Detection of phase synchronization of coupled chaotic oscillators is examined experimentally for the case of a linear laser array. Phase variables are computed by applying a Gaussian filter, peaked at a positive frequency, to the signal obtained from the intensity time series of the individual lasers. Relationships between different frequency components of the oscillator dynamics that are not otherwise apparent are unambiguously detected.

Clustering in ensembles of globally coupled identical chaotic oscillators is reconsidered using a twofold approach. Stability of clusters towards “emanation” of the elements is described with the evaporation Lyapunov exponents. It appears that direct numerical simulations of ensembles often lead to spurious clusters that have positive evaporation exponents, due to a numerical trap. We propose a numerical method that surmounts the spurious clustering. We also demonstrate that clustering can be very sensitive to the number of elements in the ensemble.

The statistical properties of the local topology of two-dimensional turbulence are investigated using an electromagnetically forced soap film. The local topology of the incompressible 2D flow is characterized by the Jacobian determinant $\Lambda (x,y)=\frac{1}{4}({\omega }^2-{\sigma }^2)$, where $\omega (x,y)$ is the local vorticity and $\sigma (x,y)$ is the local strain rate. For turbulent flows driven by different external force configurations, $P\left(\Lambda \right)$ is found to be a universal function when rescaled using the turbulent intensity. A simple model that agrees with the measured functional form of $P\left(\Lambda \right)$ is constructed using the assumption that the stream function, $\psi (x,y)$, is a Gaussian random field.

We study linear and nonlinear wave scattering by an optical vortex in a self-defocusing nonlinear Kerr medium. In the linear case, we find a splitting of a plane-wave front at the vortex proportional to its circulation, similar to what occurs in the scattered wave of electrons for the Aharonov-Bohm effect. For larger wave amplitudes, we study analytically and numerically the scattering of a dark-soliton stripe (a nonlinear analog of a small-amplitude wave packet) by a vortex and observe a significant asymmetry of the scattered wave. Subsequently, a wave-front splitting of the scattered wave develops into transverse modulational instability, “unzipping” the stripe into trains of vortices with opposite charges.

Through a detailed spectral analysis of the propagation of square-shaped laser pulses in optical fibers, we provide the experimental demonstration of the Fermi-Pasta-Ulam recurrence phenomenon in modulationally unstable optical waves ruled by the nonlinear Schrödinger equation.

We study numerically and analytically the dynamics of charged particles on the Galton board, a regular lattice of disk scatters, in the presence of constant external force, magnetic field, and friction. It is shown that under certain conditions friction leads to the appearance of a strange chaotic attractor. In this regime the average velocity and direction of particle flow can be effectively affected by electric and magnetic fields. We discuss the applications of these results to the charge transport in antidot superlattices and the stream of suspended particles in a viscous flow through scatters.

We introduce novel classes of optical vector solitons that consist of incoherently coupled self-trapped “necklace” beams carrying zero, integer, and even fractional angular momentum. Because of the stabilizing mutual attraction between the components, such stationary localized structures exhibit quasistable propagation for much larger distances than the corresponding scalar vortex solitons and expanding scalar necklace beams.

We investigate the near-field inverse scattering problem with evanescent waves. An analytic solution to this problem within the weak-scattering approximation is used to show that the usual Rayleigh limit may be overcome even when measurements are made without phase information. Applications to a novel form of three-dimensional microscopy with subwavelength resolution are described.

A statistic, the BV (bred vector) dimension, is introduced to measure the effective local finite-time dimensionality of a spatiotemporally chaotic system. It is shown that the Earth’s atmosphere often has low BV dimension, and the implications for improving weather forecasting are discussed.

A general formulation is developed to study heat conduction in disordered harmonic chains with arbitrary heat baths, satisfying the fluctuation-dissipation theorem. A simple formal expression for the heat current $J$ is obtained, from which its asymptotic system-size $\left(N\right)$ dependence is extracted. It is shown that “thermal conductivity” depends not just on the system itself but also on the spectral properties of the heat baths. As special cases we recover earlier results that gave $J\sim {1/N}^{3/2}$ for fixed boundaries and $J\sim {1/N}^{1/2}$ for free boundaries. Other choices give other power laws including the “Fourier behavior” $J\sim 1/N$.

We present a new instability observed in rapid granular flows down rough inclined planes. For high inclinations and flow rates, the free surface of the flow experiences a regular deformation in the transverse direction. Measurements of the surface velocities imply that this instability is associated with the formation of longitudinal vortices in the granular flow. From the experimental observations, we propose a mechanism for the longitudinal vortex formation based on the concept of granular temperature.

Passive scalars advected by a magnetically driven two-dimensional turbulent flow are analyzed using methods of statistical topography. The passive tracer concentration is interpreted as the height of a random surface, and the scaling properties of its contour loops are analyzed. Various exponents that describe the loop ensemble are measured and compared to a scaling theory. This leads to a geometrical criterion for the intermittency of scalar fluctuations.

The sun provides an excellent natural laboratory for nonlinear phenomena. We use motions of magnetic bright points on the solar surface, at the smallest scales yet observed, to study the small scale dynamics of the photospheric plasma. The paths of the bright points are analyzed within a continuous time random walk framework. Their spatial and temporal scaling suggests that the observed motions are the walks of imperfectly correlated tracers on a turbulent fluid flow in the lanes between granular convection cells.

We report on experimental measurements of the growth of regular domains evolving from an irregular pattern in electroconvection. The late-time growth of the domains is consistent with the size of the domains scaling as $t^n$. We use two isotropic measurements of the domain size: the structure factor and the domain wall length. Measurements using the structure factor are consistent with $t^{1/5}$ growth. Measurements using the domain wall length are consistent with $t^{1/4}$ growth. One source of this discrepancy is the fact that the distribution of local wave numbers is approximately independent of the domain size. In addition, we measure the anisotropy of the growing domains.

We report what is believed to be the first detailed experimental observation of the dynamic inversion of the topological charge of an optical vortex under free-space propagation. The vortex self-transformation occurs through continuous deformation of the noncanonical strength of the corresponding screw wave front dislocation, and is mediated by the occurrence of an extremely sharp turn in a Berry vortex trajectory, which observed at a Freund critical foliation appears as an edge-line dislocation orthogonal to the propagation direction, at a crucial point of the light evolution.

Random-matrix ensembles serve as models for quantum chaotic systems. We develop the theory of skew-orthogonal polynomials to study matrix ensembles with non-Gaussian weight functions. From the asymptotic properties of these and the orthogonal polynomials, we show that the local energy level correlations in the ensembles become universal properties independent of the global level density. This provides a rigorous justification for the universality of the Gaussian ensemble results observed in quantum chaotic systems.

We demonstrate theoretically and experimentally a novel epidetection scheme for coherent anti-Stokes Raman scattering (CARS) microscopy that significantly improves the detection sensitivity. Calculations show that epidetected CARS (E-CARS) signals are present for scatterers smaller than the wavelength of light, whereas the large background signals from the surrounding bulk solvent are suppressed by destructive interference. E-CARS microscopy is capable of revealing small intracellular features that are otherwise buried by the strong water CARS signal.

We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the parameter space the periodicity of the collective output is enhanced by the considered coupling. This system can be used as a new model to describe synchronizationlike phenomena in systems of units with two or more oscillation modes. The model can also explain how periodic dynamics can be generated by coupling largely stochastic units. Similar systems could be responsible for the emergence of rhythmic behavior in complex biological or sociological systems.

Introducing a short time delay into the coupling of two synchronizing chaotic systems, it was shown recently that the driven system may anticipate the driving system in real time. Augmenting the phase space of the driven system, we accomplish anticipation times that are multiples of the coupling delay time and exceed characteristic time scales of the chaotic dynamics. The stability properties of the associated anticipatory synchronization manifold in certain cases turn out to be the same as for identically synchronizing oscillators.

We perform an elastostatic analysis of a periodic array of cracks under constant loading. We give an analytical solution and show that there is a limitation to the fracture spacing, due to a transition from an opening to a compressive loading. For this configuration, the threshold of the fracture spacing depends on neither the applied strain nor the elastic parameters of the material. This result shows that, in the general case of layered materials, the physical mechanism that is responsible for the limitation in the density of fractures is related mainly to the geometry of the problem. This is in agreement with observations and with recent numerical results.