We develop a general theory of spatial solitons in a liquid crystalline medium exhibiting a nonlinearity with an arbitrary degree of effective nonlocality. The model accounts the observability of accessible solitons and establishes an important link with parametric solitons.

We put forward a mechanism for tailoring, and even arresting, the collapse of wave packets in nonlinear media, whose dynamics is governed by nonlocal two-dimensional nonlinear Schrödinger-like equations. The key ingredient of the scheme is the self-generation of nonlocal nonlinearities mediated by wave rectification.

We analyze the effects of asymmetric couplings in setting different synchronization states for a pair of unidimensional fields obeying complex Ginzburg-Landau equations. Novel features such as asymmetry enhanced complete synchronization, limits for the appearance of phase synchronized states, and selection of the final synchronized dynamics are reported and characterized.

We show that the structure of a dense, free-surface boundary layer granular flow is similar to the structure of a laminar liquid flow: There is a strong component of order (stratification parallel to the mean flow) superposed with a mild component of disorder (self-diffusion perpendicular to the mean flow). We also show that the self-diffusion coefficient scales with the mean velocity and propose a model that relates this scaling to the ordered structure of the flow. Last, we show that the structure of the flow imprints an oscillatory signature (similar to that found in confined granular flow) on the mean velocity profile.

We report the measurement of instantaneous resonant four-photon absorption in the polydiacetylene-PTS [polymer poly(bis para-toluene sulfonate) of 2,4-hexadyine-1,6 diol]. Although normally too weak to be observable, an exact degeneracy between three- and four-photon absorption into the dominant exciton and two-photon states, respectively, resonantly enhances this effect so that it can be measured (four-photon coefficient ${\alpha }_4=0.01{\mathrm{c}\mathrm{m}}^5/{\mathrm{G}\mathrm{W}}^3$) at its peak wavelength of 1900 nm. Femtosecond measurements from 1200 to 2200 nm of two- and three-photon absorption, and the nonlinear refractive index coefficient are also reported.

We have studied both experimentally and numerically the dynamic effect of nonlinearity on lasing in disordered medium. The third-order nonlinearity not only changes the frequency and size of lasing modes, but also modifies the laser emission intensity and laser pulse width. When the nonlinear response time is longer than the lifetime of the lasing mode, the nonlinearity changes the laser output through modifying the size of the lasing mode. When the nonlinear response is faster than the buildup of the lasing mode, positive nonlinearity always extracts more laser emission from the random medium due to the enhancement of single particle scattering.

In this Letter, the effects of random shortcuts in an array of coupled nonlinear chaotic pendulums and their ability to control the dynamical behavior of the system are investigated. We show that random shortcuts can induce periodic synchronized spatiotemporal motions, even though all oscillators are chaotic when uncoupled. This process exhibits a nonmonotonic dependence on the density of shortcuts. Specifically, there is an optimal amount of random shortcuts, which can induce the most ordered motion characterized by the largest order parameter that is introduced to measure the spatiotemporal order. Our results imply that topological randomness can tame spatiotemporal chaos.

We report the observation of two types of Sommerfeld precursors (or forerunners) on the surface of a layer of mercury. When the fluid depth increases, we observe a transition between these two precursor surface waves in good agreement with the predictions of asymptotic analysis. At depths thin enough compared to the capillary length, high frequency precursors propagate ahead of the “main signal” and their period and amplitude, measured at a fixed point, increase in time. For larger depths, low frequency “precursors” follow the main signal with a decreasing period and amplitude. These behaviors are understood in the framework of the analysis first introduced for linear transient electromagnetic waves in a dielectric medium by Sommerfeld [Ann. Phys. (Leipzig) 44, 177 (1914)] and Brillouin [Ann. Phys. (Leipzig) 44, 203 (1914)].

Internal imaging using index matching, and sensitive volume measurement, are used to investigate the spatial order and dynamics of a deep disordered layer of spheres sheared under a fixed load. Shearing triggers a crystallization transition accompanied by a step compaction event. The delay preceding the transition depends strongly on the layer thickness and can require a translation of about ${10}^5$ particle diameters. The mean velocity varies with depth by more than five decades, and its profile is qualitatively altered by the transition.

The linear entropy and the Loschmidt echo have proved to be of interest recently in the context of quantum information and of the quantum to classical transitions. We study the asymptotic long-time behavior of these quantities for open quantum maps and relate the decays to the eigenvalues of a coarse-grained superoperator. In specific ranges of coarse graining, and for chaotic maps, these decay rates are given by the Ruelle-Pollicott resonances of the classical map.

The absolute timing of the high-harmonic attosecond pulse train with respect to the generating IR pump cycle has been measured for the first time. The attosecond pulses occur $190\pm 20\mathrm{a}\mathrm{s}$ after each pump field maxima (twice per optical cycle), in agreement with the “short” quantum path of the quasiclassical model of harmonic generation.

Direct numerical simulations of Rayleigh-Bénard convection in a plane layer with periodic boundary conditions at Rayleigh numbers up to ${10}^7$ show that flow structures can be objectively classified as large or small scale structures because of a gap in spatial spectra. The typical size of the large scale structures does not always vary monotonically as a function of the Rayleigh number but broadly increases with increasing Rayleigh number. A mean flow (whose average over horizontal planes differs from zero) is also excited but is weak in comparison with the large scale structures. The large scale circulation observed in experiments should therefore be a manifestation of the large scale structures identified here.

We investigate the settling of heavy particles in a steady, two-dimensional random velocity field, and find instances in which particle suspension occurs. This leads to a bimodal velocity distribution that may explain some apparently conflicting results reported in the literature. The bimodal distribution is typically smeared out by a time dependence of the ambient flow but, if the time variation is slow, the settling rates of some particles will be as well. The resulting broadbanded velocity distribution of the settling particles will have significance for processes such as rain drop formation, in which the spread of particle velocities affects the statistics of particle collisions.

We show dissipative spatial solitons in nonlinear optical microresonators in which the refractive index is laterally modulated. In addition to “normal” and “staggered” dissipative solitons, similar to those in spatially modulated conservative systems, a narrow “midband” soliton is shown, having no counterparts in conservative systems.

A novel optical method is used both to probe and to control dynamics in experiments on the spreading of microscale liquid films over solid substrates. The flow is manipulated by thermally induced surface-tension gradients that are regulated by controlling the absorption of light in the substrate. This approach permits, for the first time, the measurement of the dispersion relation for the well-known contact line instability; the measurements are compared with theoretical predictions from the slip model for spreading films. The experiments also demonstrate the use of feedback control to suppress instability. These results show that optical control can provide dynamically reconfigurable manipulations of fluid flow, thereby suggesting a general approach for constructing reprogrammable microfluidic devices.

Based on simulations of femtosecond pulse propagation in water we elucidate the physical factors that limit the attainable spectral extent of supercontinuum generation in bulk media. In contrast to the standard scenario, where arrest of self-focusing collapse by multiphoton absorption and plasma defocusing are viewed as imposing a limit to supercontinuum broadening, we show that linear chromatic dispersion also plays a major role. This insight provides an intuitive explanation of the observed band gap dependence of the attainable supercontinuum generation in condensed media.

We describe the first measurements of the diffusion of broadband single-cycle optical pulses through a highly scattering medium. Using terahertz time-domain spectroscopy, we measure the electric field of a multiply scattered wave with a time resolution shorter than one optical cycle. This time-domain measurement provides information on the statistics of both the amplitude and phase distributions of the diffusive wave. We develop a theoretical description, suitable for broadband radiation, which adequately describes the experimental results.

We derive the magnetic transport-of-intensity equation (MTIE) that links defocused contrast of magnetic nanoobjects imaged by partially coherent electron waves to their micromagnetic parameters. This provides Maxwell’s explanation for observable contrast in terms of the $Z$ component of currents existing around vortices in superconductors and domain vortices and walls in ferromagnets. The solution of the MTIE via Fourier transform is used for quantitative mapping of magnetic flux and projected induction in magnetic and superconducting materials imaged by Lorentz microscopy.

Discretization of phase space usually nullifies chaos in dynamical systems. We show that if randomness is associated with discretization dynamical chaos may survive and be indistinguishable from that of the original chaotic system, when an entropic, coarse-grained analysis is performed. Relevance of this phenomenon to the problem of quantum chaos is discussed.

We establish a connection between anomalous heat conduction and anomalous diffusion in one-dimensional systems. It is shown that if the mean square of the displacement of the particle is $⟨\Delta x^2⟩=2D{t}^{\alpha }(0<\alpha \le 2)$, then the thermal conductivity can be expressed in terms of the system size $L$ as $\kappa =c{L}^{\beta }$ with $\beta =2-2/\alpha$. This result predicts that normal diffusion ($\alpha =1$) implies normal heat conduction obeying the Fourier law ($\beta =0$) and that superdiffusion ($\alpha >1$) implies anomalous heat conduction with a divergent thermal conductivity ($\beta >0$). More interestingly, subdiffusion ($\alpha <1$) implies anomalous heat conduction with a convergent thermal conductivity ($\beta <0$), and, consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our results.