Chaos synchronization of nonidentical unidirectionally coupled systems is investigated and characterized in terms of the entrainment ratios of unstable periodic orbits. The implications of subharmonic entrainment for generalized synchronization are discussed and illustrated for discrete and continuous systems.

We present an analytical theory for the optical properties of a novel three-level medium for which the degree of its initial excitation is a function of the position. The spatial distribution of the excitation can be imaged on the temporal profile of an electromagnetic signal that is created inside the medium when traversed by a cw-laser field. We propose an experimental scheme to generate arbitrary spatial excitations.

Measurements of the diffusive transport of multiply scattered ultrasonic waves show that the energy velocity is very similar in magnitude and frequency dependence to the group velocity. Our data are accurately described using a theoretical model that accounts for the renormalization of scattering by the coupling between neighboring scatterers, quantitatively predicting the scattering delay that causes the strong frequency dependence of these velocities seen in our experiments. This gives a unified physical picture of the velocities of energy transport by both diffusive and ballistic waves.

We take advantage of the violation of time-reversal invariance for acoustic waves to achieve a new way of characterizing a vorticity field with a double time-reversal mirror (TRM). In particular, we show experimentally that the double TRM works as a vorticity amplifier. In the case of a vorticity filament, the sound-vorticity interaction is interpreted as the acoustical analog of the Aharonov-Bohm effect. Numerical experiments simulate the acoustical Aharonov-Bohm effect by propagating a plane wave which is scattered by a heterogeneous motionless medium.

We present the first experimental tests of the recently derived fusion rules for Navier-Stokes turbulence. The fusion rules address the asymptotic properties of many-point correlation functions as some of the coordinates coalesce, and form an important ingredient of the nonperturbative statistical theory of turbulence. Here we test the fusion rules when the spatial separations lie within the inertial range, and find good agreement between experiment and theory. For inertial-range separations and for velocity increments which are not too large, a simple linear relation appears to exist for the Laplacian of the velocity fluctuation conditioned on velocity increments.

A new linear mechanism of wave abrupt emergence from vortices in smooth shear flows is found. The phenomenon is closely related to non-normality of linear dynamics of disturbances in shear flows and is best interpreted in the framework of a nonmodal approach—by tracing of linear dynamics of spatial Fourier harmonics of vortex in time. Found phenomenon, demonstrated in the Letter for the simplest example of unbounded, compressible, plane Couette flow, should be important for numerous engineering applications and should be realized in various terrestrial and astrophysical shear flows.

In this Letter we show, in a particular example, how extensive data may lead to the identification of a high-dimensional system: we study data obtained in an extended system of hydrodynamical wakes. We improved a partial-inversion method designed to identify the parameters of a set of coupled Stuart-Landau equations. In the new, total-inversion method we search for both parameters and initial conditions. The total-inversion method allows one for the first time to reconstruct accurately the entire time series, except for regions of low-amplitude oscillation.

Ultrafast laser pulses from a Ti:sapphire laser centered at 800 nm, with 26 fs pulse duration, were used to generate coherent soft-x-ray harmonics, at wavelengths down to 2.7 nm (460 eV) in He, and 5.2 nm (239 eV) in Ne. In He, discrete harmonic peaks are observed up to order 221, and unresolved harmonic emission is observed up to order 297. These wavelengths are well within the “water window” region of x-ray transmission. Our work represents the shortest wavelength coherent light generated to date. The harmonic cutoff from all the noble gases is consistent with analytic theory.

Recent advances in solid state laser technology enable efficient generation of optical frequency laser pulses a few cycles in duration with focused intensities in excess of ${10}^{15}\mathrm{W}/{\mathrm{cm}}^2$. When such pulses are propagated in neutral gases such as helium, ionization rates comparable to the optical frequency are induced. The very high ionization rates and the corresponding optical field strengths to which neutral atoms can be exposed with few cycle pulses present an intriguing possibility for coherent XUV generation. In this Letter, we will examine phase matching issues associated with this phenomenon.

Mixtures of granular media often exhibit size segregation along the axis of a partially filled, horizontal, rotating cylinder. Previous experiments have observed axial bands of segregation that grow from concentration fluctuations and merge in a manner analogous to spinodal decomposition. We have observed that a new dynamical state precedes this effect in certain mixtures: bidirectional traveling waves. By preparing initial conditions, we found that the wave speed decreased with wavelength. Such waves appear to be inconsistent with simple partial differential equation models which are first order in time.

We use group-theoretic methods to analyze phase-locking in a ring of identical integrate-and-fire oscillators with distributed delays. It is shown how certain phase-locked solutions emerge through symmetry breaking bifurcations as some characteristic delay of the system is varied. The reduction to a phase-coupled model in the weak coupling regime is discussed.

Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a coupled map lattice as an example. The optimal arrangement of the control sites is shown to depend on the symmetry properties of the system, while their minimal density depends on the strength of noise in the system. The method is shown to work in any region of parameter space and requires a significantly smaller number of controllers compared to the method proposed earlier by Hu and Qu [Phys. Rev. Lett. 72, 68 (1994)]. A nonlinear generalization of the method for a 1D lattice is also presented.

We have measured the variation of the spatial coherence with plasma column length in a saturated table-top 46.9-nm Ne-like Ar capillary discharge soft x-ray amplifier for lengths up to 16.4 cm. The measurements, which are in good agreement with time dependent wave-optics model computations, provide the first experimental evidence of a monotonic increase of the coherence with length in a soft x-ray amplifier. The variation of the coherence across the beam profile was also studied. Off axis, the coherence is larger in the tangential than in the radial direction.

We analyze the transition from annihilation to preservation of colliding waves. The analysis exploits the similarity between the local and global phase portraits of the system. The transition is shown to be the infinite-dimensional analog of the creation and annihilation of limit cycles in the plane via a homoclinic Andronov bifurcation, and has parallels to the nucleation theory of first-order phase transitions.

The self-similar decay of energy in magnetohydrodynamic flows is examined in the spirit of the Kolmogorov phenomenology while incorporating in the expression for the energy transfer to small scales the interactions between turbulent eddies and Alfvén waves due to a large-scale magnetic field. The model is parameter-free and does not rely on the existence of the several invariants of ideal MHD except energy. High-resolution numerical simulations in two dimensions confirm its validity in a way that leads as expected to a decay significantly slower than for neutral fluids.

Vortices, shocks, domains of tilted waves, and cross-roll patterns are typical patterns of the complex Swift-Hohenberg equation, which describes spatiotemporal dynamics in nonlinear optical systems of large Fresnel number, such as lasers, optical parametric oscillators, and photorefractive oscillators. We show the occurrence of such “essentially nonlinear” patterns experimentally on a photorefractive oscillator and compare it with numerical solutions of the complex Swift-Hohenberg equation.

We study the viscous fingering instability and the motion of long bubbles in tubes for two different polymer solutions. For similar non-Newtonian viscosities, the results are strikingly different: Flexible polymers widen the viscous fingers, whereas stiff polymers narrow the fingers. A study of the motion of air bubbles in a tube filled with the polymer solution shows that the difference is due to normal stress effects; these are large for the flexible polymer and undetectable for the stiff polymer.

We study the pattern selection and the dynamics of a bifurcating system such as Taylor-Couette flow or Rayleigh-Bénard convection, subject to an externally imposed cross flow using the complex Ginzburg-Landau equation as a qualitative model. We show that the bifurcation scenario is radically modified by the introduction of a cross flow, and that a nonlinear global mode, i.e., a nonlinear oscillating solution in a semi-infinite domain $[0,+\infty )$, with a homogeneous condition at $x=0\mathrm{}$, exists only when the basic state is linearly absolutely unstable. We derive the scaling law for the characteristic growth size, which varies as ${\epsilon }^{-1\mathrm{}/2}$ ( $\epsilon$ being the criticality parameter), and compares satisfactorily with numerical and experimental results from the literature.

We present a systematic nonlinear theory of pattern selection for parametric surface waves (Faraday waves), not restricted to fluids of low viscosity. A standing wave amplitude equation is derived from the Navier-Stokes equation that is of gradient form. The associated Lyapunov function is calculated for different regular patterns to determine the selected pattern near threshold as a function of a damping parameter $\gamma$. For $\gamma \sim 1$, we show that a single wave (or stripe) pattern is selected. For $\gamma \ll 1$, we predict patterns of square symmetry in the capillary regime, a sequence of sixfold (hexagonal), eightfold, $\dots$ in the mixed gravity-capillary regime, and stripe patterns in the gravity dominated regime.

The Richtmyer-Meshkov (RM) instability is an interfacial interface between two fluids of different densities driven by shock waves and plays an important role in the studies of inertial confinement fusion and of supernovas. So far, most of the studies are for RM unstable interfaces driven by weak or intermediate shocks in planar geometry. For experiments conducted at the Nova laser, the unstable material interface is accelerated by very strong shocks. In this Letter, we present scaling laws for the RM unstable interface driven by strong imploding and exploding shocks.