We examine theoretically the effects of random topographical substrates on the motion of two-dimensional droplets via statistical approaches, by representing substrate families as stationary random functions. The droplet shift variance at both early times and in the long-time limit is deduced and the droplet footprint is found to be a normal random variable at all times. It is shown that substrate roughness inhibits wetting, illustrating also the tendency of the droplet to slide without spreading as equilibrium is approached. Our theoretical predictions are verified by numerical experiments.

The phonon analog of an optical laser has long been a subject of interest. We demonstrate a compound microcavity system, coupled to a radio-frequency mechanical mode, that operates in close analogy to a two-level laser system. An inversion produces gain, causing phonon laser action above a pump power threshold of around $7\mu \mathrm{W}$. The device features a continuously tunable gain spectrum to selectively amplify mechanical modes from radio frequency to microwave rates. Viewed as a Brillouin process, the system accesses a regime in which the phonon plays what has traditionally been the role of the Stokes wave. For this reason, it should also be possible to controllably switch between phonon and photon laser regimes. Cooling of the mechanical mode is also possible.

We describe the resonant excitation of a single quantum dot that is strongly coupled to a photonic crystal nanocavity. The cavity represents a spectral window for resonantly probing the optical transitions of the quantum dot. We observe narrow absorption lines attributed to the single and biexcition quantum dot transitions and measure antibunched population of the detuned cavity mode [$g^{(2)}(0)=0.19$].

Wearless friction force experiments [Science 309, 1354 (2005)] have recently demonstrated that tribological response in quasicrystals could be related to the exotic atomic structure of the bulk material. Here, by numerical simulations, we address the origin of the experimentally observed friction anisotropy on a twofold decagonal quasicrystal surface. We predict the distinct stick-slip patterns in the lateral force along the periodic and quasiperiodic directions, specifically exploring the temperature dependence that rules the transitions between single and multiple-slip regimes of motion.

Much of the surface of Mars is covered by dunes, ripples, and other features formed by the blowing of sand by wind, known as saltation. In addition, saltation loads the atmosphere with dust aerosols, which dominate the Martian climate. We show here that saltation can be maintained on Mars by wind speeds an order of magnitude less than required to initiate it. We further show that this hysteresis effect causes saltation to occur for much lower wind speeds than previously thought. These findings have important implications for the formation of dust storms, sand dunes, and ripples on Mars.

We consider the nonlinear tunneling of a plane wave through a small barrier potential in a medium with self-defocusing, or repulsive, interactions. We show that nonlinearity can either suppress or enhance transmission rates, determined by whether the initial kinetic energy is above or below the barrier height. Associated with this threshold is the appearance of two distinct hysteresis loops, going clockwise or counterclockwise, respectively. Spatial dynamics upon reflection and transmission reveals the formation of dispersive shock waves (dark soliton trains) due to phase jumps at the interfaces and wave steepening during propagation. The results are demonstrated experimentally for optical wave tunneling through a refractive index defect but will hold for any Schrödinger system that contains a nonlinear junction.

The first observation of fast and slow magnetocoriolis (MC) waves in a laboratory experiment is reported. Rotating nonaxisymmetric modes arising from a magnetized turbulent Taylor-Couette flow of liquid metal are identified as the fast and slow MC waves by the dependence of the rotation frequency on the applied field strength. The observed slow MC wave is damped but the observation provides a means for predicting the onset of the magnetorotational instability.

We demonstrate that a single subcycle optical pulse can be generated when a pulse with a few optical cycles penetrates through resonant two-level dense media with a subwavelength structure. The single-cycle gap soliton phenomenon in the full Maxwell-Bloch equations without the frame of the slowly varying envelope and rotating wave approximations is observed. Our study shows that the subwavelength structure can be used to suppress the frequency shift caused by intrapulse four-wave mixing in continuous media and supports the formation of single-cycle gap solitons even in the case when the structure period breaks the Bragg condition. This suggests a way toward shortening high-intensity laser fields to few- and even single-cycle pulse durations.

Under appropriate conditions, a column of viscous liquid falling onto a rigid surface undergoes a buckling instability. Here we show experimentally and theoretically that liquid buckling exhibits a hitherto unsuspected complexity involving three different modes—viscous, gravitational, and inertial—depending on how the viscous forces that resist bending of the column are balanced. We also find that the nonlinear evolution of the buckling exhibits a surprising multistability with three distinct states: steady stagnation flow, “liquid rope coiling,” and a new state in which the column simultaneously folds periodically and rotates about a vertical axis. The transitions among these states are subcritical, leading to a complex phase diagram in which different combinations of states coexist in different regions of the parameter space.

Simulations show that a static electric field periodically distributed in space can be used to control the production of coherent light by high-order harmonic generation in a wide spectral range covering extreme-ultraviolet and soft x-ray radiation. The radiation yield is selectively enhanced due to symmetry breaking induced by a static electric field on the interaction between the driving laser and the medium. The spectral position of the enhancement is tuned by varying the periodicity of the static electric field which matches twice the coherence length of the harmonics in the desired region. We find that the static electric field strength inducing enhancement decreases for shorter wavelengths and predict an increase of more than two orders of magnitude for harmonics in the water window spectral range with a static electric field as weak as $1.12\mathrm{MV}/\mathrm{cm}$.

We study the scattering of waves off a potential step in deformed honeycomb lattices. For deformations below a critical value, perfect Klein tunneling is obtained; i.e., a potential step transmits waves at normal incidence with nonresonant unit-transmission probability. Beyond the critical deformation a gap forms in the spectrum, and a potential step perpendicular to the deformation direction reflects all normally incident waves, exhibiting a dramatic transition form unit transmission to total reflection. These phenomena are generic to honeycomb lattices and apply to electromagnetic waves in photonic lattices, quasiparticles in graphene, and cold atoms in optical lattices.

We reveal that orbital angular momentum can suppress catastrophic self-focusing in nonlinear Kerr media supporting stable spiraling solitons with an elliptic cross section. We discuss the necessary requirements for observation of this effect with coherent optical and matter waves.

We show how discrete solitary waves in one and two-dimensional waveguide arrays can be steered across the lattice via the introduction of a longitudinal periodic modulation of the nonlinear response. Through parametric energy transfer from the modulation to the solitary wave, the latter can increase its width and overcome the Peierls-Nabarro potential to propagate freely.

We study a new class of chaotic systems with dynamical localization, where gain or loss mechanisms break the Hermiticity, while allowing for parity-time ($\mathcal{P}\mathcal{T}$) symmetry. For a value ${\gamma }_{\mathcal{P}\mathcal{T}}$ of the gain or loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for ${\gamma }_{\mathcal{P}\mathcal{T}}$, and show that chaos assists the exact $\mathcal{P}\mathcal{T}$ phase. Our results have applications to the design of optical elements with $\mathcal{P}\mathcal{T}$ symmetry.

We fabricated an acoustic composite structure consisting of a periodic array of interspaced membranes and side holes. Experimental data on the transmission, effective density, and phase velocity are presented. The system exhibits two critical frequencies, ${\omega }_{\mathrm{SH}}$ and ${\omega }_c$. Our metamaterial is double negative and transparent for frequencies lower than ${\omega }_{\mathrm{SH}}$. For the frequencies ${\omega }_{\mathrm{SH}}<\omega <{\omega }_c$, the medium is opaque and only the density is negative. For the frequencies above ${\omega }_c$, the system is double positive and transparent. The present medium exhibits a very wide double negative spectral range that opens the possibility of the application of metamaterials for “white lights.”

A one-dimensional model of the coherent amplification in a high- and swept-gain amplifier in the presence of strong spontaneous emission is presented and applied to seeding an x-ray laser with a high harmonic pulse. The atomic structure of the amplifying medium includes level degeneracy, and the Maxwell-Bloch equations are used to describe the propagation and interaction processes. This analysis elucidates, in the most comprehensive way, the influence of the random spontaneous emission on the coherent amplification process, as reflected in the basic pulse parameters such as its shape, polarization, and coherence.

We report theoretically and experimentally in an optical system a process of anomalous thermalization of one-dimensional nonlinear Hamiltonian waves. It is characterized by an irreversible evolution of the waves towards a specific equilibrium state of a fundamental different nature than the expected thermodynamic equilibrium state. A kinetic approach of the problem reveals that this phenomenon is due to the existence of a local invariant in frequency space. A novel family of equilibrium distributions is discovered, which is found in quantitative agreement with the numerical simulations.

Using cinematic digital holography, we demonstrate that turbulent breakup of crude oil mixed with dispersants into microdroplets starts with the formation of very long and quite stable, single or multiple microthreads that trail behind $300–1400\mu \mathrm{m}$ droplets. These threads extend from Reynolds number dependent regions with high surfactant concentration, which, along with associated viscosities and stretching by turbulence stabilizes the threads. The subsequent breakup, producing $2.8\mu \mathrm{m}$ droplets, is due to an increasing surface area and diffusion of dispersants into the continuous phase.

Photonic graphene is a two-dimensional photonic crystal structure that is analogous to graphene. We use 5 mm diameter ${\mathrm{Al}}_2{\mathrm{O}}_3$ rods placed on a triangular lattice with a lattice constant $a=8\mathrm{mm}$ to create an isolated conical singularity in the photonic band structure at a microwave frequency of 17.6 GHz. At this frequency, the measured transmission of microwaves through a perfectly ordered structure enters a pseudodiffusive regime where the transmission scales inversely with the thickness $L$ of the crystal ($L/a\gtrsim 5$). The transmission depends critically on the configuration of the edges: distinct oscillations with an amplitude comparable to the transmission are observed for structures terminated with zigzag edges, while these oscillations are absent for samples with a straight edge configuration.

Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to zero. But if the coupling is nonlocal, a new kind of spiral can occur, with a circular core consisting of desynchronized oscillators running at full amplitude. Here, we provide the first analytical description of such a spiral wave chimera and use perturbation theory to calculate its rotation speed and the size of its incoherent core.