As is well known, the extrusion rate of polymers from a cylindrical tube or slit (a “die”) is in practice limited by the appearance of “melt fracture” instabilities which give rise to unwanted distortions or even fracture of the extrudate. We present the results of a weakly nonlinear analysis which gives evidence for an intrinsic generic route to melt fracture via a weakly nonlinear subcritical instability of viscoelastic Poiseuille flow. This instability and the onset of associated melt fracture phenomena appear at a well-defined ratio of the elastic stresses to viscous stresses of the polymer solution.

The field near a sharp metal tip can be strongly enhanced if irradiated with an optical field polarized along the tip axis. We demonstrate that the enhanced field gives rise to local second-harmonic (SH) generation at the tip surface thereby creating a highly confined photon source. A theoretical model for the excitation and emission of SH radiation at the tip is developed and it is found that this source can be represented by a single on-axis oscillating dipole. The model is experimentally verified by imaging the spatial field distribution of strongly focused laser modes.

We demonstrate an interferometer for hard x rays with two back-reflecting sapphire crystal mirrors—a prototype x-ray Fabry-Pérot interferometer. A finesse of $15$ and $0.76\mu \mathrm{e}\mathrm{V}$ broad Fabry-Pérot transmission resonances are measured by the time response of the interferometer. Interference patterns are observed directly in spectral dependences of reflectivity.

The quantum to classical transition for a system depends on many parameters, including a scale length for its action, $\hslash$, a measure of its coupling to the environment, $D$, and, for chaotic systems, the classical Lyapunov exponent, $\lambda$. We propose measuring the proximity of quantum and classical evolutions as a multivariate function of $(\hslash ,\lambda ,D)$ and searching for transformations that collapse this hypersurface into a function of a composite parameter $\zeta ={\hslash }^{\alpha }{\lambda }^{\beta }{D}^{\gamma }$. We report results for the quantum Cat Map and Duffing oscillator, showing accurate scaling behavior over a wide parameter range, indicating that this may be used to construct universality classes for this transition.

We present an experimental demonstration showing that, contrary to first intuition, the more scattering a mesoscopic medium is, the more information can be conveyed through it. We used a multiple input—multiple output configuration: a multichannel ultrasonic time-reversal antenna is used to transmit random series of bits simultaneously to different receivers which were only a few wavelengths apart. Whereas the transmission is free of error when multiple scattering occurs in the propagation medium, the error rate is huge in a homogeneous medium.

We report on experiments on vertically shaken binary granular mixtures, which separate into their components due to the external excitation. This well-known phenomenon, where large particles rise to the top of the mixture, is called the Brazil-nut effect. Recent theoretical findings predict also a reverse Brazil-nut effect, where large particles sink to the bottom of the container. We choose spherical beads of various diameters and materials in order to observe the transition from Brazil-nut effect to its reverse form. The direction of demixing depends sensitively on the external excitation, so that it is possible to switch between both effects for a given mass density ratio.

We investigate experimentally the influence of suspended particles on the transition to turbulence. The particles are monodisperse and neutrally buoyant with the liquid. The role of the particles on the transition depends upon both the pipe to particle diameter ratios and the concentration. For large pipe-to-particle diameter ratios the transition is delayed while it is lowered for small ratios. A scaling is proposed to collapse the departure from the critical Reynolds number for pure fluid as a function of concentration into a single master curve.

We consider the evolution of optical solitons inside a nonlinear dispersive fiber with random birefringence, causing polarization-mode dispersion. We convert the pair of coupled nonlinear Schrödinger equations satisfied by the orthogonally polarized components into a Fokker-Planck equation using the collective-variable approach. We solve this equation and derive expressions for the probability density functions associated with the differential group delay and the pulse width in the limit of large propagation distances.

The classical problem of determining the solitons generated from symmetric real initial conditions in the nonlinear Schrödinger equation is revisited. The corresponding Zakharov-Shabat scattering problem is solved for real and symmetric double-humped rectangular initial pulse forms. It is found that such real symmetric pulses may generate eigenvalues with nonzero real parts corresponding to separating soliton pulse pairs. Moreover, it is found that the classical formula relating the number of eigenvalues to the area of the pulse is not always correct.

The spectral properties of a two-dimensional microwave billiard showing threefold symmetry have been studied with a new experimental technique. This method is based on the behavior of the eigenmodes under variation of a phase shift between two input channels, which strongly depends on the symmetries of the eigenfunctions. Thereby a complete set of 108 Kramers doublets has been identified by a simple and purely experimental method. This set clearly shows Gaussian unitary ensemble statistics, although the system is time-reversal invariant.

We study the phase synchronization and cluster formation in coupled maps on different networks. We identify two different mechanisms of cluster formation: (a) self-organized phase synchronization which leads to clusters with dominant intracluster couplings and (b) driven phase synchronization which leads to clusters with dominant intercluster couplings. In the novel driven synchronization the nodes of one cluster are driven by those of the others. We also discuss the dynamical origin of these two mechanisms for small networks with two and three nodes.

A new technique for directly measuring the electric field of linearly polarized few-cycle laser pulses is proposed. Based on the solution of the time-dependent Schrödinger equation (TDSE) for an H atom in the combined field of infrared (IR) femtosecond (fs) and ultraviolet (UV) attosecond (as) laser pulses we show that, as a function of the time delay between two pulses, the difference (or equivalently, asymmetry) of photoelectron signals in opposite directions (along the polarization vector of laser pulses) reproduces very well the profile of the electric field (or vector potential) in the IR pulse. Such ionization asymmetry can be used for directly measuring the carrier-envelope phase difference (i.e., the relative phase of the carrier frequency with respect to the pulse envelope) of the IR fs laser pulse.

We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured efficiently on a quantum information processor, and analyze the conditions under which this indicator is a reliable probe of quantum chaos. The type and rate of the decay are not dependent on the eigenvalue statistics of the unperturbed system, but depend on the system's eigenvector statistics in the eigenbasis of the perturbation. For random eigenvector statistics, the decay is exponential with a rate fixed by the variance of the perturbation's energy spectrum. Hence, even classically regular models can exhibit an exponential fidelity decay under generic quantum perturbations. These results clarify which perturbations can distinguish classically regular and chaotic quantum systems.

Chaos is a class of ubiquitous phenomena and controlling chaos is of great interest and importance. In this Letter, we introduce wavelet controlled dynamics as a new paradigm of dynamical control. We find that by modifying a tiny fraction of the wavelet subspaces of a coupling matrix, we could dramatically enhance the transverse stability of the synchronous manifold of a chaotic system. Wavelet controlled Hopf bifurcation from chaos is observed. Our approach provides a robust strategy for controlling chaos and other dynamical systems in nature.

A unidirectional optical pulse propagation equation, derived directly from Maxwell’s equations, provides a seamless transition between various nonlinear envelope equations in the literature and the full vector Maxwell’s equations. The equation is illustrated in the context of supercontinuum generation in air and is compared to a recent scalar model of Brabec and Krausz. Fully vectorial aspects of the model are illustrated in the context of extreme focusing of a femtosecond pulse.

The long-time algebraic relaxation process in spatially periodic billiards with infinite horizon is shown to display a self-similar time-asymptotic form. This form is identical for a class of such billiards, but can be different in an important special case.

A one-dimensional optically coupled array of colloidal particles is created in a potential well formed by two counterpropagating Gaussian light beams. This array has analogies to linear chains of trapped atomic ions. Breathing modes and oscillations of the center of mass are observed. The stability of the array is in accordance with the Kramers model.

Coherent vortices are an important component of the dynamics of geophysical turbulence, but direct estimates of the properties of the vortex population from measured data is usually difficult. Motivated by this problem, we propose a new method for determining the statistical properties of coherent vortices in two-dimensional turbulence based on a small number of Lagrangian and Eulerian time series. The method provides reliable estimates of the mean vortex size and vortex number density.

We reveal numerically the remarkably robust propagation of quasistationary two-color soliton clusters in media with competing quadratic and cubic nonlinearities. We predict that such clusters carrying nonzero angular momentum can propagate over any practically feasible crystal length before they decay, even in the presence of input random perturbations.

We report the first combined experimental-theoretical study to realize and control the behavior of common resonances in a periodically driven system. Experimental data for the ionization of $\mathrm{H}(n=51)$ atoms by a bichromatic (6 and 18 GHz), linearly polarized electric field pulse show how the relative field phase can be used to control the ionization. 1D classical calculations show how this results from the phase control of the pendulumlike, common resonances, whose existence requires, at lowest order, two commensurate frequencies.