We have solved the long-standing problem of the mechanism of terahertz (THz) generation by a two-color filament in air and found that both neutrals and plasma contribute to the radiation. We reveal that the contribution from neutrals by four-wave mixing is much weaker and higher in frequency than the distinctive plasma lower-frequency contribution. The former is in the forward direction while the latter is in a cone and reveals an abrupt down-shift to the plasma frequency. Ring-shaped spatial distributions of the THz radiation are shown to be of universal nature and they occur in both collimated and focusing propagation geometries. Experimental measurements of the frequency-angular spectrum generated by 130-fs laser pulses agree with numerical simulations based on a unidirectional pulse propagation model.

We use 57 recently found topological satellites of Broucke-Hadjidemetriou-Hénon’s periodic orbits with values of the topological exponent $k$ ranging from $k=3$ to $k=58$ to plot the angular momentum $L$ as a function of the period $T$, with both $L$ and $T$ rescaled to energy $E=-0.5$. Upon plotting $L(T/k)$ we find that all our solutions fall on a curve that is virtually indiscernible by the naked eye from the $L(T)$ curve for nonsatellite solutions. The standard deviation of the satellite data from the sixth-order polynomial fit to the progenitor data is $\sigma =0.13$. This regularity supports Hénon’s 1976 conjecture that the linearly stable Broucke-Hadjidemetriou-Hénon orbits are also perpetually, or Kol’mogorov-Arnol’d-Moser, stable.

When a liquid droplet impacts a hot solid surface, enough vapor may be generated under it to prevent its contact with the solid. The minimum solid temperature for this so-called Leidenfrost effect to occur is termed the Leidenfrost temperature, or the dynamic Leidenfrost temperature when the droplet velocity is non-negligible. We observe the wetting or drying and the levitation dynamics of the droplet impacting on an (isothermal) smooth sapphire surface using high-speed total internal reflection imaging, which enables us to observe the droplet base up to about 100 nm above the substrate surface. By this method we are able to reveal the processes responsible for the transitional regime between the fully wetting and the fully levitated droplet as the solid temperature increases, thus shedding light on the characteristic time and length scales setting the dynamic Leidenfrost temperature for droplet impact on an isothermal substrate.

We demonstrate that waves excited on a fluid surface produce local surface rotation owing to hydrodynamic nonlinearity. We examine theoretically the effect and obtain an explicit formula for the vertical vorticity in terms of the surface elevation. Our theoretical predictions are confirmed by measurements of surface motion in a cell with water where surface waves are excited by vertical and harmonic shaking the cell. The experimental data are in good agreement with the theoretical predictions. We discuss physical consequences of the effect.

The statistical properties of interacting strongly chaotic systems are investigated for varying interaction strength. In order to model tunable entangling interactions between such systems, we introduce a new class of random matrix transition ensembles. The nearest-neighbor-spacing distribution shows a very sensitive transition from Poisson statistics to those of random matrix theory as the interaction increases. The transition is universal and depends on a single scaling parameter only. We derive the analytic relationship between the model parameters and those of a bipartite system, with explicit results for coupled kicked rotors, a dynamical systems paradigm for interacting chaotic systems. With this relationship the spectral fluctuations for both are in perfect agreement. An accurate approximation of the nearest-neighbor-spacing distribution as a function of the transition parameter is derived using perturbation theory.

An optimal parametric feedback excitation principle is sought, found, and investigated. The principle is shown to provide an adaptive resonance condition that enables unprecedentedly robust movement generation in a large class of oscillatory dynamical systems. Experimental demonstration of the theory is provided by a nonlinear electronic circuit that realizes self-adaptive parametric excitation without model information, signal processing, and control computation. The observed behavior dramatically differs from the one achievable using classical parametric modulation, which is fundamentally limited by uncertainties in model information and nonlinear effects inevitably present in real world applications.

We demonstrate the existence of stable three-dimensional dissipative localized structures in the output of a laser coupled to a distant saturable absorber. These phase invariant cavity light bullets are individually addressable and can be envisioned for three-dimensional optical information storage. An effective theory provides for an intuitive picture and allows us to relate their formation to the morphogenesis of static spatial autosolitons and temporal cellular patterns.

We characterize the nonlinear stage of modulational instability (MI) by studying the longtime asymptotics of the focusing nonlinear Schrödinger (NLS) equation on the infinite line with initial conditions tending to constant values at infinity. Asymptotically in time, the spatial domain divides into three regions: a far left and a far right field, in which the solution is approximately equal to its initial value, and a central region in which the solution has oscillatory behavior described by slow modulations of the periodic traveling wave solutions of the focusing NLS equation. These results demonstrate that the asymptotic stage of MI is universal since the behavior of a large class of perturbations characterized by a continuous spectrum is described by the same asymptotic state.

We present a spatiotemporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction, and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg-Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatiotemporal vortex-mediated turbulence with high excursions in amplitude. Nonlinear amplification leads to rogue waves close to turbulent optical vortices, where the amplitude tends to zero, and to probability density functions (PDFs) with long tails typical of extreme optical events.

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms of a Duffing oscillator. Using a real-time analog indicator able to discriminate on-the-fly periodic behaviors from chaos, we reconstruct experimentally the phase versus perturbation strength stability areas when periodic perturbations are applied to different terms governing the oscillator. We verify the system to be more sensitive to perturbations applied to the quadratic term of the double-well Duffing oscillator and to the quartic term of the single-well Duffing oscillator.

In this work, the manipulation of an electrically charged droplet bouncing on a vertically vibrated bath is investigated. When a horizontal, uniform, and static electric field is applied to it, a motion is induced. The droplet is accelerated when the droplet is small. On the other hand, large droplets appear to move with a constant speed that depends linearly on the applied electrical field. In the latter regime, high-speed imaging of one bounce reveals that the droplet experiences an acceleration due to the electrical force during the flight and decelerates to 0 when interacting with the surface of the bath. Thus, the droplet moves with a constant average speed on a large time scale. We propose a criterion based on the force necessary to move a charged droplet at the surface of the bath to discriminate between constant speed and accelerated droplet regimes.

We use advanced statistical tools of time-series analysis to characterize the dynamical complexity of the transition to optical wave turbulence in a fiber laser. Ordinal analysis and the horizontal visibility graph applied to the experimentally measured laser output intensity reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods unveil coherent structures with well-defined time scales and strong correlations both, in the timing of the laser pulses and in their peak intensities. Our approach is generic and may be used in other complex systems that undergo similar transitions involving the generation of extreme fluctuations.

We report the Prandtl-number (Pr) and Rayleigh-number (Ra) dependencies of the Reynolds number (Re) and mean convective heat transport, measured by the Nusselt number (Nu), in horizontal convection (HC) systems, where the heat supply and removal are provided exclusively through a lower horizontal surface of a fluid layer. For laminar HC, we find that $\mathrm{Re}\sim {\mathrm{Ra}}^{2/5}{\mathrm{Pr}}^{-4/5}$, $\mathrm{Nu}\sim {\mathrm{Ra}}^{1/5}{\mathrm{Pr}}^{1/10}$ with a transition to $\mathrm{Re}\sim {\mathrm{Ra}}^{1/2}{\mathrm{Pr}}^{-1}$, $\mathrm{Nu}\sim {\mathrm{Ra}}^{1/4}{\mathrm{Pr}}^0$ for large Pr. The results are based on direct numerical simulations for Ra from $3\times {10}^8$ to $5\times {10}^{10}$ and Pr from 0.05 to 50 and are explained by applying the Grossmann-Lohse approach [J. Fluid Mech. 407, 27 (2000)] transferred from the case of Rayleigh-Bénard convection to the case of laminar HC.

We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to the well-known macroscopic theories in appropriate limits, including compressible Navier-Stokes and wave equations. Moreover, we show that the dynamics proposed allows for long wavelength phonon modes and demonstrate the theory numerically showing that the elastic excitations in the system are relaxed through phonon emission.

We study distributions of the ratios of level spacings of rectangular and Africa-shaped superconducting microwave resonators containing circular scatterers on a triangular grid, so-called Dirac billiards (DBs). The high-precision measurements allowed the determination of, respectively, all 1651 and 1823 eigenfrequencies in the first two bands. The resonance densities are similar to that of graphene. They exhibit two sharp peaks at the van Hove singularities which separate the band structure into regions with a linear and a quadratic dispersion relation, respectively. In the vicinity of the van Hove singularities we observe rapid changes in, e.g., the wave function structure. Accordingly, we question whether the spectral properties are there still determined by the shapes of the DBs. The commonly used statistical measures are no longer applicable; however, we demonstrate in this Letter that the ratio distributions provide suitable measures.

Extreme events such as rogue waves in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme event appearance in a spatially extended semiconductor microcavity laser with an intracavity saturable absorber. This system can display deterministic irregular dynamics only, thanks to spatial coupling through diffraction of light. We have identified parameter regions where extreme events are encountered and established the origin of this dynamics in the emergence of deterministic spatiotemporal chaos, through the correspondence between the proportion of extreme events and the dimension of the strange attractor.

Spherical shock wave implosion in argon is studied both theoretically and experimentally. It is shown that as the strength of the converging shock increases the nonideal gas effects become dominant and govern the evolution of thermal and transport gas properties limiting the shock acceleration, lowering the gas adiabatic index and the achievable energy density at the focus. Accounting for multiple-level ionization, excitation, Coulomb interaction and radiation effects, the limiting equilibrium temperatures to be achieved during the shock implosion are estimated. Focal temperatures of the order of 30 000 K are measured in experiments where converging spherical shock waves are created using a conventional gas-dynamic shock tube facility.