We propose a method to discover couplings in multivariate time series, based on partial mutual information, an information-theoretic generalization of partial correlation. It represents the part of mutual information of two random quantities that is not contained in a third one. By suitable choice of the latter, we can differentiate between direct and indirect interactions and derive an appropriate graphical model. An efficient estimator for partial mutual information is presented as well.

We present measurements of fluid particle accelerations in turbulent water flow between counterrotating disks using three-dimensional Lagrangian particle tracking. By simultaneously following multiple particles with sub-Kolmogorov-time-scale temporal resolution, we measured the spatial correlation of fluid particle acceleration at Taylor microscale Reynolds numbers between 200 and 690. We also obtained indirect, nonintrusive measurements of the Eulerian pressure structure functions by integrating the acceleration correlations. Our measurements are in good agreement with the theoretical predictions of the acceleration correlations and the pressure structure function in isotropic high-Reynolds number turbulence by Obukhov and Yaglom in 1951 [Prikl. Mat. Mekh. 15, 3 (1951)]. The measured pressure structure functions display $K41$ scaling in the inertial range.

In a transparent medium with instantaneous Kerr nonlinearity we find a new class of few-optical-cycle solitons and prove them to be the fundamental structures in pulse propagation dynamics. We demonstrate numerically that in the asymptotic stage of pulse propagation the input pulse splits into isolated few-cycle solitons where the quantity and their parameters are determined by the initial pulse. We generalize the concept of the high-order Schrödinger solitons to the few-cycle regime and show how it can be used for efficient pulse compression down to the single cycle duration.

The statistics of the field structure in the vortex core surrounding phase singularities in random wave fields are measured and calculated for diffusive and localized waves. Excellent agreement is found between experiment and theory. The variation of phase with the geometric angle is deterministic, depending only upon the eccentricity of elliptical intensity contours, $ϵ$, whose probability distribution is shown to be universal. The distribution of vorticity is shown to reflect both the vorticity distributions within a Gaussian random wave field with a given value of the total transmission and the mesoscopic distribution of total transmission.

We study wave propagation in mixed, 1D disordered stacks of alternating right- and left-handed layers and reveal that the introduction of metamaterials substantially suppresses Anderson localization. At long wavelengths, the localization length in mixed stacks is orders of magnitude larger than for normal structures, proportional to the sixth power of the wavelength, in contrast to the usual quadratic wavelength dependence of normal systems. Suppression of localization is also exemplified in long-wavelength resonances which largely disappear when left-handed materials are introduced.

Inertial modes are oscillatory modes in rotating fluids. Shear layers appear in inertial modes in spherical shells that become singularities in the inviscid limit. It is shown here that the nonlinearity in the shear layers drives a zonal flow whose amplitude diverges in the inviscid limit. These results are relevant for the dynamics of planets and stars in which inertial modes are excited by tidal forcing.

The curvature field is measured from tracer-particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to the forcing when the driving is weak, but wander over the domain and interact in pairs at stronger driving, changing the local topology of the flow. Their behavior reveals a two-stage transition to spatiotemporal chaos: a gradual loss of spatial and temporal order followed by an abrupt onset of topological changes.

Spontaneous emission rate enhancements from a single quantum dot embedded in a finite-size, planar photonic-crystal waveguide are investigated. Short waveguide lengths of only 10 to 20 unit cells are found to produce very large Purcell factors associated with a waveguidelike sharp resonance feature in the local density of photon states. Aided by theoretical insight and rigorous computational calculations, we explain the physics behind these remarkable emission enhancements and subsequently propose a “single-photon gun” with on-chip unidirectional collection efficiencies greater than 60% into an output wire waveguide. The advantages over recent proposals for infinitely long photonic-crystal waveguides are highlighted.

The response of the electronic system of LiH to a few-cycle strong field is computed by a time-dependent multiconfiguration method using a large, adaptive, basis set. The intensity, pulse duration, polarization, and phase of carrier frequency can all be tuned to steer the motion of the electrons. It is shown possible to, e.g., direct the electrons to move along the Li-H bond or normal to it. By shifting the phase, the electrons can be driven toward the Li nucleus or away from it. When the pulse is polarized not along the bond the result is a rotation of the charge density.

We describe how local mixing transforms a convectively unstable active field in an open flow into absolutely unstable. Presenting the mixing region as one with a locally enhanced effective diffusion allows us to find the linear transition point to an unstable global mode analytically. We derive the critical exponent that characterizes weakly nonlinear regimes beyond the instability threshold and compare it with numerical simulations of a full two-dimensional flow problem.

We present experimental Lagrangian statistics of finite sized, neutrally bouyant, particles transported in an isotropic turbulent flow. The particle’s diameter is varied over turbulent inertial scales. Finite size effects are shown not to be trivially related to velocity intermittency. The global shape of the particle’s acceleration probability density functions is not found to depend significantly on its size while the particle’s acceleration variance decreases as it becomes larger in quantitative agreement with the classical $k^{\mathrm{\text{−}}7/3}$ scaling for the spectrum of Eulerian pressure fluctuations in the carrier flow.

We describe new configurations of electromagnetic (EM) material parameters, the electric permittivity $ϵ$ and magnetic permeability $\mu$, which allow one to construct devices that function as invisible tunnels. These allow EM wave propagation between the regions at the two ends of a tunnel, but the tunnels themselves and the regions they enclose are not detectable to lateral EM observations. Such devices act as wormholes with respect to Maxwell’s equations and effectively change the topology of space vis-à-vis EM wave propagation. We suggest several applications, including devices behaving as virtual magnetic monopoles, invisible cables, and scopes for MRI-assisted surgery.

The entrainment transition of coupled random frequency oscillators is revisited. The Kuramoto model (global coupling) is shown to exhibit unusual sample-dependent finite-size effects leading to a correlation size exponent $\overline{\nu }=5/2$. Simulations of locally coupled oscillators in $d$ dimensions reveal two types of frequency entrainment: mean-field behavior at $d>4$ and aggregation of compact synchronized domains in three and four dimensions. In the latter case, scaling arguments yield a correlation length exponent $\nu =2/(d-2)$, in good agreement with numerical results.

From the flow of a suspension of micrometer-scale carbon particles, the photoacoustic Doppler shift is observed. As predicted theoretically, the observed Doppler shift equals half of that in Doppler ultrasound and does not depend on the direction of laser illumination. This new physical phenomenon provides a basis for developing photoacoustic Doppler flowmetry, which can potentially be used for detecting fluid flow in optically scattering media and especially low-speed blood flow of relatively deep microcirculation in biological tissue.

We study the propagation of fronts in extended oscillatory reaction-diffusion systems that contain several coexisting limit cycles. In contrast with the variational behavior, fronts between regions oscillating in two different limit cycles are found to propagate not necessarily towards the region of the less stable limit cycle, but towards the regions of the largest amplitudes, provided that the frequency mismatch between the cycles is sufficiently large. In other words, the smaller oscillations can always be made to control the whole system.

We study the impact and subsequent retraction dynamics of aqueous liquid droplets upon high-speed impact on hydrophobic surfaces. Often a spectacular “rebound” of the droplet can be observed: after the impact and expansion, the drop retracts rapidly, leading to ejection of part of the material from the surface. We show how non-Newtonian flow properties can be used to slow down the retraction sufficiently to completely inhibit rebound. The slowing down is due to non-Newtonian normal stresses generated near the moving contact line of the droplet. We provide a quantitative theory for the slowing down, and show that the non-Newtonian effects profoundly change the contact line dynamics.

Glassy and elastomeric nematic networks with dye molecules present can be very responsive to illumination, huge reversible strains being possible. If absorption is appreciable, strain decreases with depth into a cantilever, leading to bend that is the basis of micro-opto-mechanical systems (MOMS). Bend actually occurs even when Beer’s law suggests a tiny penetration of light into a heavily dye-doped system. We model the nonlinear opto-elastic processes behind this effect. In the regime of cantilever thickness giving optimal bending for a given incident light intensity, there are three neutral surfaces. In practice such nonlinear absorptive effects are very important since heavily doped systems are commonly used.

Recently, there has been an increased interest in studying extraordinary optical transmission (EOT) through subwavelength aperture arrays perforated in a metallic film. In this Letter, we report that the transmission of an incident acoustic wave through a one-dimensional acoustic grating can also be drastically enhanced. This extraordinary acoustic transmission (EAT) has been investigated both theoretically and experimentally, showing that the coupling between the diffractive wave and the wave-guide mode plays an important role in EAT. This phenomenon can have potential applications in acoustics and also might provide a better understanding of EOT in optical subwavelength systems.

We study the Saffman-Taylor instability in a granular suspension formed by micrometric beads immersed in a viscous liquid. When using an effective viscosity for the flow of the suspension in the Hele-Shaw cell to define the control parameter of the system, the results for the finger width of stable fingers are found to be close to the classical results of Saffman-Taylor. One observes, however, an early destabilization of the fingers that can be attributed to the discrete nature of the individual grains. Classically, the threshold of destabilization is linked to the noise in the cell and is thus difficult to quantify. We show that the grains represent a “controlled noise” and produce an initial perturbation of the interface with an amplitude proportional to the grain size. The finite amplitude instability mechanism proposed by Bensimon et al. allows us to link this perturbation to the value of the threshold observed.

Rankine vortex characteristics of a partially coherent optical vortex are explored using classical and physical optics. Unlike a perfectly coherent vortex mode, the circulation is not quantized. Excess circulation is predicted owing to the wave nature of composite vortex fields. Based on these findings, we propose a vortex stellar interferometer.