We experimentally demonstrate the direct measurement of net group and reshaping delays for arbitrary optical pulses in dispersive media, verifying the earlier prediction of Peatross et al. [Phys. Rev. Lett. 84, 2370 (2000)]. Incoherent pulse propagation in an absorptionless system is well described by net group delay; even the medium causes a great deal of deformation in the transmitted pulse. However, in the case of phase modulated chirping pulses in a resonant absorber, the so-called superluminal or subluminal propagation velocity is strongly influenced by the reshaping delay.

We investigate long time numerical simulations of the inviscid Rayleigh-Taylor instability at Atwood number one using a boundary integral method. We are able to attain the asymptotic behavior for the spikes predicted by Clavin and Williams for which we give a simplified demonstration. In particular, we observe that the spike’s curvature evolves as $t^3$, while the overshoot in acceleration shows good agreement with the suggested $1/t^5$ law. Moreover, we obtain consistent results for the prefactor coefficients of the asymptotic laws. Eventually we exhibit the self-similar behavior of the interface profile near the spike.

Determining the effective conductivity of heterogeneous media is a central problem in different fields of physics. The medium considered here contains cylinders (inclusions) of random conductivities that are distributed at random in an embedding matrix. For random systems, widely encountered in applications, we derive an approximative analytical solution that applies to significantly denser configurations than Maxwell first-order approximations. The analytic solution is tested against accurate numerical simulations. The widely used effective medium approach is shown to be exact for symmetric conductivity distributions and quite accurate for asymmetrical cases.

We present an experimental investigation of gravitational billiards where the particle undergoes inelastic collisions with its boundary. The motion is mapped for an inelastic particle contained within parabolic, wedge, and hyperbolic boundaries. For the parabola, stable orbits are found and the wedge demonstrates a characteristic instability for its vertex angle. In the instance of the hyperbola, there are several features of the dynamics similar to the parabola at low driving and the wedge for higher driving. However, the low driving case for a hyperbola can only be completely understood by considering inelasticity effects predicted by a numerical simulation and the observation that the velocity dependent inelasticity allows the particle to sample several nearby trajectories for fixed driving.

We consider the pattern-formation dynamics of a two-dimensional (2D) nonlinear evolution equation that includes the effects of instability, dissipation, and dispersion. We construct 2D stationary solitary pulse solutions of this equation, and we develop a coherent structures theory that describes the weak interaction of these pulses. We show that in the strongly dispersive case, 2D pulses organize themselves into V shapes. Our theoretical findings are in good agreement with time-dependent computations of the fully nonlinear system.

We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states and eventually into chaos. We demonstrate this method by using numerical examples and a laboratory experiment with a Duffing type of electronic circuit driven by a phase-locked loop. The phase-locked loop can track the instantaneous frequency and phase of the Duffing circuit and deliver resonant perturbations to generate robust chaos.

We analyze the multipoint correlation functions of a tracer in an incompressible flow at scales far exceeding the scale $L$ at which fluctuations are generated (quasiequilibrium domain) and compare them with the correlation functions at scales smaller than $L$ (turbulence domain). We demonstrate that scale invariance can be broken in the equilibrium domain and trace this breakdown to the statistical integrals of motion (zero modes) as has been done before for turbulence. Employing the Kraichnan model of short-correlated velocity we identify the new type of zero modes, which break scale invariance and determine an anomalously slow decay of correlations at large scales.

We investigate the large-scale statistics of a passive scalar transported by a turbulent velocity field by means of direct numerical simulations. We focus on scales larger than the characteristic length scale of scalar injection, yet smaller than the correlation length of the velocity. We show the existence of nontrivial long-range correlations in the form of new power laws for the decay of high-order coarse-grained scalar cumulants. This result contradicts the classical scenario of Gibbs equilibrium statistics that should hold in the absence of scalar flux. The breakdown of “thermal equilibrium” at large scales is traced back to the statistical geometry of turbulent dispersion of two scalar blobs. The numerical values obtained for the scaling exponents of the coarse-grained scalar cumulants are in agreement with recent theoretical results.

Utilizing the Soret effect, we have employed a moderately focused laser beam ($30\mu \mathrm{m}$, 20 mW) to write spatial composition patterns into layers of the critical polymer blend poly(dimethyl siloxane)/poly(ethyl-methyl siloxane) (PDMS/PEMS, $M_w=16.4/22.8\mathrm{kg}/\mathrm{mol}$) both in the one- and in the two-phase region a few degrees above and below the critical temperature $T_c=37.7°\mathrm{C}$. Because of the critical divergence of the Soret coefficient, moderate temperature gradients are sufficient to induce composition modulations of large amplitude. In the two-phase regime the spinodal demixing pattern can be locally manipulated in a controlled way. 2D simulations based on a modified Cahn-Hilliard equation are able to reproduce the essential spatial and temporal features observed in the experiments.

Inspired by rattleback toys, we created small chiral wires that rotate in a preferred direction on a vertically oscillating platform and quantified their motion with experiment and simulation. We demonstrate experimentally that angular momentum of rotation about particle centers of mass is converted to collective angular momentum of center-of-mass motion in a granular gas of these wires, and we introduce a continuum model that explains our observations.

We propose and demonstrate a “bottom-up” approach to constructing photonic structures for photon manipulation. Supermonodispersive polymer microspheres are used as building blocks and a size uniformity better than 0.05% could be obtained by sorting the spheres using spectroscopic methods. The spheres are positioned in a V groove on a silicon substrate and form a photonic chain with resonant coupling of the optical whispering-gallery modes. Photonic band modes are clearly observed in fluorescence and resonant scattering spectra, and an excellent agreement with a tight-binding model calculation is found. Heavy photon states and a group index as high as 40 are obtained.

We show how an effective nonlocality in imaging can lead to the sampling of a spatial region which is not significantly illuminated by an imaging probe. The nonlocality is embodied in the effective nonlocal potential describing inelastic scattering which occurs when coupled channel Schrödinger equations are reduced to a single integro-differential equation. The context in which this prediction will be illustrated is atomic resolution imaging based on energy-loss spectroscopy in scanning transmission electron microscopy.

In this Letter, the formation of complex oscillations of the type $2^{n}M$ oscillations per period at the $M$th superharmonic excitation is reported for electrostatic microelectromechanical systems. A dc bias (beyond “dc symmetry breaking”) and an ac signal (at the $M$th superharmonic frequency) with an amplitude around “ac symmetry breaking” gives rise to $M$ oscillations per period or period $M$ response. On increasing the ac voltage, a cascade of period doubling bifurcations take place giving rise to $2^{n}M$ oscillations per period. An interesting chaotic transition (1-band and 2-band chaos) is observed during the first period doubling bifurcation. The nonlinear nature of the electrostatic force is shown to be responsible for the reported observations.

We report on the dynamics of the periodic collision process occurring between different pulse bound states in a stretched-pulse erbium-doped fiber laser. The acquisition of a large number of second-order correlation traces allows us to reconstruct the dynamics of a single collision event. The measurements clearly demonstrate that, unlike true solitons in the case of integrable systems, the pulses do not fully overlap in the course of a collision. Instead, the collision proceeds through the exchange of bonds between the individual pulses constituting the bound states.

We use a new technique to disseminate microwave reference signals along ordinary optical fiber. The fractional frequency resolution of a link of 86 km in length is ${10}^{-17}$ for a one day integration time, a resolution higher than the stability of the best microwave or optical clocks. We use the link to compare the microwave reference and a ${\mathrm{CO}}_2/{\mathrm{OsO}}_4$ frequency standard that stabilizes a femtosecond laser frequency comb. This demonstrates a resolution of $3\times {10}^{-14}$ at 1 s. An upper value of the instability introduced by the femtosecond laser-based synthesizer is estimated as $1\times {10}^{-14}$ at 1 s.

We construct a variety of novel localized topological structures in the 3D discrete nonlinear Schrödinger equation. The states can be created in Bose-Einstein condensates trapped in strong optical lattices and crystals built of microresonators. These new structures, most of which have no counterparts in lower dimensions, range from multipole patterns and diagonal vortices to vortex “cubes” (stack of two quasiplanar vortices) and “diamonds” (formed by two orthogonal vortices).

The theory of the inverse Doppler effect recently observed in magnetic nonlinear transmission lines is developed. We explain the crucial role of the backward spatial harmonic in the occurrence of an inverse Doppler effect and draw analogies of the magnetic nonlinear transmission line to the backward wave oscillator.

Gravity waves were generated at the interface between miscible fluids, or at the top of a settling suspension or a fluidized bed. For these three systems the dispersion relation was measured and compared to the theory and calculated between two buoyant viscous fluids without surface tension. The experimental findings are found to be in good agreement with theory when effective viscosity and volume-averaged density values are used.

Incompressible magnetohydrodynamics is often assumed to describe solar wind turbulence. We use extended self-similarity to reveal scaling in the structure functions of density fluctuations in the solar wind. The obtained scaling is then compared with that found in the inertial range of quantities identified as passive scalars in other turbulent systems. We find that these are not coincident. This implies that either solar wind turbulence is compressible or that straightforward comparison of structure functions does not adequately capture its inertial range properties.

By using a self-referencing technique, we have experimentally measured the influence of the carrier-envelope phase of femtosecond light pulses on the phase of the electric field of the radiation produced by high-order harmonic generation. We show that, in particular experimental conditions, the temporal evolution of the electric field of the attosecond pulses, is directly controlled by the carrier-envelope phase of the driving pulses.