynamical systems. For the case of a two dimensional map, this boundary has the character of the graph of a function that is smooth and differentiable except on a set of fractal dimensions less than one. In spite of the basin boundary being smooth “almost everywhere,” its fractal dimension exceeds one (implying degradation of one's ability to predict the attractor an orbit approaches in the presence of small initial condition uncertainty). We call such a boundary sporadically fractal.

We use two input beams (control and probe) in the same plane of incidence to study second-harmonic generation from achiral thin films with in-plane isotropy. Appropriate linear control polarizations break the reflection symmetry of the setup and lead to different second-harmonic efficiency for left- and right-hand circular probe polarizations. Circular control polarizations are described by the spin vector, which is also in the plane of incidence and apparently does not break the symmetry. Because of spin being an axial vector, the symmetry is nevertheless broken and optical activity observed.

A reduced formulation of tangent dynamics and the Lyapunov spectrum for a Hamiltonian system using its underlying symplectic symmetry is developed. It applies to a symplectic dynamical system of any dimension and leads to differential equations dealing directly with the characteristic exponents. These equations do not contain exponentially growing quantities nor require any orthonormality maintenance, and they are capable of dealing with degeneracies in the spectrum.

A quasi-two-dimensional, lateral ac-powered gas discharge system is investigated experimentally from the point of view of pattern formation. In a certain parameter range, well localized self-organized quasiparticles in the shape of current density filaments are observed. By varying the supply voltage, such objects can be destabilized and stationary filaments with a circular symmetry undergo a transition towards breathing filaments of dumbbell shape.

We present a new scheme for quantum nondemolition measurement, where the backaction noise due to self-phase modulation in an optical fiber is canceled by passing a probe soliton through a near-resonant two-level system with negative ${\chi }^{\left(3\right)}$ nonlinearity.

Stationary velocity distribution functions are determined for a particle in a gravitational field driven by a vibrating surface in the limit of small dissipation. It is found that the form of the distribution function is sensitive to the mechanism of energy dissipation, inelastic collisions or viscous drag, and also to the form of the amplitude function of the vibrating surface. The velocity distributions obtained analytically are found to be in excellent agreement with the results of computer simulations in the limit of low dissipation.

We present and analyze experimental results on the dynamics of hydrothermal waves occurring in a laterally heated fluid layer. We argue that the large-scale modulations of the waves are governed by a one-dimensional complex Ginzburg-Landau equation (CGLE). We determine quantitatively all the coefficients of this amplitude equation using the localized amplitude holes observed in the experiment, which we show to be well described as Bekki-Nozaki hole solutions of the CGLE.

An exact solution to the problem of parametric level statistics in non-Gaussian ensembles of $N\times N$ Hermitian random matrices with either soft or strong level confinement is formulated within the framework of the orthogonal polynomial technique. Being applied to random matrices with strong level confinement, the solution obtained leads to emergence of a new connection relation that makes a link between the parametric level statistics and the scalar two-point kernel in the thermodynamic limit.

A class of simplified measures is constructed to capture the key features of generic spatiotemporally chaotic systems. A combined analytical and numerical investigation allows us to establish the scaling behavior of the fractal dimension in open systems. Our results improve a previous conjecture and, what is more important, furnish a clear framework for both numerical and analytical checks of the underlying assumptions.

A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence function up to, in principle, infinite length. As in our recent work the recurrence signal is inverted by means of a high resolution spectral analyzer (harmonic inversion) to obtain the semiclassical eigenenergies. The method is demonstrated for the hydrogen atom in a magnetic field. To our knowledge this is the first successful application of periodic orbit quantization in the deep mixed regular chaotic regime.

In partially linear systems, such as the Lorenz model, chaotic synchronization is possible in only some of the variables. We show that, for the nonsynchronizing variable, synchronization up to a scale factor is possible. We explain the mechanism for this projective form of chaotic synchronization in three-dimensional systems. Projective synchronization is illustrated for the Lorenz and disk dynamo systems. We also introduce a vector field that can be used to predict the scaling factor.

We show the generation of a strong phase-matched third harmonic in a simple parallel nematic liquid crystal cell. A single laser beam of femtosecond pulses is used to deform the internal structure of the molecular orientation distribution, and to generate the third harmonic from the twisted structure that is formed. Up to ${10}^{-5\mathrm{}}$ of the laser power was converted to the third harmonic, in a volume as small as 5 $\mu {\mathrm{m}}^3$.