We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from superdiffusion to normal diffusion, as a function of the distance fallen, independent of the flow speed. In the superdiffusive (but sub-ballistic) regime, which occurs before a particle falls through its diameter, the displacements have fat-tailed and anisotropic distributions. In the diffusive regime, we observe very slow cage breaking and Péclet numbers of order 100, contrary to the only previous microscopic model (based on diffusing voids). Overall, our experiments show that diffusion and mixing are dominated by geometry, consistent with long-lasting contacts but not thermal collisions, as in normal fluids.

Phase domains and phase solitons in two-level amplifying media damped by a squeezed vacuum are predicted for the first time. Two different types of pattern formation are found depending on the relative value of the cavity detuning to the squeezed parameter: the usual one in lasers via a supercritical Hopf bifurcation and a new one via pitchfork bifurcation.

We report the first experimental observation of modulation instability in a discrete optical nonlinear array.

A method is presented to reconstruct the structure of a scattering object from data acquired with a photon scanning tunneling microscope . The data may be understood to form a Gabor type near-field hologram and are obtained at a distance from the sample where the field is defocused and normally uninterpretable. Object structure is obtained by the solution of the inverse scattering problem within the accuracy of a perturbative, two-dimensional model of the object.

A new approach to the construction and optimization of local models is proposed in the context of data streams, that is, unlimited sources of data where the utilization of all observations is impractical. Real-time revision of the learning set allows selective coverage of regions in state space which contribute most to reconstructing the underlying dynamical system.

We study the statistics of the power flux into a collection of inelastic beads maintained in a fluidized steady state by external mechanical driving. The power shows large fluctuations, including frequent large negative fluctuations, about its average value. The relative probabilities of positive and negative fluctuations in the power flux are in close accord with the fluctuation theorem of Gallavotti and Cohen, even at time scales shorter than those required by the theorem. We also compare an effective temperature that emerges from this analysis to the kinetic granular temperature.

By using high molecular weight fluorescent passive tracers with different diffusion coefficients and by changing the fluid velocity we study the dependence of a characteristic mixing length on the Peclet number, Pe, which controls the mixing efficiency. The mixing length is found to be related to Pe by a power law, $L_{\mathrm{mix}}\propto {\mathrm{Pe}}^{0.26\pm 0.01}$, and increases faster than expected for an unbounded chaotic flow. The role of the boundaries in the mixing length abnormal growth is clarified. The experimental findings are in good quantitative agreement with recent theoretical predictions.

Vortex streets formed behind oscillating bluff bodies consist of arrays of groups of two, three, or four vortices classified as $2S$, $P+S$, and $2P$ shedding modes, respectively. The prevailing dominant mode depends primarily on the amplitude and the frequency of the oscillation and on the Reynolds number. We investigate the effect of noise at the inflow on the stability of these vortex modes in laminar flow past a circular cylinder. We employ stochastic simulations based on a new polynomial chaos method to study the shedding-mode switching from a $P+S$ pattern to a $2S$ mode in the presence of noise.

We report experimental evidence of a time-lag synchronization of spatiotemporal complexity. The experiments were performed on two unidirectionally coupled, nonlinear-optical systems of single-feedback type. Synchronization was investigated for different degrees of complexity of the spontaneous structures, which were analyzed with cross-correlation functions and mutual information. Numerical simulations yield comparable results and throw a light on the impeding role of spatial inhomogeneities.

Microstructured metallic devices will play a vital role in the continuing search to manipulate the passage of electromagnetic radiation relevant to optical, microwave, and communication technologies. Here, we investigate the electromagnetic response of a completely novel and ultrathin ($\ll$ wavelength) structure within which is buried a metal-clad waveguiding layer (“core”) of subwavelength width. By removing metal from the core cladding to form a periodic array of slits, radiation is coupled into a standing wave within the layer and the structure resonantly absorbs or transmits radiation of wavelength more than 100 times its thickness. Additionally, such structures display the truly remarkable capability of compressing half of the standing-wave wavelength into a fraction of the expected distance.

Experimental and numerical techniques allowed us to predict and verify the existence of a robust phase singularity in the spatial coherence function when a vortex is present. Though observed in the optical domain, this phenomenon may occur in any partially coherent vortex wave.

We show theoretically and experimentally in an optical fiber system that solitons can be spontaneously generated from incoherent light in an instantaneous response nonlinear Kerr medium. The theory reveals that the unexpected existence of these incoherent solitons relies on a phase-locking mechanism, which leads to the emergence of a mutual coherence between the incoherent waves that constitute the soliton.

Using direct numerical simulation of a fully developed turbulent channel flow, we investigate the behavior of acceleration near a solid wall. We find that acceleration near the wall is highly intermittent and the intermittency is in large part associated with the near wall organized coherent turbulence structures. We also find that acceleration of large magnitude is mostly directed towards the rotation axis of the coherent vortical structures, indicating that the source of the intermittent acceleration is the rotational motion associated with the vortices that causes centripetal acceleration.

We consider the induction of a magnetic field in flows of an electrically conducting fluid at low magnetic Prandtl number and large kinetic Reynolds number. Using the separation between the magnetic and kinetic diffusive length scales, we propose a new numerical approach. The coupled magnetic and fluid equations are solved using a mixed scheme, where the magnetic field fluctuations are fully resolved and the velocity fluctuations at small scale are modeled using a large eddy simulation (LES) scheme. We study the response of a forced Taylor-Green flow to an externally applied field: topology of the mean induction and time fluctuations at fixed locations. The results are in remarkable agreement with existing experimental data; a global $1/f$ behavior at long times is also evidenced.

We investigate the dynamics of a realization of Fermi’s relativistic acceleration mechanism that is a charged test particle oscillating between two reflecting plates that move stochastically. By allowing the charge to radiate energy during each collision, we find that the main features of the system are (1) due to the radiation drag the energy gained by the particle is bounded, and (2) the radiated energy represents a typical realization of an on-off intermittent process, due to numerous continuous encounters with a very small emission, interrupted by short and intense bursts of radiation. This intermittent radiative process exhibits non-Gaussian statistical features.

We demonstrate anisotropic enhancement of discrete diffraction and formation of discrete-soliton trains in an optically induced photonic lattice. Such discrete behavior of light propagation was observed when a one-dimensional stripe beam was launched appropriately into a two-dimensional lattice created with partially coherent light. Our experimental results are corroborated with numerical simulations.

Colored conical emission was observed experimentally in a thick $\beta$-barium borate crystal as a result of spatiotemporal modulational instability. In the presence of both dispersion and diffraction, colored conical emission showed specific features that were characteristic of the nonlinear dynamics of the strongly coupled fundamental and harmonic fields. Experimental observation directly demonstrated that beam angular spectra were substantially modified as a result of exponential growth of perturbations by means of parametric wave mixing. Seeded amplification of colored conical emission was demonstrated to support ultrabroadband up-conversion.

We consider networks of coupled maps where the connections between units involve time delays. We show that, similar to the undelayed case, the synchronization of the network depends on the connection topology, characterized by the spectrum of the graph Laplacian. Consequently, scale-free and random networks are capable of synchronizing despite the delayed flow of information, whereas regular networks with nearest-neighbor connections and their small-world variants generally exhibit poor synchronization. On the other hand, connection delays can actually be conducive to synchronization, so that it is possible for the delayed system to synchronize where the undelayed system does not. Furthermore, the delays determine the synchronized dynamics, leading to the emergence of a wide range of new collective behavior which the individual units are incapable of producing in isolation.

The size of the light-emitting region is a key parameter toward understanding the light-emitting processes in a sonoluminescing bubble. Here we present measurements of interference effects from particles with a diameter of approximately $2\mu \mathrm{m}$ situated $6–10\mu \mathrm{m}$ from a sonoluminescing bubble. From the angular size of the pattern and from an estimated distance to the particles we conclude that the light-emitting region of a sonoluminescing bubble is smaller than commonly believed $\{$see, e.g., S. Hilgenfeldt, S. Grossman, and D. Lohse [Nature (London) 398, 402 (1999)]$\}$. We argue that an upper limit of the size of the light-emitting region is approximately 200 nm.

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, $v(l)\sim l^{\alpha }$, $\alpha <1$. This regime is relevant to the problem of magnetic field generation in fluids with small magnetic Prandtl number, i.e., with Ohmic resistivity much larger than viscosity. We propose that the smaller the roughness exponent $\alpha$, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.