We compare the behavior of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability density, predictability, power spectrum, and two-point correlation with increasing truncated lattice size. This suggests that spatiotemporal embedding techniques using local observations cannot detect the presence of spatial extent in such systems and hence they may equally well be modeled by a local low dimensional stochastically driven system.

The dynamics of optical hexagon excitation is studied experimentally in photorefractive barium titanate. The hard mode of the oscillation onset is discovered as well as a pronounced hysteresis loop in the dependence of the hexagon intensity on the crystal coupling strength. The analogy of excitation threshold of optical hexagon and first order optical phase transition is confirmed.

${\mathrm{SF}}_6$ in the vicinity of its critical point was used to study turbulent convection up to exceptionally high Rayleigh numbers, Ra (up to $5\times {10}^{14}$) and to verify for the first time the generalized scaling laws for the heat transport and the large scale circulation velocity as a function of Ra and the Prandtl number, Pr, in a very wide range of these parameters. Both scaling laws obtained are consistent with theoretical predictions by Shraiman and Siggia [Phys. Rev. A 42, 3650 (1990)].

A property of nonlinear oscillators—mutual dependence between their instantaneous amplitude and frequency—is tested in the yearly and monthly records of the sunspot numbers using the histogram-adjusted isospectral surrogate data and the Barnes model as the autoregressive moving average surrogates. The instantaneous amplitudes and frequencies are obtained by means of the analytic signal approach using the discrete Hilbert transform. In several tests the amplitude-frequency correlation has been found significant on levels ranging from $p<\mathrm{}0.03\mathrm{}$ to $p<\mathrm{}0.07,$ which supports the hypothesis of a driven nonlinear oscillator as a mechanism underlying the sunspot cycle.

We report a direct observation of the predicted polarity reversal due to the Gouy phase shift for single-cycle terahertz pulses passing through a focus.

Hydrodynamically mediated particle interactions in creeping flows of suspensions are investigated to address the open question as to whether they are screened. A numerical study of lattice configurations, over the full range of volume fractions, reveals that only the longitudinal part (in wave vector space) of the force-velocity interaction is unscreened, and the general lattice form of the long-range interaction is found to be in qualitative but not quantitative agreement with a mean field result.

We report the first extensive experimental observation of the two-dimensional enstrophy cascade, along with the determination of the high order vorticity statistics. The energy spectra we obtain are remarkably close to the Kraichnan Batchelor expectation. The distributions of the vorticity increments, in the inertial range, deviate little from Gaussianity, and the corresponding structure function exponents are indistinguishable from zero. It is thus shown that there is no substantial small scale intermittency in the enstrophy cascade, in agreement with recent theoretical analyses.

We apply a recently developed method for the analysis of spatiotemporal data to extract the dynamical equations that describe an experiment on traveling-wave convection in a binary fluid. The technique is based on nonlinear regression analysis and allows the nonparametric estimation of the functions involved in these equations. We find that the system is well described by a pair of coupled complex Ginzburg-Landau equations, and the coefficient of the term that describes the interaction between the two oppositely propagating waves can be determined.

The power law exponent for the wave number power spectrum of a passive scalar field in Lagrangian chaotic flows is found to differ from the classical value of $-1\mathrm{}$ (Batchelor's law) when the passive particles have a finite lifetime for exponential decay. A theory based on the chaotic dynamics of the passive scalar is developed and compared to numerical simulation results.

By studying recurrence time statistics for chaotic systems, we identify two different types of recurrences and develop scaling laws relating the mean recurrence time to the information dimension of the chaotic attractor. We then design two novel and simple ways of using the recurrence time statistics for analyzing transient as well as nonstationary time series. We show that the methods are capable of detecting nonstationarity due to drift of parameters, locating bifurcations, telling the periodicity of major transient periodic motions, and other types of changes in the dynamics.

We have observed two-dimensional bright photovoltaic photorefractive spatial soliton for the first time in a Cu:KNSBN ${\mathrm{K}}_{0.25}{\mathrm{Na}}_{0.75}{\mathrm{Sr}}_{1.5}{\mathrm{Ba}}_{0.5}{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ crystal. Characteristics of the observed spatial soliton are explained by an equivalent electric field induced by the background irradiance.

We study segregation of granular mixtures in the continuous avalanche regime (for frequencies above $\approx 1\mathrm{rpm}$) in thin rotating drums using a continuum theory for surface flows of grains. The theory predicts profiles in agreement with experiments only when we consider a flux-dependent velocity of flowing grains. We find the segregation of species of different size and surface properties, with the smallest and roughest grains being found at the center of the drum. For a wide difference between the species we find a complete segregation in agreement with experiments. In addition, we predict a transition to a smooth segregation regime as the size ratio between the grains is decreased towards one.

The observation of localized stationary structures, coined oscillons, in granular media has evoked much interest. By parametric excitation of clay suspensions, we demonstrate a hysteretic transition to oscillon-type states in a nongranular medium. When the symmetry of up-down $\mathrm{reflection}+\mathrm{time}$ translation is lost, these states undergo a transition to propagating localized states previously seen in Newtonian fluids. These observations are in accord with recent theoretical predictions of sufficient conditions for oscillon formation. In addition, a novel measurement technique for the effective suspension viscosity demonstrates their shear-thinning properties.

The dynamics of Rydberg states of atomic hydrogen perturbed simultaneously by a static electric field and a resonant microwave field of elliptical polarization is analyzed in the quantum perturbative limit of small amplitudes. For some configurations, the secular motion (i.e., evolution in time of the elliptical electronic trajectory) may be classically predominantly chaotic. By changing the orientation of the static field with respect to the polarization of the microwave field, one can modify the global symmetries of the system and break any generalized time-reversal invariance. This has a dramatic effect on the statistical properties of the energy levels.

Previous investigations of riddling have focused on the case where the dynamical invariant set in the symmetric invariant manifold of the system is a chaotic attractor. A situation expected to arise commonly in physical systems, however, is that the dynamics in the invariant manifold is in a periodic window. We argue and demonstrate that riddling can be more pervasive in this case because it can occur regardless of whether the chaotic set in the invariant manifold is transversly stable or unstable. Scaling behavior associated with this type of riddling is analyzed and is supported by numerical experiments.

A novel equation for light propagation in underdense field-ionizing media is derived by extending concepts of nonlinear optics into the strong-field domain. The equation is first order in the propagation coordinate and is valid for arbitrarily short pulse durations. Solutions of the first-order wave equation are found to be in excellent agreement with solutions of the scalar wave equation. Furthermore, the polarization response of a field-ionizing medium is derived from semiclassical considerations. The polarization reveals, in agreement with experiments, a previously unrecognized contribution that is shown to significantly affect the absorption loss in the presence of ionization.

Using full vector Maxwell simulations we elucidate a fundamental source of temporal splitting of the second harmonic field generated by a femtosecond fundamental pulse under phase-mismatched conditions. One component of the generated field propagates at the second harmonic group velocity while the other is driven by the fundamental field and propagates at the fundamental group velocity. We analyze the conditions under which the temporal splitting should be observable.

The onset and recurrence of multiple light filaments during the long-distance propagation of intense femtosecond infrared pulses in air is shown to share features with strong turbulence in other physical systems. Here, however, space-time collapse events drive the turbulence, and plasma defocusing, not dissipation, is the dominant mechanism regularizing the collapse.

We have used phase-sensitive ultrashort-pulse interferometry to study the modification of optical pulse propagation near the photonic band edges in colloidal crystals consisting of polystyrene spheres in water. A strong suppression of the group velocity is found at frequencies near the $L$ gap of the fcc lattice. The group velocity dispersion diverges at the band edges and shows branches of both normal dispersion and anomalous dispersion, which can be interpreted as large changes in the effective mass, both positive and negative. We obtain excellent agreement with the dynamical diffraction theory.

We obtain an analytical solution of a one-dimensional sandpile problem in a thick flow regime, when it can be formulated in terms of linear equations. It is shown that a space periodicity takes place during the sandpile evolution even for a sandpile of only one type of particle. Similar periodicity was observed previously for many component sandpiles. Space periods are proportional to an input flow of particles $r_0$. We find that the surface angle $\theta$ of the pile reaches its final critical value ( ${\theta }_f$) from lower values only at long times. The deviation ( ${\theta }_f-\theta$) behaves as $(t/r_0{)}^{-1\mathrm{}/2}$.