We investigate the transition route to phase synchronization in a chaotic laser with external modulation. Such a transition is characterized by the presence of a regime of periodic phase synchronization, in which phase slips occur with maximal coherence in the phase difference between output signal and external modulation. We provide the first experimental evidence of such a regime and demonstrate that it occurs at the crossover point between two different scaling laws of the intermittent-type behavior of phase slips.

Statistical properties of the temperature field in turbulent convection are studied experimentally. We show that the skewness of the plus and minus temperature increments can be used to quantitatively characterize the mixing zone in the convective flow and the result reveals how the mixing zone evolves with the Rayleigh number. We also present evidence for the saturation of the temperature structure function exponent and that the saturation is related to thermal plumes. A more direct study of the thermal plumes suggests that their sizes have a distribution that is approximately log-normal.

Granular material on an inclined plane will flow like a fluid if the angle $\theta$ the plane makes with the horizontal is large enough. We study chute flow down a plane using a hydrodynamic model previously used to describe granular Couette flow. Our model predicts a jammed-to-flowing transition as $\theta$ is increased even though it does not include solid friction, which might seem necessary to stabilize a state without flow. The transition is driven by coupling between mean and fluctuating velocity. In agreement with experiments and simulations, it predicts flow for layers with a thickness $H$ larger than a critical value $H_{\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}}(\theta )$ and absence of flow for $H<H_{\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}}(\theta )$.

We consider the energy spectrum of a quasigeostrophic model of forced, rotating turbulent flow. We provide a rigorous a priori bound $E(k)\le C{k}^{-2}$ valid for wave numbers that are smaller than a wave number associated with the forcing injection scale. This upper bound separates this spectrum from the Kolmogorov-Kraichnan $k^{-\frac{5}{3}}$ energy spectrum that is expected in a two-dimensional Navier-Stokes inverse cascade. Our bound provides theoretical support for the $k^{-2}$ spectrum observed in recent experiments.

We study, theoretically and experimentally, the evolution of patterns in a passive nonlinear cavity that is longer than the coherence length of the light circulating in it. The patterns exhibit spatial line narrowing as the feedback is increased, resembling the line narrowing in lasers.

At microwave frequencies, hollow metallic waveguides behave in certain aspects as a “one-dimensional plasma.” This feature will be advantageously used for simulating the propagation of electromagnetic (EM) waves in left-handed metamaterials provided the hollow waveguide is periodically loaded with split ring resonators. It will be shown that EM transmission in this structure is feasible within a certain frequency band even if the transverse dimensions of the waveguide are much smaller than the associated free-space wavelength. This effect can be qualitatively and quantitatively explained by the left-handed metamaterial theory, thus providing a new experimental validation for such a theory.

We ask whether statistical averages in chaotic systems can be computed or measured reliably under the influence of noise. Situations are identified where the invariance of such averages breaks down as the noise amplitude increases through a critical level. An algebraic scaling law is obtained which relates the change of the averages to the noise variation. This breakdown of shadowability of statistical averages, as characterized by the algebraic scaling law, can be expected in both low- and high-dimensional chaotic systems.

We investigate the dynamics generated by a type of equation which is common to a variety of physical systems where the undesirable effects of a number of self-consistent nonlinear forces are balanced by an externally imposed controlling harmonic force. We show that the equation presents a new sequence of bifurcations where periodic orbits are created and destroyed in such a nonsimultaneous way that may leave the appropriate phase-space occasionally empty of fundamental harmonic orbits and confined trajectories. A generic analytical model is developed and compared with a concrete physical example.

Recent images of electron flow through a two-dimensional electron gas device show branching behavior that is reproduced in numerical simulations of motion in a correlated random potential [M. A. Topinka et al., Nature 410, 183 (2001)]. We show how such branching arises from caustics in the classical flow and find a simple scaling behavior of the branching under variation of the random potential strength. Analytic results describing statistical properties of the branching are confirmed by classical and quantum numerical tests.

Length scales are determined that govern the behavior at small separations of the correlations of fluid-particle acceleration, viscous force, and pressure gradient. The length scales and an associated universal constant are quantified on the basis of published data. The length scale governing pressure spectra at high wave numbers is discussed. Fluid-particle acceleration correlation is governed by two length scales: one arises from the pressure gradient, the other from the viscous force.

Interference fringes can result from the measurement of four-time fourth-order correlation functions of a wave field. These fringes have a statistical origin and, as a consequence, they show the greatest contrast when the coherence time of the field is finite. A simple acoustic experiment is presented in which these fringes are observed, and it is demonstrated that the contrast is maximal for partial coherence. Random telegraph phase noise is used to vary the field coherence in order to highlight the problem of interpreting this interference; for this noise, the Gaussian moment theorem may not be invoked to reduce the description of the interference to one in terms of first-order interference.

Parametrically driven systems sustaining sech solitons are shown to support a new kind of localized state. These structures are walls connecting two regions oscillating in antiphase that form in the parameter domain where the sech soliton is unstable. Depending on the parameter set the oppositely phased domains can be either spatially uniform or patterned. Both chiral (Bloch) and nonchiral (Ising) walls are found, which bifurcate one into the other via an Ising-Bloch transition. While Ising walls are at rest Bloch walls move and may display secondary bifurcations leading to chaotic wall motion.

We study the shape of the coherent-backscattering (CBS) cone obtained when resonant light illuminates a thick cloud of laser-cooled rubidium atoms in the presence of a homogenous magnetic field. We observe new magnetic field-dependent anisotropies in the CBS signal. We show that the observed behavior is due to the modification of the atomic-radiation pattern by the magnetic field (Hanle effect in the excited state).

We investigate the effects of finite size and inertia of a small spherical particle immersed in an open unsteady flow which, for ideal tracers, generates transiently chaotic trajectories. The inertia effects may strongly modify the chaotic motion to the point that attractors may appear in the configuration space. These studies are performed in a model of the two-dimensional flow past a cylindrical obstacle. The relevance to modeling efforts of biological pathogen transport in large-scale flows is discussed. Since the tracer dynamics is sensitive to the particle inertia and size, simple geometric setups in such flows could be used as a particle mixture segregator separating and trapping particles.

A new type of steep two-dimensional irrotational symmetric periodic gravity wave with local singular point inside the flow domain is revealed on inviscid incompressible fluid of infinite depth. The speed of fluid particles in the vicinity of the crest of these waves is greater than their phase speed. Corresponding particle trajectories provide insight into how gravity waves overturn and break.

A quantum kinetic equation coupled with Maxwell’s equation is used to estimate the laser power required at an x-ray free-electron laser (XFEL) facility to expose intrinsically quantum effects in the process of QED vacuum decay via spontaneous pair production. A $9$-TW-peak XFEL laser with photon energy of $8.3\mathrm{k}\mathrm{e}\mathrm{V}$ could be sufficient to initiate particle accumulation and the consequent formation of a plasma of spontaneously produced pairs. The evolution of the particle number in the plasma will exhibit non-Markovian aspects of the strong-field pair production process, and the plasma’s internal currents will generate an electric field whose interference with that of the laser leads to plasma oscillations.

The theory of focusing light pulses in Kerr media with normal group-velocity dispersion in $(2+1)$ and $(3+1)$ dimensions is revisited. It is shown that pulse splitting introduced by this dispersion follows from shock fronts that develop along hyperbolas separating the region of transverse self-focusing from the domain of temporal dispersion. Justified by a self-similar approach, this property is confirmed by numerical simulations using an adaptive-mesh refinement code.

We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are unstable. These unstable attractors occur in networks of pulse-coupled oscillators, and become prevalent with increasing network size for a wide range of parameters. They are enclosed by basins of attraction of other attractors but are remote from their own basin volume such that arbitrarily small noise leads to a switching among attractors.

Quantum states extended over a large volume in phase space have oscillations from quantum interferences in their Wigner distribution on scales smaller than $\hslash$ [W. H. Zurek, Nature (London) 412, 712 (2001)]. We investigate the influence of those sub-Planck-scale structures on the sensitivity to an external perturbation of the state’s time evolution. While we do find an accelerated decay of the Loschmidt Echo for an extended state in comparison to a localized wave packet, the acceleration is described entirely by the classical Lyapunov exponent and hence cannot originate from quantum interference.

We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control parameter in this study. It is found that distance-dependent time delays induce various patterns including traveling rolls, squarelike and rhombuslike patterns, spirals, and targets. We analyzed the stability boundaries of the emerging patterns and briefly pointed out the possible empirical implications of such time-delayed patterns.