The response of a nonlinear state to a variable forcing periodic in space is studied in an extended dynamical system consisting of a liquid crystal layer driven to convection. Both the statics and the dynamics of the entrainment and the locking effects are analyzed. The dynamics of the evolution are controlled by topological singularities that allow a diffusion of the phase. The mechanisms involved are related to the role of the defects in systems undergoing spontaneous symmetry breakings.

We present experiments and theory for the “bathtub vortex,” which forms when a fluid drains out of a rotating cylindrical container through a small drain hole. The fast down-flow is found to be confined to a narrow and rapidly rotating “drainpipe” from the free surface down to the drain hole. Surrounding this drainpipe is a region with slow upward flow generated by the Ekman layer at the bottom of the container. This flow structure leads us to a theoretical model similar to one obtained earlier by Lundgren [J. Fluid Mech. 155, 381 (1985)], but here including surface tension and Ekman upwelling, comparing favorably with our measurements. At the tip of the needlelike surface depression, we observe a bubble-forming instability at high rotation rates.

We present the results of experiments on impact craters formed by dropping a steel ball vertically into a container of small glass beads. As the energy of impact increases, we observe a progression of crater morphologies analogous to that seen in craters on the moon. We find that both the diameter and the depth of the craters are proportional to the $1/4$ power of the energy. The ratio of crater diameter to rim-to-floor depth is constant for low-energy impacts, but increases at higher energy, similar to what is observed for lunar craters.

In this Letter we present a simple and novel theoretical approach for modeling the intensity distribution from an arbitrarily shaped turbid volume in a noncontact geometry by considering diffuse light propagation in free space. This theory is validated with experiments for a diffusive volume of known geometry in a noncontact situation, both with and without the presence of an embedded absorber. The implications of this new formulation in the context of optical tomography in turbid media are discussed.

The development of modulation instability for two beams copropagating in a medium with noninstantaneous nonlinear response is investigated. The frequency dependence of the experimentally observed spectral broadening reveals the presence of two-beam coupling, resulting from the time-delayed Raman part of the third-order nonlinear susceptibility. We present an analysis of the experimental data, which yields a value of $\tau =27(1)\mathrm{f}\mathrm{s}$ for the lifetime of the optical phonons in silica fibers. To our knowledge, this is the first experimentally determined value for this important material parameter.

We observe the formation of an intense optical wave packet fully localized in all dimensions, i.e., both longitudinally (in time) and in the transverse plane, with an extension of a few tens of fsec and microns, respectively. Our measurements show that the self-trapped wave is an X-shaped light bullet spontaneously generated from a standard laser wave packet via the nonlinear material response (i.e., second-harmonic generation), which extend the soliton concept to a new realm, where the main hump coexists with conical tails which reflect the symmetry of linear dispersion relationship.

The validity of the diffusion approximation for the intensity of multiply scattered waves is tested with numerical simulations in a strongly scattering 2D medium of finite extent. We show that the diffusion equation underestimates the intensity and attribute this to both the neglect of recurrent scattering paths and interference within diffusion theory. We present a theory to quantify this discrepancy based on counting all possible scattering paths between point scatterers. Interference phenomena, due to loop paths, are incorporated in a way similar to coherent backscattering.

The fluorescence of individual pairs of perylenemonoimide chromophores coupled via a short rigid linker is investigated. Photon antibunching is reported, indicating collective effects in the fluorescence, which are further substantiated by the observation of collective triplet off times and triplet lifetime shortening. The experimental findings are analyzed in terms of singlet-singlet and singlet-triplet annihilation based on Förster type energy transfer. The results reported here demonstrate that the statistical properties of the emission light of isolated single quantum systems can serve as a hallmark of intermolecular interactions.

Coupled oscillators are shown to experience amplitude death for a much larger set of parameter values when they are connected with time delays distributed over an interval rather than concentrated at a point. Distributed delays enlarge and merge death islands in the parameter space. Furthermore, when the variance of the distribution is larger than a threshold, the death region becomes unbounded and amplitude death can occur for any average value of delay. These phenomena are observed even with a small spread of delays, for different distribution functions, and an arbitrary number of oscillators.

We report measurements of fluctuation and roll patterns near the transition to Rayleigh-Bénard convection which are consistent with a fluctuation-induced first-order transition, as predicted by Swift and Hohenberg. Above onset, we find convection rolls with noise-induced fluctuations, time-dependent amplitude modulation and roll undulation, and homogeneous dislocation nucleation.

The conventional coherence theory suggests that the fields radiated by statistically homogeneous sources correlate over spatial regions of the order of the wavelength irrespective of the distance from the surface of the source. Contrary to these predictions, we show that the spatial correlations of optical fields in close proximity of highly scattering, randomly inhomogeneous media depend on this distance and, moreover, their extent can be significantly smaller than the wavelength. The contribution of evanescent fields is experimentally demonstrated and the coherence length in the near field is shown to relate to the coherence properties at the surface which are, in turn, determined by the structural characteristics of the random media.

Local-field effects are known to induce bistability in dense optical media. We examine theoretically whether this property is preserved in broad-area cavities, and show that bistability between the homogeneous lasing and nonlasing states of the system persists provided a Fourier filtering technique is used to prevent off-axis emission. The resulting bistability gives rise to spatial light localization in the form of cavity solitons, which exhibit a particularly large degree of plasticity as a function of the characteristics of the addressing beam. This is the simplest laser able to sustain cavity solitons.

It is shown experimentally and theoretically that photorefractive wave coupling can be used for dramatic ($\lesssim 0.025\mathrm{c}\mathrm{m}/\mathrm{s}$) deceleration of light pulses whose width is larger than (or comparable with) the nonlinear response time. This classical nonlinear scheme exhibits similarities with the technique based on the quantum effect of electromagnetically induced transparency. The main distinctive feature of our scheme is amplification of the delayed output pulse. Advantages of the novel technique and its prospects for manipulation with light photons are discussed.

A symbolic analysis of observed time series requires a discrete partition of a continuous state space containing the dynamics. A particular kind of partition, called “generating,” preserves all deterministic dynamical information in the symbolic representation, but such partitions are not obvious beyond one dimension. Existing methods to find them require significant knowledge of the dynamical evolution operator. We introduce a statistic and algorithm to refine empirical partitions for symbolic state reconstruction. This method optimizes an essential property of a generating partition, avoiding topological degeneracies, by minimizing the number of “symbolic false nearest neighbors.” It requires only the observed time series and is sensible even in the presence of noise when no truly generating partition is possible.

The Lagrangian stochastic model of Reynolds [Phys. Fluids 15, L1–4 (2003)] for the accelerations of fluid particles in turbulence is shown to predict precisely the observed Reynolds-number dependency of the distribution of Lagrangian accelerations and the exponents characterizing the observed extended self-similarity scaling of the Lagrangian velocity structure functions. Departures from superstatistics of the log-normal kind are accounted for and their impact upon model predictions is quantified.

The effect of stirring in an inhomogeneous oscillatory medium is investigated. We show that the stirring rate can control the macroscopic behavior of the system producing collective oscillations (synchronization) or complete quenching of the oscillations (oscillator death). We interpret the homogenization rate due to mixing as a measure of global coupling and compare the phase diagrams of stirred oscillatory media and of populations of globally coupled oscillators.

We present high-precision measurements of the Nusselt number $\mathcal{N}$ as a function of the Rayleigh number $R$ for a cylindrical sample of water (Prandtl number $\sigma =4.4$) of height $L\simeq 50\mathrm{c}\mathrm{m}$ and aspect ratio $\Gamma \equiv D/L\simeq 1$ ($D$ is the diameter) for $3\times {10}^9\le R\le 6\times {10}^{10}$. For $R\simeq 3\times {10}^9$ the data are consistent with existing results for acetone ($\sigma =4.0$, $R\le 3\times {10}^9$). There the measurements are also consistent with a model by Grossmann and Lohse (GL). As $R$ increases, the measurements fall below the GL prediction. Near $R=6\times {10}^{10}$ the prediction is 8% above the data.

The friction force on a nanometer-sized tip sliding on a surface is related to the thermally activated hopping of the contact atoms on an effective atomic interaction potential. A general analytical expression relates the height of this potential and the hopping attempt frequency to measurements of the velocity dependence of the friction force performed with an atomic force microscope. While the height of the potential is roughly proportional to the normal load, the attempt frequency falls in the range of mechanical eigenfrequencies of the probing tip in contact with the surface.

Locking of two resonance modes of different symmetry classes and different frequencies in 2D resonant microcavity lasers is investigated by using a nonlinear dynamical model. The patterns of stationary lasing states and far fields are asymmetric in spite of the symmetric shape of the resonant microcavity. The corresponding phenomenon is actually observed in the experiment of a 2D semiconductor microcavity laser diode.

We show experimentally that light scattering in cholesteric liquid crystals shows strongly resonant magnetochiral anisotropy near the Bragg resonance; the optical transmission of unpolarized light depends linearly on an external longitudinal magnetic field and on the handedness of the medium.