We study the collision of two orthogonally polarized and equal-amplitude vector solitons in the nonintegrable coupled nonlinear Schrödinger equations. We show that the separation velocity versus collision velocity graph has a fractal structure. When we zoom into this graph, we get a structure qualitatively identical to the original one. In addition, collision dynamics in the zoomed-in windows is intimately related to that in the original graph. We explain this fractal dependence of the collision by a resonance mechanism between the translational motion of vector solitons and internal oscillations inside a vector soliton.

The series of equilibrium states reached by disordered packings of rigid, frictionless disks in two dimensions, under gradually varying stress, are studied by numerical simulations. Statistical properties of trajectories in configuration space are found to be independent of specific assumptions ruling granular dynamics, and determined by geometry only. A monotonic increase in some macroscopic loading parameter causes a discrete sequence of rearrangements. For a biaxial compression, we show that, due to the statistical importance of such events of large magnitude, the dependence of the resulting strain on stress direction is a Lévy flight in the thermodynamic limit.

We present a combined experimental and theoretical study of memory effects in vibration-induced compaction of granular materials. In particular, the response of the system to an abrupt change in shaking intensity is measured. At short times after the perturbation a granular analog of aging in glasses is observed. Using a simple two-state model, we are able to explain this short-time response. We also discuss the possibility for the system to obey an approximate pseudo-fluctuation-dissipation theorem relationship and relate our work to earlier experimental and theoretical studies of the problem.

We report the first detailed experimental observation of the Batchelor regime [G. K. Batchelor, J. Fluid. Mech. 5, 113 (1959)], in which a passive scalar is dispersed by a large scale strain, at high Péclet numbers. The observation is performed in a controlled two-dimensional flow, forced at large scale, in conditions where a direct enstrophy cascade develops [J. Paret, M.-C. Jullien, and P. Tabeling, Phys. Rev. Lett. 83, 3418 (1999)]. The expected $k^{-1\mathrm{}}$ spectrum is observed, along with exponential tails for the distributions of the concentration and concentration increments and logarithmlike behavior for the structure functions. These observations, confirmed by using simulated particles, provide a support to the theory.

We show that in systems whose output must compete with a noise source, stochastic resonance (maximization of output signal-noise separation as a nonmonotonic function of input noise strength) exists even when measured in terms of fundamental statistical measures and optimal detector performance. This is in contrast to the commonly considered scenario where, without the competing noise, the system (e.g., a driven, overdamped particle moving in a double well potential) is essentially invertible and optimal detector performance monotonically deteriorates with increasing input noise strength.

We show that for an open quantum system which is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators) the rate of entropy production has, as a function of time, two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system-environment coupling strength). For longer times (but before equilibration) there is a regime where the entropy production rate is fixed by the Lyapunov exponent. The nature of the transition time between both regimes is investigated.

The dynamic behavior of coupled chaotic oscillators is investigated. For small coupling, chaotic state undergoes a transition from a spatially disordered phase to an ordered phase with an orientation symmetry breaking. For large coupling, a transition from full synchronization to partial synchronization with translation symmetry breaking is observed. Two bifurcation branches, one in-phase branch starting from synchronous chaos and the other antiphase branch bifurcated from spatially random chaos, are identified by varying coupling strength $\epsilon$. Hysteresis, bistability, and first-order transitions between these two branches are observed.

Experimental observations of time-delay-induced amplitude death in two coupled nonlinear electronic circuits that are individually capable of exhibiting limit-cycle oscillations are described. The existence of multiply connected death islands in the parameter space of coupling strength and time delay for coupled identical oscillators is established. The existence of such regions was predicted earlier on theoretical grounds [Phys. Rev. Lett. 80, 5109 (1998); Physica (Amsterdam) 129D, 15 (1999)]. The experiments also reveal the occurrence of multiple frequency states, frequency suppression of oscillations with increased time delay, and the onset of both in-phase and antiphase collective oscillations.

Utilizing a rotatable thin birefringent crystal and two polarizers, the three-dimensional (3D) wave front of any light wave can be measured conveniently. In first experiments phase-front distortions as small as $15\mu \mathrm{m}$ are detected with a dynamic range of 3 mm and a spatial resolution of $50\mu \mathrm{m}$. Such a dynamic range and spatial resolution exceed the performance of conventional wave front sensors of, e.g., the Shack-Hartmann type, significantly. Furthermore, the new system is rather insensitive against mechanical instabilities in opposition to interferometric and holographic techniques.

The average power spectrum of a pulse reflected by a disordered medium embedded in an $N$-mode waveguide decays in time with a power law $t^{-p}$. We show that the exponent $p$ increases from $\frac{3}{2}$ to $2$ after $N^2$ scattering times, due to the onset of localization. We compare two methods to arrive at this result. The first method involves the analytic continuation to an imaginary absorption rate of a static scattering problem. The second method involves the solution of a Fokker-Planck equation for the frequency dependent reflection matrix, by means of a mapping onto a problem in non-Hermitian quantum mechanics.

Using few-cycle-driven coherent laser harmonics, $K$-shell vacancies have been created in light elements, such as boron $(E_B=188\mathrm{}\mathrm{eV})$ and carbon $(E_B=284\mathrm{}\mathrm{eV})$, on a time scale of a few femtoseconds for the first time. The capability of detecting x-ray fluorescence excited by few-femtosecond radiation with an accuracy of the order of 1 eV paves the way for probing the evolution of the microscopic environment of selected atoms in chemical and biochemical reactions on previously inaccessible time scales $(<100\mathrm{}\mathrm{fs})$ by tracing the temporal evolution of the “chemical shift” of peaks associated with inner-shell electronic transitions in time-resolved x-ray fluorescence and photoelectron spectra.

We describe experiments on a horizontally shaken $[x=A\sin (\omega t\left)\right]$ single layer of hard spheres rolling on a nearly horizontal surface. We identify a novel substrate-mediated convective flow which occurs when the system is tilted slightly so that the weak gravitational force, ${\overrightarrow{g}}_{\mathrm{eff}}$, acting on the particles is not parallel to the driving direction. As the shaking amplitude is increased, the system progresses through four regimes: solid-flat, solid-inclined, convective, and disordered. The control parameter is the driving velocity, $A\omega$, rather than the usual $A{\omega }^2$ of vertically shaken 3D systems. At the onset of convection, the critical velocity is $V_c\simeq \sqrt{{2g}_{\mathrm{eff}}d}$.

The instability of a vortex subjected to a stationary dipolar or tripolar constraint is studied experimentally by using a rotating deformable cylinder on which two or three rollers are applied. As the Reynolds number and the aspect ratio of the cylinder are varied, different modes of instability are observed and their wavelength and frequency are compared to theoretical predictions. Secondary instability and cyclic breakup are also evidenced in the elliptic geometry.

This paper is devoted to study of the classical-to-quantum crossover of the shot noise in chaotic systems. This crossover is determined by the ratio of the particle dwell time in the system, ${\tau }_d$, to the characteristic time for diffraction $t_E\simeq {\lambda }^{-1\mathrm{}}|\ln ħ|$, where $\lambda$ is the Lyapunov exponent. The shot noise vanishes when $t_E\gg {\tau }_d$, while it reaches a universal value in the opposite limit. Thus, the Lyapunov exponent of chaotic mesoscopic systems may be found by shot noise measurements.

We study a multimode semiconductor laser subject to a moderate optical feedback. The steady state is destabilized by either a simple Hopf bifurcation leading to in phase dynamics or by a degenerate Hopf bifurcation leading to antiphase dynamics. The degenerate bifurcation is also a source of multiple coexisting attractors. We show that a simple interpretation of the low frequency fluctuations in the multimode regime is provided by a chaotic itinerancy among the many coexisting unstable attractors produced by the degenerate Hopf bifurcation.

A microcavity laser based on the gain only in the evanescent field region of whispering gallery modes has been demonstrated. A cylindrical microcavity of $125\mu \mathrm{m}$ diam was surrounded by rhodamine $6G$ dye molecules in an ethanol solution of lower refractive index such that whispering gallery modes of the microcavity underwent laser oscillation when the dye molecules in the evanescent field region outside the cavity were excited by a second harmonic of a Nd:YAG laser. For particular pumping spots, single-mode laser oscillation of a transverse magnetic mode was observed at about 600 nm with associated cavity $Q$ of $3\times {10}^7$.

Experimental results for single-bubble sonoluminescence of air bubbles at very low frequency $f=7.1\mathrm{}\mathrm{kHz}$ are presented: In contrast to the predictions of a recent model [S. Hilgenfeldt and D. Lohse, Phys. Rev. Lett. 82, 1036 (1999)], the bubbles are only as bright ( ${10}^4–{10}^5$ photons per pulse) and the pulses as long ( $\approx 150\mathrm{ps}$) as at $f=20\mathrm{}\mathrm{kHz}$. We can theoretically account for this effect by incorporating water vapor into the model: During the rapid bubble collapse a large amount of water vapor is trapped inside the bubble, resulting in an increased heat capacity and hence lower temperatures, i.e., hindering upscaling. At this low frequency water vapor also dominates the light emission process.

A Comment on the Letter by P. Azaria et al., Phys. Rev. Lett. 81, 1694 (1998). The authors of the Letter offer a Reply.

A Reply to the Comment by Steven R. White and Rajiv R. P. Singh.

Experimental phase synchronization of chaos in a plasma discharge is studied using a phase variable lift technique (i.e., phase points separated by $2\pi$ are not considered as the same). Real-time observation of synchronized and unsynchronized states is made possible through a real-time sampling procedure. Parameter space regions of synchronization and unsynchronization are identified, and a set of equations is suggested to model the real plasma circuit.