We analyze axisymmetric near-contact motion of two drops under the action of an external force or imposed flow. It is shown that hydrodynamic stresses in the near-contact region that are associated with the outer (drop-scale) flow can qualitatively affect the drainage of the thin fluid film separating the drops. If this far-field stress acts radially inward, film drainage is arrested at long times; exponential film drainage occurs if this stress acts outward. An asymptotic analysis of the stationary long-time film profile is presented for small-deformation conditions, and the critical strength of van der Waals attraction for film rupture is calculated. The effect of an insoluble surfactant is also considered. Hindered and enhanced drop coalescence are not predicted by the current theories, because the influence of the outer flow on film drainage is ignored.

We develop a transport theory to describe the dynamics of (weakly) localized waves in a quasi-1D tube geometry both in reflection and in transmission. We compare our results to recent experiments with microwaves and to other theories, such as random matrix theory and supersymmetric theory.

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. An important issue, not only from a theoretical point of view but also for their experimental detection, is their energy properties. We considerably enlarge the scenario of possible energy properties presented by Flach, Kladko, and MacKay [Phys. Rev. Lett. 78, 1207 (1997)]. Breather energies have a positive lower bound if the lattice dimension is greater than or equal to a certain critical value $d_c$. We show that $d_c$ can generically be greater than 2 for a large class of Hamiltonian systems. Furthermore, examples are provided for systems where discrete breathers exist but do not emerge from the bifurcation of a band edge plane wave. Some of these systems support breathers of arbitrarily low energy in any spatial dimension.

We study the gravity induced instability of a liquid film formed below a plane grid which is used as a porous media in an original hydrodynamic experiment. The film is continuously supplied with a controlled flow rate. We give through a phase diagram the full spectrum of the different flow regimes and we investigate the dynamics of the observed structures. True secondary instabilities of a 2D periodic pattern are described. The control parameters are the flow rate and the viscosity.

In the generic Hamiltonian problem of parametric wave interaction, we show theoretically the existence of a sudden transition leading the wave system from completely incoherent states towards highly coherent states. This self-organization process is characterized by a reduction of the nonequilibrium entropy, in contrast with the $H$ theorem of entropy growth inherent to the random phase approximation approach. The mechanism underlying this intriguing condensation process is in essence a reversible nonlinear damping. As a result, the lower the coherence of the initial state, the higher the coherence of the final state.

We investigate correlations of the intensity fluctuations of two-dimensional arrays of nonidentical, locally coupled lasers, numerically and experimentally. We find evidence of a power-law dependence of spatial correlations as a function of laser pair distance (or coupling strength) near the phase-locking threshold.

Although deterministic chaos has been predicted to occur in the triply resonant optical parametric oscillator (TROPO) 15 years ago, experimental evidence of chaotic behavior in this system has been lacking so far, in marked contrast with most nonlinear systems, where chaos has been actively tracked and found. This situation is probably linked to the high sensitivity of the TROPO to perturbations, which adversely affects stationary operation at high power. We report the experimental observation in this system of a burst of irregular behavior of duration $80\mu \mathrm{s}$. Although the system is highly nonstationary over this time interval, a topological analysis allows us to extract a clear-cut signature of deterministic chaos from a time series segment of only nine base cycles ($3\mu \mathrm{s}$). This result suggests that nonstationarity is not necessarily an obstacle to the characterization of chaos.

We present the results of a numerical investigation of three-dimensional homogeneous and isotropic turbulence, stirred by a random forcing with a power-law spectrum, $E_f(k)\sim k^{3-y}$. Numerical simulations are performed at different resolutions up to ${512}^3$. We show that at varying the spectrum slope $y$, small-scale turbulent fluctuations change from a forcing independent to a forcing dominated statistics. We argue that the critical value separating the two behaviors, in three dimensions, is $y_c=4$. When the statistics is forcing dominated, for $y<y_c$, we find dimensional scaling, i.e., intermittency is vanishingly small. On the other hand, for $y>y_c$, we find the same anomalous scaling measured in flows forced only at large scales. We connect these results with the issue of universality in turbulent flows.

Three-dimensional fractals called the Menger sponge, with a fractal dimension $D=\log 20/\log 3$, were fabricated from epoxy resin by stereolithography. Clear attenuation of both reflection and transmission intensity was observed at 12.8 GHz for a cubic specimen with an edge size of 27 mm that was constructed up to the third stage of the self-similar patterns. The electromagnetic field was found to be confined in the central part of the specimen at this frequency. The localization is not caused by the presence of a photonic band gap as in photonic crystals but should be attributed to a singular photon density of states realized in the fractal structure. This is the first report on such localization of electromagnetic waves in three-dimensional fractal cavities.

Entangled-photon coincidence imaging is a method to nonlocally image an object by transmitting a pair of entangled photons through the object and a reference optical system, respectively. The image of the object can be extracted from the coincidence rate of these two photons. From a classical perspective, the image is proportional to the fourth-order correlation function of the wave field. Using classical statistical optics, we study a particular aspect of coincidence imaging with incoherent sources. As an application, we give a proposal to realize lensless Fourier-transform imaging, and discuss its applicability in x-ray diffraction.

Bright and dark spatial gap solitons are demonstrated in waveguide arrays. These gap solitons travel across the array at zero transverse velocity, in complete analogy with stationary (immobile) temporal gap solitons. Furthermore, the launching configuration for observing these stationary gap solitons is shown to be the analog of an “ideal experiment” for observing stationary temporal gap solitons, never observed so far. A clear distinction is established between the family of Floquet-Bloch solitons in general and discrete solitons in particular, and the limiting case of gap solitons.

It is one of the basic concepts of Newtonian fluid dynamics that at low Reynolds number (Re) the Navier-Stokes equation is linear and flows are reversible. In microfluidic devices, where Re is essentially always low, this implies that flow resistance in microchannels is isotropic. Here we present a microfluidic rectifier: a microscopic channel of a special shape whose flow resistance is strongly anisotropic, differing by up to a factor of 2 for opposite flow directions. Its nonlinear operation at arbitrary small Re is due to non-Newtonian elastic properties of the working fluid, which is a 0.01% aqueous solution of a high molecular weight polymer. The rectifier works as a dynamic valve and may find applications in microfluidic pumps and other integrated devices.

We present new results for the time reversal of nonlinear pulses traveling in a random medium, in particular for solitary waves. We consider long water waves propagating in the presence of a spatially random depth. Both hyperbolic and dispersive regimes are considered. We demonstrate that in the presence of properly scaled stochastic forcing the solution to the nonlinear (shallow water) conservation law is regularized leading to a viscous shock profile. This enables time-reversal experiments beyond the critical time for shock formation. Furthermore, we present numerical experiments for the time-reversed refocusing of solitary waves in a regime where theory is not yet available. Solitary wave refocusing simulations are performed with a new Boussinesq model, both in transmission and in reflection.

We study, both theoretically and experimentally, the Bragg scattering of light in optically induced photonic lattices and reveal the key physical mechanisms which govern the nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.

We present experiments on slow granular flows in a modified (split-bottomed) Couette geometry in which wide and tunable shear zones are created away from the sidewalls. For increasing layer heights, the zones grow wider (apparently without bound) and evolve towards the inner cylinder according to a simple, particle-independent scaling law. After rescaling, the velocity profiles across the zones fall onto a universal master curve given by an error function. We study the shear zones also inside the material as a function of both their local height and the total layer height.

Employing the chiral Gaussian unitary ensemble of random matrices, we calculate the probability distribution of the local density of states for zero-dimensional (”quantum chaotic”) two-sublattice systems at the point of chiral symmetry $E=0$ and in the presence of uniform absorption. The obtained result can be used to find the distributions of the reflection coefficient and of the Wigner time delay for such systems.

We have observed a dramatic enhancement of third-harmonic generation in 3D polystyrene-air photonic crystals pumped by a near infrared laser beam. As the pump wavelength is tuned, the peak of the enhancement occurs when the third-harmonic wavelength approaches the short-wavelength edge of the band gap. We show that the origin of the enhancement is phase matching provided by the periodic structure of the photonic crystals.

The quantum resonances occurring with $\delta$-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a related system. A scaling law which characterizes the structure of the resonant peaks is derived and numerically demonstrated.

We present measurements of the normalized charge transport or Nusselt number $\mathrm{N}\mathrm{u}$ as a function of the aspect ratio $\Gamma$ for turbulent convection in an electrically driven film. In analogy with turbulent Rayleigh-Bénard convection, we develop the relevant theoretical framework in which we discuss the local power-law scaling of $\mathrm{N}\mathrm{u}$ with a dimensionless electrical forcing parameter $\mathcal{R}$. For these experiments where ${10}^4\lesssim \mathcal{R}\lesssim 2\times {10}^5$ we find that $\mathrm{N}\mathrm{u}\sim F(\Gamma ){\mathcal{R}}^{\gamma }$ with either $\gamma =0.26(\pm 0.02)$ or $\gamma =0.20(\pm 0.03)$, in excellent agreement with the theoretical predictions of $\gamma =1/4$ and $1/5$. Our measurements of the aspect-ratio dependence of $\mathrm{N}\mathrm{u}$ for $0.3\le \Gamma \le 17$ compares favorably with the function $F(\Gamma )$ from the scaling theory.

We consider the problem of incompressible, forced, nonhelical, homogeneous, and isotropic MHD turbulence with no mean magnetic field and large magnetic Prandtl number. This type of MHD turbulence is the end state of the turbulent dynamo, which generates folded fields with small-scale direction reversals. We propose a model in which saturation is achieved as a result of the velocity statistics becoming anisotropic with respect to the local direction of the magnetic folds. The model combines the effects of weakened stretching and quasi-two-dimensional mixing and produces magnetic-energy spectra in remarkable agreement with numerical results at least in the case of a one-scale flow. We conjecture that the statistics seen in numerical simulations could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.