We observe that high-stretch tails of finite-time Lyapunov exponent distributions associated with interfaces evolving under a class of nonturbulent chaotic flows can range from essentially Gaussian tails to nearly exponential tails, and show that the non-Gaussian deviations can have a significant effect on interfacial evolution. This observation motivates new insight into stretch processes under chaotic flows.

On-off intermittency is an aperiodic switching between static, or laminar, behavior and chaotic bursts of oscillation. It can be generated by systems having an unstable invariant (or quasi-invariant) manifold, within which is found a suitable attractor. We clarify the roles of such attractors in producing intermittency, provide examples, and relate them to previous work.

Starting from an assumption of universality in turbulence and building upon the work in Y. G. Sinai and V. Yakhot, Phys. Rev. Lett. 63, 1962 (1989), we construct a closed-form expression for the probability density function of temperature fluctuations. This result is found to be in good correspondence to experimental data obtained at Chicago and Yale. By extending this method, we obtain a similar expression for the probability density function of temperature differences between two times. Again the result is checked to hold very well, except for very short time separations.

We present the first direct measurements of the local velocity of a sheared polymer melt within the first 100 nm from the solid-liquid interface. For high enough shear rates we observe a sharp transition between weak and strong slip (i.e., a nonzero boundary fluid velocity) in the case of weak polymer-surface interactions [polydimethylsiloxane (PDMS) on silanated silica surfaces]. For strong polymer surface interactions the slip is strongly reduced. These results are compared to a theoretical model recently proposed by Brochard and de Gennes.

We consider the full set of equations ruling the interaction of an electromagnetic field with matter in a laser, without assuming that the direction of the transverse electric field is fixed. Near the lasing threshold, we reduce the dynamics to its normal form equation, and show that the electromagnetic field can be described by a Ginzburg-Landau equation in a vector form. Then by using topological arguments we show the possibility of vectorial topological defects which are not predictable by the scalar theory.

We discuss the relation between predictability and the sensitive dependence on initial conditions in turblent flows. We find that the maxium Lyapunov exponent λ and the variance of the effective Lyapunov exponent diverge as a power of the Reynolds number with scaling exponents which can be calculated from the eddy turnover time at the Kolmogorov length using the multifractal approach. The intermittency leads to long tails in the distribution of the predictability time. The typical predictability time T is related to the value of ${\lambda }^{\mathrm{-}1}$. We provide numerical evidence of this picture within the framework of a cascade model for three-dimensional fully developed turbulence.

The ionization of hydrogen atoms by a microwave field is numerically studied, for the first time in a realistic picture, using a fully three-dimensional quantum approach with complete inclusion of the continuum. This provides first evidence for the persistence of dynamical localization in higher-dimensional systems. Comparison to the one-dimensional dynamics as well as to experimental results is given.

We study discrete parallel dynamics of a fully connected network of nonlinear elements interacting via long-range random asymmetric couplings under the influence of external noise. Using dynamical mean-field equations, which become exact in the thermodynamical limit, we calculate the activity and the maximal Lyapunov exponent of the network in dependence of a nonlinearity (gain) parameter and the noise intensity.

We describe a new version of the well-known gedanken experiments to determine which of the two paths a particle took in a two-beam interference experiment. In this version the presence of a geometric phase can be deduced from the requirement that the interference pattern must disappear as a result of the welcher-weg (which path) information.

Recent experiments on an optical oscillator with photorefractive gain have shown that the output field undergoes periodic or chaotic alternations among a small number of patterns. The above features are explained by a dynamical model, based only on symmetry arguments, and hence applicable to a variety of physical situations.

We report the first observation of sideband mode competition in a gyrotron with an overmoded open waveguide resonator. Experiments were conducted in a gyrotron operating in the ${\mathrm{TE}}_{16,2}$ mode at 146 GHz. Up to 600 kW of power was generated in 3-μs pulses at 80 kV beam voltage and up to 40 A beam current. A pair of sidebands was excited corresponding to the ${\mathrm{TE}}_{15,2}$ and ${\mathrm{TE}}_{17,2}$ modes offset by ±5 GHz. A multimode, multifrequency, self-consistent time-dependent code predicts the excitation of the sidebands with good accuracy.

We report an imbibition experiment that involves water displacing air in a Hele-Shaw cell filled with glass beads. We varied the flow rate such that the capillary number (${\mathit{C}}_{\mathit{a}}$) spans the range ${10}^{\mathrm{-}5}$<${\mathit{C}}_{\mathit{a}}$<${10}^{\mathrm{-}2}$. The invasion front exhibits self-affine roughness and the total width ${\mathit{W}}_{\mathrm{tot}}$ increases with decreasing ${\mathit{C}}_{\mathit{a}}$. A heuristic argument suggests that ${\mathit{W}}_{\mathrm{tot}}$∝${\mathit{C}}_{\mathit{a}}^{\mathrm{-}2\mathrm{\alpha }/(2\mathrm{}\mathrm{\alpha }+1)}$, where α is the roughness scaling exponent. We also find that ${\mathit{W}}_{\mathrm{tot}}$ exhibits large fluctuations with time and the effective value of α varies over a wide range (0.65–0.91). These results suggests that the behavior of interfaces in random media is dominated by the existence of many metastable states in much the same way as the domain walls in the random-field Ising model.

Millimeter-wave phase conjugation was realized under resonantly enhanced degenerate four-wave mixing in gaseous carbonyl sulfide. The nonlinear wave interaction was caused by saturation of a transition between rotational levels. For radiation with λ=1.64 mm, phase-conjugate reflectivity of about 0.4% has been observed at a gas temperature of 200 K, and under optimal pressure.

Recently formulated techniques for controlling chaotic dynamics face a fundamental problem when the system is high dimensional, and this problem is present even when the chaotic attractor is low dimensional. Here we introduce a procedure for controlling a chaotic time signal of an arbitrarily high dimensional system, without assuming any knowledge of the underlying dynamical equations. Specifically, we formulate a feedback control that requires modeling the local dynamics of only a single or a few of the possibly infinite number of phase-space variables.

It is argued that for d>1, chaotic systems with a conserved quantity can exhibit generic scale invariance—algebraic decay of spatial correlations without the tuning of external parameters—with exponents analytically calculable from noisy nonchaotic models. Numerical confirmation of these predictions for a specific coupled map system is presented.

We show that the time-independent disordered solid-melt patterns induced on silicon thin films by a continuous laser beam possess a characteristic length scale Λ which varies with irradiance ${\mathit{I}}_0$ as ${\mathit{I}}_0^{\mathrm{-}1/3}$ in agreement with a model based on heat flow, interfacial surface tension, and the reflectivity difference of the solid and melt. When ${\mathit{I}}_0$ is varied so that Λ decreases to a value comparable to λ, optical interference effects enhance (reduce) power deposition in molten (solid) regions, forcing a transition to a grating structure with orientation parallel to the polarization of the light beam and locking the length scale to Λ=λ.

A novel wall model, including inelastic fluid-wall collisions, molecular structure of the wall, and a long-ranged fluid-wall interaction, is used in molecular dynamics simulations of flow in two dimensions. For strong fluid-wall attraction the fluid velocity goes smoothly to zero at the wall; there is no velocity slip. In less dense fluids the velocity drops to zero in an ever-narrower region. Our results differ from standard kinetic theory but agree with Eu’s theory [Phys. Rev. A 36, 400 (1987)]. The nature of the fluid-wall interaction is important; repulsive walls give velocity slip.

The kicked Harper model is numerically investigated. The long-time nature of the wave function dynamics and a multifractal analysis of the spectrum provide evidence for the existence of different regimes marked by different spectral types and diffusion exponents, with a phase diagram substantially different from that of the standard Harper model.

An ensemble of uncoupled chaotic maps with spatially synchronized parametric fluctuations violates the law of large numbers. This is clearly evident in the nonstatistical features of the mean field, whose mean-square deviation (MSD) does not fall as 1/N with increasing N, where N is the number of elements in the system. In fact the MSD saturates after a critical value of N=${\mathit{N}}_{\mathit{c}}$. This amazing phenomenon is reminiscent of the nonstatistical behavior in globally coupled chaos. Interestingly though, there is no coupling in this system, and so the emergence of a subtle coherence in the global dynamics, as suggested by the existence of size-independent fluctuations, is very intriguing.

We use numerical methods to investigate stochastic and coherence properties of the fields transverse profiles in stimulated Raman scattering. In the linear regime with diffractive coupling, the amplified signal is characterized by fluctuations that are macroscopic. We find an interesting dependence of the beam-pointing fluctuations on photon conversion efficiency. Our results for the linear regime compare well with recent experiments, and we report an increase in beam-pointing fluctuations in the nonlinear regime. We discuss the results of modeling with one and two transverse dimensions.