A circular disc hitting a water surface creates an impact crater which after collapse leads to a vigorous jet. Upon impact an axisymmetric air cavity forms and eventually pinches off in a single point halfway down the cavity. Two fast sharp-pointed jets are observed shooting up- and downwards from the closure location, which by then has turned into a stagnation point surrounded by a locally hyperbolic flow pattern. This flow, however, is not the mechanism feeding the jets. Using high-speed imaging and numerical simulations we show that jetting is fed by the local flow around the base of the jet, which is forced by the colliding cavity walls. We show how the well-known theory of a collapsing void (using a line of sinks on the symmetry axis) can be continued beyond pinch-off to obtain a new and quantitative model for jet formation which agrees well with numerical and experimental data.

We investigate co-evolving dynamics in a weighted network of phase oscillators in which the phases of the oscillators at the nodes and the weights of the links interact with each other. We find that depending on the type of the dynamics of the weights, the system exhibits three kinds of asymptotic behavior: a two-cluster state, a coherent state with a fixed phase relation, and a chaotic state with frustration. Because of its structural stability, it is believed that our model captures the essential characteristics of a class of co-evolving and adaptive networks.

We show that density-weighted moments of the dissipation rate, ${ϵ}_l$, averaged over a scale $l$, in supersonic turbulence can be successfully explained by the She and Lévêque model [Phys. Rev. Lett. 72, 336 (1994)]. A general method is developed to measure the two parameters of the model, $\gamma$ and $d$, based directly on their physical interpretations as the scaling exponent of the dissipation rate in the most intermittent structures ($\gamma$) and the dimension of the structures ($d$). We find that the best-fit parameters ($\gamma =0.71$ and $d=1.90$) derived from the ${ϵ}_l$ scalings in a simulation of supersonic turbulence at Mach 6 agree with their direct measurements, confirming the validity of the model in supersonic turbulence.

We show that initial data near an unperturbed stable plane wave can evolve into a regime of spatiotemporal chaos in the slightly forced conservative periodic one-dimensional nonlinear Schrödinger equation. Statistical measures are employed to demonstrate that this spatiotemporal chaos is intermittent: there are windows in time for which the solution gains spatial coherence. The parameters and initial profiles that lead to such intermittency are predicted by utilizing a novel geometrical description of the integrable unforced equation.

The possibility of using the self-induced transparency effect to passively modelock lasers has been discussed since the late 1960s, but has never been observed. It is proposed that quantum cascade lasers are the ideal tool to create this modelocking, due to their rapid recovery times and relatively long coherence times and because it is possible to interleave gain and absorbing layers. Conversely, it is possible to use the self-induced transparency effect to create midinfrared pulses that are less than 100 fs in duration in a semiconductor laser.

We provide a quantitative characterization of dissipative effects in one-dimensional granular crystals. We use the propagation of highly nonlinear solitary waves as a diagnostic tool and develop optimization schemes that allow one to compute the relevant exponents and prefactors of the dissipative terms in the equations of motion. We thereby propose a quantitatively accurate extension of the Hertzian model that encompasses dissipative effects via a discrete Laplacian of the velocities. Experiments and computations with steel, brass, and polytetrafluoroethylene reveal a common dissipation exponent with a material-dependent prefactor.

We report on shelled bubbles that can be manipulated with magnetic fields. The magnetic shell consists of self-assembled magnetic nanoparticles. The magnetic susceptibility of the bubbles is proportional to the surface area, ${\chi }_b=(9\pm 3\times {10}^{-6}\mathrm{m})r^2$ where $r$ is the radius. Magnetic bubbles are compressible in moderate acoustic fields. A bubble with a radius of $121\mu \mathrm{m}$ oscillates in resonance in a sound field of 27 kHz with a peak-to-peak radial amplitude of $1.7\mu \mathrm{m}$. The bubble oscillations induce a microstreaming flow with a toroidal vortex at the upper pole of the bubble. Further findings are the longevity of the magnetic bubbles and the ease of manipulation with standard magnets.

Modeling of nonlinear random wave fields in nature (and, in particular, their most common example—wind waves in the ocean) is one of the fundamental open problems of natural sciences. The existing theoretical approaches based on the kinetic equation paradigm assume a proximity to stationarity and homogeneity. In reality this assumption is often violated and how a wave field evolves is not known. We show by direct numerical simulation that after a strong perturbation the wave field evolves on the much faster $O({\epsilon }^{-2})$ “dynamic” [rather then $O({\epsilon }^{-4})$ “kinetic”] time scale; here $\epsilon$ is the characteristic wave steepness ($\epsilon \ll 1$). The phenomenon of fast evolution is universal, and it must occur whenever there is a strong external perturbation.

In the absence of nonlinearity all eigenmodes of a chain with disorder are spatially localized (Anderson localization). The width of the eigenvalue spectrum and the average eigenvalue spacing inside the localization volume set two frequency scales. An initially localized wave packet spreads in the presence of nonlinearity. Nonlinearity introduces frequency shifts, which define three different evolution outcomes: (i) localization as a transient, with subsequent subdiffusion; (ii) the absence of the transient and immediate subdiffusion; (iii) self-trapping of a part of the packet and subdiffusion of the remainder. The subdiffusive spreading is due to a finite number of packet modes being resonant. This number does not change on average and depends only on the disorder strength. Spreading is due to corresponding weak chaos inside the packet, which slowly heats the cold exterior. The second moment of the packet grows as $t^{\alpha }$. We find $\alpha =\frac{1}{3}$.

The periodic structure of a photonic crystal causes the propagating waves to be governed by Bloch’s theorem: they are composed of multiple wave vectors or harmonics. We found, by measuring the field with phase-sensitive near-field microscopy, that the evanescent field of the composite Bloch wave decays nonexponentially as a function of height. Even the individual Bloch harmonics, having only a single wave vector along the propagation direction, do not necessarily decay single exponentially, which has its origin in the spread of wave vectors required to confine the light to the waveguide. The complex decay leads to an evolution of the mode pattern as a function of the height above the structure.

We experimentally demonstrate a chiral metamaterial exhibiting negative refractive index at terahertz frequencies. The presence of strong chirality in the terahertz metamaterial lifts the degeneracy for the two circularly polarized waves and allows for the achievement of negative refractive index without requiring simultaneously negative permittivity and negative permeability. The realization of terahertz chiral negative index metamaterials offers opportunities for investigation of their novel electromagnetic properties, such as negative refraction and negative reflection, as well as important terahertz device applications.

We investigate the effect of atomic interactions on $\delta$-kicked cold atoms. We show that the clearest signature of the nonlinear dynamics is a surprisingly abrupt cutoff that appears on the leading resonances. We show that this is due to an excitation path combining both Beliaev and Landau processes, with some analogies to nonlinear self-trapping. Investigation of dynamical instability reveals further symptoms of nonlinearity such as a regime of exponential oscillations.

We report the enhanced transmission of electromagnetic waves through a single subwavelength aperture by using a split-ring resonator (SRR) at microwave frequencies. By placing a single SRR at the near field of the aperture, strongly localized electromagnetic fields are effectively coupled to the aperture with a radius that is 20 times smaller than the resonance wavelength ($r/\lambda =0.05$). We obtained 740-fold transmission enhancement by exciting the electric resonance of SRR. A different coupling mechanism, through the magnetic resonance of SRR, is also verified to lead to enhanced transmission.

Quantum cascade lasers are a unique laboratory for studying nonlinear laser dynamics because of their high intracavity intensity, strong intersubband optical nonlinearity, and an unusual combination of relaxation time scales. Here we investigate the nonlinear coupling between the transverse modes of quantum cascade lasers. We present evidence for stable phase coherence of multiple transverse modes over a large range of injection currents. We explain the phase coherence by a four-wave mixing interaction originating from the strong optical nonlinearity of the gain transition. The phase-locking conditions predicted by theory are supported by spectral data and both near- and far-field mode measurements.

We report on the experimental demonstration of an all-optical $\pi$ cross-phase modulation jump. By performing a preselection, an optically induced unitary transformation, and then a postselection on the polarization degree of freedom, the phase of the output beam acquires either a zero or $\pi$ phase shift (with no other possible values). The postselection results in optical loss in the output beam. An input state may be chosen near the resulting phase singularity, yielding a $\pi$ phase shift even for weak interaction strengths. The scheme is experimentally demonstrated using a coherently prepared dark state in a warm atomic cesium vapor.

We demonstrate, for the first time, high-order harmonic generation from ${\mathrm{C}}_{60}$ by an intense femtosecond Ti:sapphire laser. Laser-produced plasmas from ${\mathrm{C}}_{60}$-rich epoxy and ${\mathrm{C}}_{60}$ films were used as the nonlinear media. Harmonics up to the 19th order were observed. The harmonic yield from fullerene-rich plasma is about 25 times larger compared with those produced from a bulk carbon target. Structural studies of plasma debris confirm the presence and integrity of fullerenes within the plasma plume, indicating fullerenes as the source of high-order harmonics.

We report on a stochastic analysis of Earth’s vertical velocity time series by using methods originally developed for complex hierarchical systems and, in particular, for turbulent flows. Analysis of the fluctuations of the detrended increments of the series reveals a pronounced transition in their probability density function from Gaussian to non-Gaussian. The transition occurs 5–10 hours prior to a moderate or large earthquake, hence representing a new and reliable precursor for detecting such earthquakes.

We examine the complex dynamics arising when a water droplet bounces on a horizontal soap film suspended on a vertically oscillating circular frame. A variety of simple and complex periodic bouncing states are observed, in addition to multiperiodicity and period-doubling transitions to chaos. The system is simply and accurately modeled by a single ordinary differential equation, the numerical solution of which captures all the essential features of the observed behavior. Iterative maps and bifurcation diagrams indicate that the system exhibits all the features of a classic low-dimensional chaotic oscillator.

We characterize the spectral properties of weak turbulence in a liquid crystal sample driven by an external electric field, as a function of the applied voltage, and we find a $1/f$ noise spectrum $S(f)\propto 1/f^{\eta }$ within the whole range $0<\eta <2$. We theoretically explore the hypothesis that the system complexity is driven by non-Poisson events resetting the system through creation and annihilation of coherent structures, retaining no memory of previous history (crucial events). We study the time asymptotic regime by means of the density $\psi (\tau )$ of the time distances between two crucial events, yielding $\eta =3-\mu$, where $\mu$ is defined through the long-time form $\psi (\tau )\propto 1/{\tau }^{\mu }$, with $1<\mu <3$. The system regression to equilibrium after an abrupt voltage change experimentally confirms the theory, proving violations of the ordinary linear response theory for both $\eta >1$ and $\eta <1$.

We study the transition from fluid at rest to turbulence in a rotating tank. The energy is transported by inertial wave packets through the fluid volume. These high amplitude waves propagate at velocities consistent with those calculated from linearized theory [H. P. Greenspan, The Theory of Rotating Fluids (Cambridge University Press, Cambridge, England, 1968)]. A “front” in the temporal evolution of the energy power spectrum indicates a time scale for energy transport at the linear wave speed. Nonlinear energy transfer between modes is governed by a different, longer, time scale. The observed mechanisms can lead to significant differences between rotating and two-dimensional turbulent flows.