Tunable and stable ultrashort laser pulses in the visible spectrum are generated with high efficiency by four-wave mixing process during the filamentation of near-infrared and infrared laser pulses in gases. It is shown that these tunable ultrashort pulses have a very low energy fluctuation and an excellent mode quality due to the processes of intensity clamping and self-filtering in the filament.

We present the results of a derivation of the fluctuation energy transport matrix for the two-field Hasegawa-Wakatani model of drift wave turbulence. The energy transport matrix is derived from a two-scale direct interaction approximation assuming weak turbulence. We examine different classes of triad interactions and show that radially extended eddies, as occurs in penetrative convection, are the most effective in turbulence spreading. We show that in the near-adiabatic limit internal energy spreads faster than the kinetic energy. Previous theories of spreading results are discussed in the context of weak turbulence theory.

Bubbles pushed through a quasi-two-dimensional channel self-organize into a variety of periodic lattices. The structures of these lattices correspond to local minima of the interfacial energy. The “flowing crystals” are long-lived metastable states, a small subset of possible local minima of confined quasi-two-dimensional foams [P. Garstecki and G. M. Whitesides, Phys. Rev. E 73, 031603 (2006)]. Experimental results suggest that the choice of the structures that we observe is dictated by the dynamic stability of the cyclic processes of their formation. Thus, the dynamic system that we report provides a unique example of nonequilibrium self-organization that results in structures that correspond to local minima of the relevant energy functional.

A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system.

It is shown that optical pulses with an average position accuracy beyond the standard quantum limit can be produced by adiabatically expanding an optical vector soliton followed by classical dispersion management. The proposed scheme is also capable of entangling positions of optical pulses and can potentially be used for general continuous-variable quantum-information processing.

We report the first direct measurements of the atomic dipole phase in the process of high-order harmonic generation. Differently from previously reported studies based on frequency chirp measurements, we use extreme ultraviolet interferometry as the most natural and direct way to measure phase shifts. Our approach has the important advantage of allowing us to investigate the effects associated to both the main quantum paths involved in the emission of a particular harmonic, thus offering a particularly clear and simple picture of the underlying electronic dynamics.

We investigate single-file osmosis of water through a semipermeable membrane with an uncharged, a positively and a negatively charged nanopore. Molecular dynamics simulations indicate that the osmotic flux through a negatively charged pore ($J_{-}$) is higher compared to the osmotic flux in a positively charged pore ($J_{+}$) followed by the osmotic flux in the uncharged pore ($J_0$), i.e., $J_{-}>J_{+}>J_0$. The molecular mechanisms governing osmosis, steady state osmosis, and the observed osmotic flux dependence on the nanopore charge are explained by computing all the molecular interactions involved and identifying the molecular interactions that play an important role during and after osmosis. This study helps in a fundamental understanding of osmosis and in the design of advanced nanoporous membranes for various applications of osmosis.

We show analytically that bright and dark spatial self-similar waves can propagate in graded-index amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearities. The intensity profiles of the novel waves are identical with those of fundamental bright or dark spatial solitons supported by homogeneous passive waveguides with the same type of nonlinearity. Thus, we reveal a previously unnoticed connection between spatial solitons and self-similar waves. We also suggest that the discovered self-similar waves can be used in a promising scheme for the amplification and focusing of spatial solitons in future all-optical networks.

We show that the second order nonlinear generation of light, a process that it is assumed to require highly ordered materials, is also possible in structures of randomly oriented nonlinear domains. We explain theoretically why in such disordered structures the efficiency of the nonlinear generation of light grows linearly with the number of domains. Moreover, a higher degree of disorder, obtained when the dispersion is made very large, has no negative effect for the nonlinear light generation. In such conditions, light generation is shown to be equally efficient for any average size of the domains and also to grow linearly with respect to the number of domains.

We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic, and applies generally to networks for which the number of connections per node is large. We find that the critical coupling strength at which a transition to synchrony takes place depends separately on the dynamics of the individual uncoupled systems and on the largest eigenvalue of the adjacency matrix of the coupling network. Our theory directly generalizes the Kuramoto model of equal strength all-to-all coupled phase oscillators to the case of oscillators with more realistic dynamics coupled via a large heterogeneous network.

Recurrence plots were first introduced to quantify the recurrence properties of chaotic dynamics. A few years later, the recurrence quantification analysis was introduced to transform graphical representations into statistical analysis. Among the different measures introduced, a Shannon entropy was found to be correlated with the inverse of the largest Lyapunov exponent. The discrepancy between this and the usual interpretation of a Shannon entropy is solved here by using a new definition—still based on the recurrence plots—and it is verified that this new definition is correlated with the largest Lyapunov exponent, as expected from the Pesin conjecture. A comparison with a Shannon entropy computed from symbolic dynamics is also provided.

Experiments on streams of water flowing down a rigid substrate have been performed for various plate inclinations and flow rates, and we focused on the regime of stationary meanders. The outcome is that (i) the flow is highly hysteretic—the shape of the meanders varies with flow rate only for increasing flow rates, and the straight rivulet regime does not appear for decreasing flow rate, and (ii) a simple force balance, including inertia, capillary forces, and also hysteresis of wetting, accounts well for the experimental instability threshold flow rate and for the final radius of curvature of the meanders.

We formulate and model the dynamics of spatial patterns arising during the precipitation of calcium carbonate from a supersaturated shallow water flow. The model describes the formation of travertine deposits at geothermal hot springs and rimstone dams of calcite in caves. We find explicit solutions for travertine domes at low flow rates, identify the linear instabilities which generate dam and pond formation on sloped substrates, and present simulations of statistical landscape evolution.

New deformation or fission phenomena are reported for microdrops driven by an ac electric field at their resonant frequencies. The Maxwell forces that pull out the vertices from a drop can be enhanced when the ac frequency is comparable to both the drop resonant frequency and the inverse charge relaxation time of the diffuse layer. The selected polyhedra possess symmetries that ensure a global force balance of the Maxwell forces and a linear dimension consistent with a sphere whose $n$th harmonic ($n$ is up to six in the observation) coincides with the applied ac frequency. At high voltages, the resonant focusing of charges by the vibration modes produces evenly distributed and transient Taylor cones that can eject charged nanodrops.

Flat microwave cavities can be used to experimentally simulate quantum mechanical systems. By coupling two such cavities, we study the equivalent to symmetry breaking in quantum mechanics. As the coupling is tunable, we can measure resonance strength distributions as a function of the symmetry breaking. We analyze the data by employing a qualitative model based on random matrix theory and show that the results derived from the strength distribution are consistent with those previously obtained from spectral statistics.

A crisis is a global bifurcation in which a chaotic attractor has a discontinuous change in size or suddenly disappears as a scalar parameter of the system is varied. In this Letter, we describe a global bifurcation in three dimensions which can result in a crisis. This bifurcation does not involve a tangency and cannot occur in maps of dimension smaller than 3. We present evidence of unstable dimension variability as a result of the crisis. We then derive a new scaling law describing the density of the new portion of the attractor formed in the crisis. We illustrate this new type of bifurcation with a specific example of a three-dimensional chaotic attractor undergoing a crisis.

We show that front motion can be induced by noise in a spatially extended excitable system with a global constraint. Our model system is a semiconductor superlattice exhibiting complex dynamics of electron accumulation and depletion fronts. The presence of noise induces a global change in the dynamics of the system forcing stationary fronts to move through the entire device. We demonstrate the effect of coherence resonance in our model; i.e., there is an optimal level of noise at which the regularity of front motion is enhanced. Physical insight is provided by relating the space-time dynamics of the fronts with a phase-space analysis.

Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution based on exponentiated linear response will be given. For one representative case the exact solution is obtained from a supersymmetric calculation. The results agree well with dynamical calculations for a kicked top.

We develop an amended ray-optics description for reflection at the curved dielectric interfaces of optical microresonators which improves the agreement with wave optics by about one order of magnitude. The corrections are separated into two contributions of similar magnitude, corresponding to ray displacement in independent quantum-phase-space directions, which can be identified with Fresnel filtering and the Goos-Hänchen shift, respectively. Hence we unify two effects which only have been studied separately in the past.

We report on a direct experimental observation of dynamic localization (DL) of light in sinusoidally-curved lithium-niobate waveguide arrays which provides the optical analog of DL for electrons in periodic potentials subjected to ac electric fields as originally proposed by Dunlap and Kenkre [Phys. Rev. B 34, 3625 (1986)]. The theoretical condition for DL in a sinusoidal field is experimentally demonstrated.