We report an ultrafast x-ray phase-contrast imaging study of the early merging dynamics of two water drops in air. Owing to the edge-enhancement capability, the high penetrability, and the unprecedented temporal and spatial resolutions offered by this new x-ray technique, the coalescence singularity of two water drops was revisited. A finite initial contact radius was identified and the evolvement of the trapped toroidal air bubble was studied for the first time. Despite the existence of this finite initial contact radius, the subsequent meniscus radius followed power laws which agree with theoretical predictions for the inviscid regime.

We report on the observation of second-harmonic conical waves generated in a novel geometry of the transverse excitation of an annular periodically poled nonlinear photonic structure by a fundamental Gaussian beam. We show that the conical beams are formed as a result of the higher-order nonlinear Bragg diffraction involving two parametric processes in which an ordinary fundamental wave is converted simultaneously into ordinary and extraordinary polarized second harmonics.

There exists a substantial body of theory that predicts mutual screening of signed topological singularities (topological charges) in random optical fields (speckle patterns). Such screening appears to be rather mysterious because there are neither energetic nor entropic reasons for its existence. We present the first experimental confirmation of mutual screening by the stationary points of the intensity, the canonical optical scalar field, and of mutual screening by $C$ points in elliptically polarized light, the generic optical vector field. We also elucidate specific aspects of the geometry and topology of these fields that we argue give rise to screening.

We study numerically the spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schrödinger lattice with disorder. We demonstrate that above a certain critical strength of nonlinearity the Anderson localization is destroyed and an unlimited subdiffusive spreading of the field along the lattice occurs. The second moment grows with time $\propto t^{\alpha }$, with the exponent $\alpha$ being in the range 0.3–0.4. For small nonlinearities the distribution remains localized in a way similar to the linear case.

Basquin’s law of fatigue states that the lifetime of the system has a power-law dependence on the external load amplitude, $t_f\sim {\sigma }_0^{-\alpha }$, where the exponent $\alpha$ has a strong material dependence. We show that in spite of the broad scatter of the exponent $\alpha$, the fatigue fracture of heterogeneous materials exhibits universal features. We propose a generic scaling form for the macroscopic deformation and show that at the fatigue limit the system undergoes a continuous phase transition. On the microlevel, the fatigue fracture proceeds in bursts characterized by universal power-law distributions. We demonstrate that the system dependent details are contained in Basquin’s exponent for time to failure, and once this is taken into account, remaining features of failure are universal.

The expected universal dynamics associated with the initial stage of droplet coalescence are difficult to study visually due to the rapid motion of the liquid and the awkward viewing geometry. Here we employ an electrical method to study the coalescence of two low-viscosity droplets at early times. We measure the growth dynamics of the bridge connecting the two droplets and observe a new asymptotic regime inconsistent with previous theoretical predictions. The measurements are consistent with a model in which the two liquids coalesce with a slightly deformed interface.

The piston shock problem is a classical result of shock wave theory. In this work, the analogous dispersive shock wave (DSW) problem for a fluid described by the nonlinear Schrödinger equation is analyzed. Asymptotic solutions are calculated for a piston (step potential) moving with uniform speed into a dispersive fluid at rest. In contrast to the classical case, there is a bifurcation of shock behavior where, for large enough piston velocities, the DSW develops a periodic wave train in its wake with vacuum points and a maximum density that remains fixed as the piston velocity is increased further. These results have application to Bose-Einstein condensates and nonlinear optics.

Here we propose a new method, detrended cross-correlation analysis, which is a generalization of detrended fluctuation analysis and is based on detrended covariance. This method is designed to investigate power-law cross correlations between different simultaneously recorded time series in the presence of nonstationarity. We illustrate the method by selected examples from physics, physiology, and finance.

We study the spreading of an initially localized wave packet in two nonlinear chains (discrete nonlinear Schrödinger and quartic Klein-Gordon) with disorder. Previous studies suggest that there are many initial conditions such that the second moment of the norm and energy density distributions diverges with time. We find that the participation number of a wave packet does not diverge simultaneously. We prove this result analytically for norm-conserving models and strong enough nonlinearity. After long times we find a distribution of nondecaying yet interacting normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this result holds for any initially localized wave packet, we rule out the possibility of slow energy diffusion. The dynamical state could approach a quasiperiodic solution (Kolmogorov-Arnold-Moser torus) in the long time limit.

A long, smooth cylinder is dragged through a water surface to create a cavity with an initially cylindrical shape. This surface void then collapses due to the hydrostatic pressure, leading to a rapid and axisymmetric pinch-off in a single point. Surprisingly, the depth at which this pinch-off takes place does not follow the expected ${\mathrm{\text{Froude}}}^{1/3}$ power law. Instead, it displays two distinct scaling regimes separated by discrete jumps, both in experiment and in numerical simulations (employing a boundary integral code). We quantitatively explain the above behavior as a capillary wave effect. These waves are created when the top of the cylinder passes the water surface. Our work thus gives further evidence for the nonuniversality of the void collapse.

We introduce a directionality index for a time series based on a comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well as reveal and quantify asymmetry in bidirectional coupling. It is tested on a numerical model of coupled van der Pol oscillators, and applied to cardiorespiratory data from healthy subjects. There is no need for preprocessing and fine-tuning the parameters, which makes the method very simple, computationally fast and robust.

The wall shear rate distribution $P(\gamma )$ is investigated for pressure-driven Stokes flow through random arrangements of spheres at packing fractions $0.1\le \varphi \le 0.64$. For dense packings, $P(\gamma )$ is monotonic and approximately exponential. As $\varphi \to 0.1$, $P(\gamma )$ picks up additional structure which corresponds to the flow around isolated spheres, for which an exact result can be obtained. A simple expression for the mean wall shear rate is presented, based on a force-balance argument.

We use extreme-ultraviolet interferometry to measure the phase of high-order harmonic generation from transiently aligned ${\mathrm{CO}}_2$ molecules. We unambiguously observe a reversal in phase of the high-order harmonic emission for higher harmonic orders with a sufficient degree of alignment. This results from molecular-scale quantum interferences between the molecular electronic wave function and the recolliding electron as it recombines with the molecule, and is consistent with a two-center model. Furthermore, using the combined harmonic intensity and phase information, we extract accurate information on the dispersion relation of the returning electron wave packet as a function of harmonic order. This analysis shows evidence of the effect of the molecular potential on the recolliding electron wave.

We investigate the “flapping flag” instability through a model for an inextensible flexible sheet in an inviscid 2D flow with a free vortex sheet. We solve the fully-nonlinear dynamics numerically and find a transition from a power spectrum dominated by discrete frequencies to an apparently continuous spectrum of frequencies. We compute the linear stability domain which agrees with previous approximate models in scaling but differs by large multiplicative factors. We also find hysteresis, in agreement with previous experiments.

Previous works on single bubble sonoluminescence in sulfuric acid solutions have stressed the fact that the sonoluminescence (SL) emissions are the highest ever found, but at the same time the bubble moves in orbits. We have fixed the SL bubble spatially and at the same time we have reached higher SL emissions using another harmonic acoustic signal to produce the acoustic excitation. Multiple harmonic excitation produces up to a fourfold increase in SL emissions, reaching the peak value of about $40\mu \mathrm{W}$ for a moving bubble and $15\mu \mathrm{W}$ for a nonmoving bubble. The ability to have a bright stationary bubble also opens new research opportunities. In particular, we develop a new method to measure the absolute radius evolution of the bubble that exploits this stability.

We investigate theoretically and experimentally the capillary-gravity waves created by a small object moving steadily at the water-air interface along a circular trajectory. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity $c_{\min }=23\mathrm{cm}{\mathrm{s}}^{-1}$. We demonstrate that no such velocity threshold exists for a steady circular motion, for which, even for small velocities, a finite wave drag is experienced by the object. This wave drag originates from the emission of a spiral-like wave pattern. Our results are in good agreement with direct experimental observations of the wave pattern created by a circularly moving needle in contact with water. Our study leads to new insights into the problem of animal locomotion at the water-air interface.

We describe an instability of viscoelastic Couette–Taylor flow that is directly analogous to the magnetorotational instability (MRI) in astrophysical magnetohydrodynamics, with polymer molecules playing the role of magnetic field lines. By determining the conditions required for the onset of instability and the properties of the preferred modes, we distinguish it from the centrifugal and elastic instabilities studied previously. Experimental demonstration and investigation should be much easier for the viscoelastic instability than for the MRI in a liquid metal. The analogy holds with the case of a predominantly toroidal magnetic field such as is expected in an accretion disk, and it may be possible to access a turbulent regime in which many modes are unstable.

A highly efficient intracavity four-wave mixing in a Raman-active medium pumped by a continuous-wave laser is first demonstrated. Managing the intracavity dispersion to satisfy the phase matching in a high-finesse cavity substantially enhances the anti-Stokes emission. This process is observed in a region far beyond small signal approximation, indicating the generation of phase-locked sidebands arising from molecular modulation. This points to a novel approach of an optical modulator and mode-locked laser operating at a frequency of more than 10 THz.

In a previous publication [O. A. M. Boote and P. J. Thomas, Phys. Fluids 11, 2020 (1999)], we described a new banding pattern developing from particle segregation in particle-laden flow inside a partially fluid-filled, horizontal, rotating cylinder. Here we discuss long-term observations lasting up to several weeks revealing that the system can display an extremely rich spatiotemporal behavior that emerges as the patterns drift very slowly along the axis of rotation. Some of the nondimensional key parameters governing the dynamics are identified.

We investigate the influence of a uniform magnetic field ${\mathbf{B}}_0=B_0{\mathbf{e}}_{\parallel }$ on energy decay laws in incompressible magnetohydrodynamic (MHD) turbulence. The nonlinear transfer reduction along ${\mathbf{B}}_0$ is included in a model that distinguishes parallel and perpendicular directions, following a phenomenology of Kraichnan. We predict a slowing down of the energy decay due to anisotropy in the limit of strong $B_0$, with distinct power laws for energy decay of shear- and pseudo-Alfvén waves. Numerical results from the kinetic equations of Alfvén wave turbulence recover these predictions, and MHD numerical results clearly tend to follow them in the lowest perpendicular planes.