In order to determine the feasibility for a new family of nonlinear four-wave-mixing methods based on resonantly enhanced nuclear polarizations, the enhancement of a singly vibrationally resonant, nondegenerate, nonparametric process is measured using an interferometric method. The measurement shows that the resonant nuclear ${\chi }^{\left(3\right)}$ polarization is much larger than the nonresonant electronic ${\chi }^{\left(3\right)}$ polarization for typical infrared transitions and new spectroscopic methods based on vibrational coherences are feasible.

We predict a new kind of ring-profile solitary wave in nonlinear optical media, with finite orbital angular momentum. During propagation these fragment into fundamental solitons. Like free Newtonian particles, these fly off tangential to the ring, vividly demonstrating conservation of orbital angular momentum in soliton motion.

We identify two-dimensional stable and unstable bright solitary waves or localized structures in a planar resonator with a quadratically nonlinear medium driven by a field at the fundamental frequency only. These waves are extremely localized while the nonlocal interaction between the fundamental and second harmonics prevents a collapse. To a certain extent they can be regarded as residuals of coexisting hexagon patterns.

We investigate the influence of a weak uniform field $\epsilon$ on chaotic maps which in the absence of the field generate subdiffusion. The field breaks the symmetry of the maps and leads to a net drift. A crossover from an anomalous type of motion, valid at short times, to a normal behavior, at long times is found for any finite field. The diffusion coefficient behaves as $D\left(\epsilon \right)\sim {\epsilon }^{\gamma }$ where $\gamma$ depends on a single parameter of the map.

An analytical model is developed for the $N$-body largest Lyapunov exponent in the dilute plasma, and it is shown that the Lyapunov exponent relates to the dielectric response function. The relation provides a bridge between microscopic mechanical and macroscopic statistical quantities and it is expected to also be applicable for a weakly nonequilibrium system. In thermal equilibrium, the model shows that the Lyapunov exponent of dilute one component plasmas is of the same order as the plasma frequency and independent of the Coulomb coupling constant. These results agree fairly well with three dimensional particle simulations.

We argue on the basis of empirical data that Kolmogorov's refined similarity hypothesis (RSH) needs to be modified for transverse velocity increments, and propose an alternative. In this new form, transverse velocity increments bear the same relation to locally averaged enstrophy (squared vorticity) as longitudinal velocity increments bear in RSH to locally averaged dissipation. We support this hypothesis by analyzing high-resolution numerical simulation data for isotropic turbulence. RSH and its proposed modification for transverse velocity increments appear to represent two independent scaling groups.

We report experimental measurements of turbulent heat transport in rotating Rayleigh-Bénard convection. The fluid was water with Prandtl number $3<\mathrm{}\sigma <7\mathrm{}$. Heat transport and local temperature measurements were made for Rayleigh numbers $2\times {10}^5<\mathrm{Ra}<5\mathrm{}\times {10}^8$ and Taylor numbers $0\le \mathrm{Ta}\le 5\times {10}^9$. For fixed convective Rossby numbers Ro between 0.1 and 1.5, the Nusselt number $N$ scaled closely as the 2/7 power of Ra but had very little variation with the Prandtl number $\sigma$ and only a moderate increase with increasing rotation rate. Substantial disagreement is found with existing scaling theories.

We have developed a sensitive resonant four-wave mixing technique based on two-photon parametric four-wave mixing with the addition of a phase matched “seeder” field. Generation of the seeder field via the same four-wave mixing process in a high pressure cell enables automatic phase matching to be achieved in a low pressure sample cell. This arrangement facilitates sensitive detection of complex molecular spectra by simply tuning the pump laser. We demonstrate the technique with the detection of nitric oxide down to concentrations more than 4 orders of magnitude below the capability of parametric four-wave mixing alone, with an estimated detection threshold of ${10}^{12}\mathrm{molecules}/{\mathrm{cm}}^3$.

The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible representation is associated with a scalar function of $R$ which may exhibit different scaling exponents. The common practice of using moments of longitudinal and transverse fluctuations mixes different scalar functions and therefore may mix different scaling exponents. It is shown explicitly how to extract pure scaling exponents for correlation functions of arbitrary orders.

By analytical mapping of the eigenvalue problem in rough billiards onto a band random matrix model, a new regime of Wigner ergodicity is found. There, the eigenstates are extended over the whole energy surface but have a strongly peaked nonergodic structure. At the same time the level spacing statistics is still given by the Wigner-Dyson distribution.

We study the level spacing statistics $P\left(s\right)$ in many-body Fermi systems and determine a critical two-body interaction strength $U_c$ at which a crossover from Poisson to Wigner-Dyson statistics takes place. Near the Fermi level, the results allow one to find a critical temperature $T_{\mathrm{ch}}$ above which quantum chaos and thermalization set in.

The spontaneous emission rate $\gamma$ of a two-level atom inside a chaotic cavity fluctuates strongly from one point to another because of fluctuations in the local density of modes. For a cavity with perfectly conducting walls and an opening containing $N$ wave channels, the distribution of $\gamma$ is given by $P\left(\gamma \right)\propto {\gamma }^{N/2-1}(\gamma +{\gamma }_0{)}^{-N-1\mathrm{}}$, where ${\gamma }_0$ is the free-space rate. For small $N$ the most probable value of $\gamma$ is much smaller than the mean value ${\gamma }_0$.

We examine particle trajectories in capillary waves formed on a water surface subject to vertical vibrations. We focus on the role of a distinct length scale present in our experiment, namely, the wavelength $\lambda$ of the surface waves. We observe non-Brownian particle trajectories with a fractal dimension $D$ different from the random walk value $D=2\mathrm{}$. A crossover is observed from one anomalous behavior at length scales below $\lambda$, to another at larger length scales. Data collapse is shown to be feasible, and scaling functions characterizing the crossover are identified. Our results are compared to those obtained from observations of drifters in the upper ocean. The distinct length scale $\lambda$ allows us to divide the particle trajectories into flights and traps. The distribution of flight times shows a power-law behavior with an exponent between 2.3 and 3.

Perturbative expansions for intermittency scaling exponents in the Kraichnan passive scalar model [Phys. Rev. Lett. 72, 1016 (1994)] are investigated. A one-dimensional compressible model is considered for this purpose. High resolution Monte Carlo simulations using an Ito approach adapted to an advecting velocity field with a very short correlation time are performed and lead to clean scaling behavior for passive scalar structure functions. Perturbative predictions for the scaling exponents around the Gaussian limit of the model are derived as in the Kraichnan model. Their comparison with the simulations indicates that the scale-invariant perturbative scheme correctly captures the inertial range intermittency corrections associated with the intense localized structures observed in the dynamics.

For Rayleigh-Bénard convection in a square cell with a fluid of Prandtl number $\sigma \approx 1$, we report experimental results on the bistability of the spatiotemporal chaotic state of spiral defect chaos (SDC) and a stationary state of ideal straight rolls (ISR). We present the first large aspect ratio experimental confirmation of the theoretical prediction of stable ISR in the parameter regime where typical initial conditions lead to SDC. As a function of the control parameter and for typical experimental initial conditions, we also find a transition in the selection between SDC and ISR which is mediated by front propagation. We characterize the transition with two measures, the spatial correlation length and the spectral pattern entropy, and find that the transition shows similarities to equilibrium phase transitions.

The ultrametric structure of the energy cascade process in a dynamical model of turbulence is studied. The tree model we use can be viewed as an approximated one-dimensional truncation of the wavelets-resolved Navier-Stokes dynamics. Varying the tree connectiveness, the appearance of a scaling transition in the two-point moments of energy dissipation is detected, in agreement with experimental turbulent data.

The effect of horizontal heat advection on the thermal instability is studied for a general class of horizontal flows comprising forced and temperature-induced flow components as well as a possible net heat transport. The instability is usually triggered by an unstable layer of height $h_u$, which is caused by the nonlinear vertical temperature profile typical for such flows. As $h_u$ decreases, the critical values of the Rayleigh and the wave number, defined with respect to this unstable layer, become independent of $h_u$. This behavior can be explained by the scaling properties of the flow in the unstable region.

A Comment on the Letter by A. V. Andreev et al., Phys. Rev. Lett. 76, 3947 (1996). The authors of the Letter offer a Reply.

A Reply to the Comment by F. Leyvraz and T. H. Seligman.

We address the problem of unsupervised classification of time series recordings. The aim is to form groups of sequences or segments of a longer sequence which show similar dynamical behavior. Several measures of similarity between two time series are considered. Groups or clusters are then formed by minimizing a suitable cost function using simulated annealing. Apart from the classification of systems, the method can be applied to the monitoring of abrupt or continuous changes in nonstationary signals. We further discuss the inclusion of supervision and propose the use of similarity measures in tests for nonlinearity based on surrogate data.