We demonstrate that arbitrarily weak magnetic field may cause violent instability of an anticyclonic, recirculating flow with uniform mean angular velocity. This magnetohydrodynamic instability would trigger turbulence in the cores of vortices where neither centrifugal, exchange instability, nor magnetorotational instability is effective. In the accretion disk vortices this can be an important mechanism of enhanced outward transport of angular momentum.

The existence, stability properties, and dynamical evolution of localized spatiotemporal chaos are studied. We provide evidence of spatiotemporal chaotic localized structures in a liquid crystal light valve experiment with optical feedback. The observations are supported by numerical simulations of the Lifshitz model describing the system. This model exhibits coexistence between a uniform state and a spatiotemporal chaotic pattern, which emerge as the necessary ingredients to obtain localized spatiotemporal chaos. In addition, we have derived a simplified model that allows us to unveil the front interaction mechanism at the origin of the localized spatiotemporal chaotic structures.

We study experimentally the synchronization patterns in time-delayed directed Boolean networks of excitable systems. We observe a transition in the network dynamics when the refractory time of the individual systems is adjusted. When the refractory time is on the same order of magnitude as the mean link time delays or the heterogeneities of the link time delays, cluster synchronization patterns change, or are suppressed entirely, respectively. We also show that these transitions occur when we change the properties of only a small number of driver nodes identified by their larger in degree; hence, the synchronization patterns can be controlled locally by these nodes. Our findings have implications for synchronization in biological neural networks.

We study analytically, numerically, and experimentally the nonlinear symmetry breaking induced by broken reflection symmetry in an optical fiber system. In particular, we investigate the modulation instability regime and reveal the key role of the third-order dispersion on the asymmetry in the spectrum of the dissipative structures. Our theory explains early observations, and the predictions are in excellent agreement with our experimental findings.

Crumpling and folding of paper are at first sight very different ways of confining thin sheets in a small volume: the former one is random and stochastic whereas the latest one is regular and deterministic. Nevertheless, certain similarities exist. Crumpling is surprisingly inefficient: a typical crumpled paper ball in a waste-bin consists of as much as 80% air. Similarly, if one folds a sheet of paper repeatedly in two, the necessary force becomes so large that it is impossible to fold it more than six or seven times. Here we show that the stiffness that builds up in the two processes is of the same nature, and therefore simple folding models allow us to capture also the main features of crumpling. An original geometrical approach shows that crumpling is hierarchical, just as the repeated folding. For both processes the number of layers increases with the degree of compaction. We find that for both processes the crumpling force increases as a power law with the number of folded layers, and that the dimensionality of the compaction process (crumpling or folding) controls the exponent of the scaling law between the force and the compaction ratio.

We present direct statistical simulation of jet formation on a $\beta$ plane, solving for the statistics of a fluid flow via an expansion in cumulants. Here we compare an expansion truncated at second order (CE2) to statistics accumulated by direct numerical simulations. We show that, for jets near equilibrium, CE2 is capable of reproducing the jet structure (although some differences remain in the second cumulant). However, as the degree of departure from equilibrium is increased (as measured by the zonostrophy parameter), the jets meander more and CE2 becomes less accurate. We discuss a possible remedy by inclusion of higher cumulants.

We demonstrate an inverse energy cascade in a minimal model of forced 2D quantum vortex turbulence. We simulate the Gross-Pitaevskii equation for a moving superfluid subject to forcing by a stationary grid of obstacle potentials, and damping by a stationary thermal cloud. The forcing injects large amounts of vortex energy into the system at the scale of a few healing lengths. A regime of forcing and damping is identified where vortex energy is efficiently transported to large length scales via an inverse energy cascade associated with the growth of clusters of same-circulation vortices, a Kolmogorov scaling law in the kinetic energy spectrum over a substantial inertial range, and spectral condensation of kinetic energy at the scale of the system size. Our results provide clear evidence that the inverse energy cascade phenomenon, previously observed in a diverse range of classical systems, can also occur in quantum fluids.

Do parametrically driven systems distinguish periodic excitations that are time mirrors of each other? Faraday waves in a Newtonian fluid are studied under excitation with superimposed harmonic wave forms. We demonstrate that the threshold parameters for the stability of the ground state are insensitive to a time inversion of the driving function. This is a peculiarity of some dynamic systems. The Faraday system shares this property with standard electroconvection in nematic liquid crystals [J. Heuer et al., Phys. Rev. E 78, 036218 (2008)]. In general, time inversion of the excitation affects the asymptotic stability of a parametrically driven system, even when it is described by linear ordinary differential equations. Obviously, the observed symmetry has to be attributed to the particular structure of the underlying differential equation system. The pattern selection of the Faraday waves above threshold, on the other hand, discriminates between time-mirrored excitation functions.

We prepare arrays of gold nanoparticles that include both noncentrosymmetric particles with a second-order nonlinear optical response (active particles) and centrosymmetric particles with no second-order response (passive particles). The plasmon resonances of the active and passive particles are at distinct wavelengths, yet the passive particles modify the electromagnetic modes of the structure in such a way that second-harmonic generation from the active particles is enhanced. Our results provide a completely new concept for optimizing the nonlinear responses of metamaterials.

We report a new type of standing gravity wave of large amplitude, having alternatively the shape of a star and of a polygon. This wave is observed by means of a laboratory experiment by vertically vibrating a tank. The symmetry of the star (i.e., the number of branches) is independent of the container form and size, and can be changed according to the amplitude and frequency of the vibration. We show that a nonlinear resonant coupling between three gravity waves can be envisaged to trigger the observed symmetry breaking, although more complex interactions certainly take place in the final periodic state.

We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph—its topology. We consider generic open graphs and show that any cycle leads to narrow resonances which do not fit in any of the prominent paradigms for narrow resonances (classical barriers, localization due to disorder, chaotic scattering). We call these resonances “topological” to emphasize their origin in the nontrivial connectivity. Topological resonances have a clear and unique signature which is apparent in the statistics of the resonance parameters (such as, e.g., the width, the delay time, or the wave-function intensity in the graph). We discuss this phenomenon by providing analytical arguments supported by numerical simulation, and identify the features of the above distributions which depend on genuine topological quantities such as the length of the shortest cycle (girth). These signatures cannot be explained using any of the other paradigms for narrow resonances. Finally, we propose an experimental setting where the topological resonances could be demonstrated, and study the stability of the relevant distribution functions to moderate dissipation.

Chimera states are surprising spatiotemporal patterns in which regions of coherence and incoherence coexist. Initially observed numerically, these mathematical oddities were recently reproduced in a laboratory setting, sparking a flurry of interest in their properties. Here we use asymptotic methods to derive the conditions under which two-dimensional “spot” and “stripe” chimeras (similar to those observed in experiments) can exist in a periodic space. We also discover a previously unobserved asymmetric chimera state, whose existence plays a major role in determining when other chimera states are observable in experiment and simulation. Finally, we use numerical methods to verify theoretical predictions and determine which states are dynamically stable.

Films are nanoscopic elements of foams, emulsions, and suspensions that form a paradigm for nanochannel transport that eventually tests the limits of hydrodynamic descriptions. Here, we study the collapse of a freestanding film to its equilibrium. The generation of nanoscale films usually is a slow linear process; using thermal forcing we find unprecedented dynamics with exponentially fast thinning. The complex interplay of thermal convection, interface, and gravitational forces yields optimal turbulent mixing and transport. Domains of collapsed film are generated, elongated, and convected in a beautiful display of chaotic mixing. With a time scale analysis, we identify mixing as the dominant dynamical process responsible for exponential thinning.

Optical diodes controlling the flow of light are of principal significance for optical information processing. They transmit light from an input to an output, but not in the reverse direction. This breaking of time reversal symmetry is conventionally achieved via Faraday or nonlinear effects. For applications in a quantum network, features such as the abilities of all-optical control, on-chip integration, and single-photon operation are important. Here we propose an all-optical optical diode which requires neither magnetic fields nor strong input fields. It is based on a “moving” photonic crystal generated in a three-level electromagnetically induced transparency medium in which the refractive index of a weak probe is modulated by the moving periodic intensity of a strong standing coupling field with two detuned counterpropagating components. Because of the Doppler effect, the frequency range of the crystal’s band gap for the probe copropagating with the moving crystal is shifted from that for the counterpropagating probe. This mechanism is experimentally demonstrated in a room temperature Cs vapor cell.

The one-dimensional Marchenko equation forms the basis for inverse scattering problems in which the scattering object is accessible from one side only. Here we derive a three-dimensional (3D) Marchenko equation which relates the single-sided reflection response of a 3D inhomogeneous medium to a field inside the medium. We show that this equation is solved by a 3D iterative data-driven focusing method, which yields the 3D Green’s function with its virtual source inside the medium. The 3D single-sided Marchenko equation and its iterative solution method form the basis for imaging of 3D strongly scattering inhomogeneous media that are accessible from one side only.

High order harmonic generation from clusters is a controversial topic: conflicting theories exist, with different explanations for similar experimental observations. From an experimental point of view, separating the contributions from monomers and clusters is challenging. By performing a spectrally and spatially resolved study in a controlled mixture of clusters and monomers, we are able to isolate a region of the spectrum where the emission purely originates from clusters. Surprisingly, the emission from clusters is depolarized, which is the signature of statistical inhomogeneous emission from a low-density source. The harmonic response to laser ellipticity shows that this generation is produced by a new recollisional mechanism, which opens the way to future theoretical studies.

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.

We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudospectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be recovered to full numerical precision by solving small-scale dynamical equations with the given large-scale solution as an input, regardless of initial condition. The synchronization rate exponent scales with the Kolmogorov dissipation time scale, with possible weak corrections due to intermittency. Our results suggest that all sub-Kolmogorov length modes should be fully recoverable from numerical simulations with standard, Kolmogorov-length grid resolutions.

High Reynolds number magnetohydrodynamic turbulence in the presence of zero-flux large-scale magnetic fields is investigated as a function of the magnetic field strength. For a variety of flow configurations, the energy dissipation rate $ϵ$ follows the scaling $ϵ\propto U_{\mathrm{rms}}^3/\ell$ even when the large-scale magnetic field energy is twenty times larger than the kinetic energy. A further increase of the magnetic energy showed a transition to the $ϵ\propto U_{\mathrm{rms}}^2{B}_{\mathrm{rms}}/\ell$ scaling implying that magnetic shear becomes more efficient at this point at cascading the energy than the velocity fluctuations. Strongly helical configurations form nonturbulent helicity condensates that deviate from these scalings. Weak turbulence scaling was absent from the investigation. Finally, the magnetic energy spectra support the Kolmogorov spectrum $k^{-5/3}$ while kinetic energy spectra are closer to the Iroshnikov-Kraichnan spectrum $k^{-3/2}$ as observed in the solar wind.

In this Letter we present experimental results concerning the retrieval of images of absorbing objects immersed in turbid media via differential ghost imaging (DGI) in a backscattering configuration. The method has been applied, for the first time to our knowledge, to the imaging of thin black objects located inside a turbid solution in proximity of its surface. We show that it recovers images with a contrast better than standard noncorrelated direct imaging, but equivalent to noncorrelated diffusive imaging. A simple theoretical model capable of describing the basic optics of DGI in turbid media is proposed.