We observe from simulations that a doubly resonant structure can exhibit spectral behavior analogous to electromagnetically induced transparency, as well as superscattering, depending on the excitation. We develop a coupled-mode theory that explains this behavior in terms of the orthogonality of the radiation patterns of the eigenmodes. These results provide insight in the general electromagnetic properties of photonic nanostructures and metamaterials.

We show experimentally and numerically that an intrinsic localized mode (ILM) can be stably produced (and experimentally observed) via subharmonic, spatially homogeneous driving in the context of a nonlinear electrical lattice. The precise nonlinear spatial response of the system has been seen to depend on the relative location in frequency between the driver frequency, ${\omega }_d$, and the bottom of the linear dispersion curve, ${\omega }_0$. If ${\omega }_d/2$ lies just below ${\omega }_0$, then a single ILM can be generated in a 32-node lattice, whereas, when ${\omega }_d/2$ lies within the dispersion band, a spatially extended waveform resembling a train of ILMs results. To our knowledge, and despite its apparently broad relevance, such an experimental observation of subharmonically driven ILMs has not been previously reported.

Liquid drops hitting solid surfaces deform substantially under the influence of the ambient air that needs to be squeezed out before the liquid actually touches the solid. Nanometer- and microsecond-resolved dual wavelength interferometry reveals a complex evolution of the interface between the drop and the gas layer underneath. For intermediate impact speeds ($\mathrm{We}\sim 1\dots 10$) the layer thickness can develop one or two local minima—reproduced in numerical calculations—that eventually lead to the nucleation of solid-liquid contact at a We-dependent radial position, from a film thickness $>200\mathrm{nm}$. Solid-liquid contact spreads at a speed involving capillarity, liquid viscosity and inertia.

Whether a thin filament of liquid separates into two or more droplets or eventually condenses lengthwise to form a single larger drop depends on the liquid’s density, viscosity, and surface tension and on the initial dimensions of the filament. Surface tension drives two competing processes, pinching-off and shortening, and the relative time scales of these, controlled by the balance between capillary and viscous forces, determine the final outcome. Here we provide experimental evidence for the conditions under which a liquid filament will break up into drops, in terms of a wide range of two dimensionless quantities: the aspect ratio of the filament and the Ohnesorge number. Filaments which do not break up into multiple droplets demand a high liquid viscosity or a small aspect ratio.

We address the crumpling of thin sheets in between large scale curved cylinders. In contrast with the usual crushing of a paper ball, one curvature of the sheet is fixed here by the cylinders radius, yielding an anisotropic compaction. As compaction proceeds, it is found that sheets first develop singular folds involving ridges or developable cones, but eventually turn to regular folds free of any geometrical singularities, without ever having entered the plastic regime. This surprising uncrumpling transition corresponds to a stress defocusing. It is understood from a balance between bending and stretching energies on regular states.

The commonly accepted description of drops impacting on a surface typically ignores the essential role of the air that is trapped between the impacting drop and the surface. Here we describe a new imaging modality that is sensitive to the behavior right at the surface. We show that a very thin film of air, only a few tens of nanometers thick, remains trapped between the falling drop and the surface as the drop spreads. The thin film of air serves to lubricate the drop enabling the fluid to skate on the air film laterally outward at surprisingly high velocities, consistent with theoretical predictions. Eventually this thin film of air breaks down as the fluid wets the surface via a spinodal-like mechanism. Our results show that the dynamics of impacting drops are much more complex than previously thought, with a rich array of unexpected phenomena that require rethinking classic paradigms.

Three-wave interactions form the basis of our understanding of many pattern-forming systems because they encapsulate the most basic nonlinear interactions. In problems with two comparable length scales, it is possible for two waves of the shorter wavelength to interact with one wave of the longer, as well as for two waves of the longer wavelength to interact with one wave of the shorter. Consideration of both types of three-wave interactions can generically explain the presence of complex patterns and spatiotemporal chaos. Two length scales arise naturally in the Faraday wave experiment, and our results enable some previously unexplained experimental observations of spatiotemporal chaos to be interpreted in a new light. Our predictions are illustrated with numerical simulations of a model partial differential equation.

Ptychographic coherent diffractive imaging (CDI) has been extensively applied using both x rays and electrons. The extension to atomic resolution has been elusive. This Letter demonstrates ptychographic electron diffractive imaging at atomic resolution, permitting identification of structure in a boron nitride helical cone at a resolution of order 1 Å, beyond that of comparative $Z$-contrast images. A scanning transmission electron microscope is used to create a diverging illumination in a defocused Fresnel CDI geometry, providing a robust strategy leading to a unique solution.

Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap between two parallel plates is an archetypical problem of pattern formation. We find a surprisingly effective means of suppressing this instability by replacing one of the plates with an elastic membrane. The resulting fluid-structure interaction fundamentally alters the interfacial patterns that develop and considerably delays the onset of fingering. We analyze the dependence of the instability on the parameters of the system and present scaling arguments to explain the experimentally observed behavior.

Fractal decimation reduces the effective dimensionality $D$ of a flow by keeping only a (randomly chosen) set of Fourier modes whose number in a ball of radius $k$ is proportional to $k^D$ for large $k$. At the critical dimension $D_c=4/3$ there is an equilibrium Gibbs state with a $k^{-5/3}$ spectrum, as in V. L’vov et al., Phys. Rev. Lett. 89, 064501 (2002). Spectral simulations of fractally decimated two-dimensional turbulence show that the inverse cascade persists below $D=2$ with a rapidly rising Kolmogorov constant, likely to diverge as $(D-4/3{)}^{-2/3}$.

We show that the powerful framework of transformation optics may be exploited for engineering the nonlocal response of artificial electromagnetic materials. Relying on the form-invariant properties of coordinate-transformed Maxwell’s equations in the spectral domain, we derive the general constitutive “blueprints” of transformation media yielding prescribed nonlocal field-manipulation effects and provide a physically incisive and powerful geometrical interpretation in terms of deformation of the equifrequency contours. In order to illustrate the potentials of our approach, we present an example of application to a wave-splitting refraction scenario, which may be implemented via a simple class of artificial materials. Our results provide a systematic and versatile framework which may open intriguing venues in dispersion engineering of artificial materials.

We study a classical billiard of charged particles in a strong nonuniform magnetic field. We provide an adiabatic description for skipping motion along the boundary of the billiard. We show that a sequence of many changes of regimes of motion from skipping to motion without collisions with the boundary and back to skipping leads to destruction of the adiabatic invariance and chaotic dynamics in a large domain in the phase space. This is a new mechanism of the origin of chaotic dynamics for systems with impacts.

It is shown that the evolution equations describing partially coherent wave propagation in noninstantaneous Kerr media are integrable and have an infinite number of invariants. A recursion relation for generating these invariants is presented, and it is demonstrated how to express them in the coherent density, self-consistent multimode, mutual coherence, and Wigner formalisms.

A record is an entry in a time series that is larger or smaller than all previous entries. If the time series consists of independent, identically distributed random variables with a superimposed linear trend, record events are positively (negatively) correlated when the tail of the distribution is heavier (lighter) than exponential. Here we use these correlations to detect heavy-tailed behavior in small sets of independent random variables. The method consists of converting random subsets of the data into time series with a tunable linear drift and computing the resulting record correlations.

Efflorescence refers to crystallized salt structures that form at the surface of a porous medium. The challenge is to understand why these structures do not form everywhere at the surface of the porous medium but at some specific locations and why there exists an exclusion distance around an efflorescence where no new efflorescence forms. These are explained from a visualization experiment, pore-network simulations and a simple efflorescence growth model.

Using compressed gases with Prandtl numbers near 0.7, we obtained flow visualizations of turbulent Rayleigh-Bénard convection in a cylindrical sample with an aspect ratio $\Gamma \equiv D/L\cong 10$ ($D$ is the diameter and $L$ the height) by the shadowgraph method. Focusing on the plumes under the top plate, we found that their length had a log-normal distribution, suggesting a fragmentation process. Fragmentation events could be visually identified in the images and involved plume interactions with bulk fluctuations or upwelling domain walls. We found the mean spacing between plumes to vary with the Rayleigh number in proportion to the volume-averaged Kolmogorov length of the turbulent bulk fluctuations, providing further evidence for plume-bulk interactions.

In this Letter we present turbulent flame speeds and their scaling from experimental measurements on constant-pressure, unity Lewis number expanding turbulent flames, propagating in nearly homogeneous isotropic turbulence in a dual-chamber, fan-stirred vessel. It is found that the normalized turbulent flame speed as a function of the average radius scales as a turbulent Reynolds number to the one-half power, where the average radius is the length scale and the thermal diffusivity is the transport property, thus showing self-similar propagation. Utilizing this dependence it is found that the turbulent flame speeds from the present expanding flames and those from the Bunsen geometry in the literature can be unified by a turbulent Reynolds number based on flame length scales using recent theoretical results obtained by spectral closure of the transformed $G$ equation.

We experimentally investigate the phase of an optical field after it has undergone wave collapse. We confirm the theoretical prediction that it acquires a large cumulative nonlinear phase shift that is highly sensitive to small fluctuations of the laser input power. This results in an effective postcollapse “loss of phase,” whereby the phase of the transmitted beam shows a significant increase in sensitivity to the input fluctuations of the pulse energy. We also investigate interactions between two beams that each undergoes collapse and observe large fluctuations in the output mode profiles, which are due to the postcollapse loss of their relative phase difference. Such effects should occur in all systems that exhibit wave collapse.

We show that a new type of coherent structure, a shock modon, exists in a rotating shallow water model at large Rossby numbers. It is a combination of an asymmetric vortex dipole with a stationary hydraulic jump. The structure is long living, despite the energy dissipation by the hydraulic jump, and moving along a circular path. Collisions of shock modons can be elastic, or lead to formation of shock tripoles.

When a boundary layer starts to develop spatially over a flat plate, only disturbances of sufficiently large amplitude survive and trigger turbulence subcritically. Direct numerical simulation of the Blasius boundary-layer flow is carried out to track the dynamics in the region of phase space separating transitional from relaminarizing trajectories. In this intermediate regime, the corresponding disturbance is fully localized and spreads slowly in space. This structure is dominated by a robust pair of low-speed streaks, whose convective instabilities spawn hairpin vortices evolving downstream into transient disturbances. A quasicyclic mechanism for the generation of offspring is unfolded using dynamical rescaling with the local boundary-layer thickness.