In seeking to understand experiments on low-Reynolds-number mixing and flow transitions in viscoelastic fluids, we simulate the dynamics of the Oldroyd-B model, with a simple background force driving the flow. We find that at small Weissenberg number, flows are “slaved” to the extensional geometry imposed by forcing. For large Weissenberg number, such solutions become unstable and transit to a structurally dissimilar state dominated by a single large vortex. This new state can show persistent oscillatory behavior with the production and destruction of smaller-scale vortices that drive mixing.

The main topological feature of a superfluid is a quantum vortex with an identifiable inner and outer radius. A novel unitary quantum lattice gas algorithm is used to simulate quantum turbulence of a Bose-Einstein condensate superfluid described by the Gross-Pitaevskii equation on grids up to ${5760}^3$. For the first time, an accurate power-law scaling for the quantum Kelvin wave cascade is determined: $k^{-3}$. The incompressible kinetic energy spectrum exhibits very distinct power-law spectra in 3 ranges of $k$ space: a classical Kolmogorov $k^{-(5/3)}$ spectrum at scales greater than the outer radius of individual quantum vortex cores and a quantum Kelvin wave cascade spectrum $k^{-3}$ on scales smaller than the inner radius of the quantum vortex core. The $k^{-3}$ quantum Kelvin wave spectrum due to phonon radiation is robust, while the $k^{-(5/3)}$ classical Kolmogorov spectrum becomes robust on large grids.

Using longer wavelength laser drivers for high harmonic generation is desirable because the highest extreme ultraviolet frequency scales as the square of the wavelength. Recent numerical studies predict that high harmonic efficiency falls dramatically with increasing wavelength, with a very unfavorable ${\lambda }^{-(5-6)}$ scaling. We performed an experimental study of the high harmonic yield over a wavelength range of 800–1850 nm. A thin gas jet was employed to minimize phase matching effects, and the laser intensity and focal spot size were kept constant as the wavelength was changed. Ion yield was simultaneously measured so that the total number of emitting atoms was known. We found that the scaling at constant laser intensity is ${\lambda }^{-6.3\pm 1.1}$ in Xe and ${\lambda }^{-6.5\pm 1.1}$ in Kr over the wavelength range of 800–1850 nm, somewhat worse than the theoretical predictions.

We seek an explanation for the neurophysiological phenomenon of event-related desynchronization (ERD) by using models of diffusively coupled nonlinear oscillators. We demonstrate that when the strength of the event is sufficient, ERD is found to emerge and the accomplishment of a behavioral or functional task is determined by the nature of the desynchronized state. We illustrate the phenomenon for the case of limit cycle and chaotic systems. We numerically demonstrate the occurrence of ERD and provide an analytical explanation. We also discuss possible applications of the observed phenomenon in real physical systems other than the brain.

We propose a new mechanism for turbulent transport in systems which support radiating nonlinear solitary wave packets or pulses. The direct energy cascade is provided by adiabatically evolving pulses, whose widths and carrier wavelengths decrease. The inverse cascade is due to the excitation of radiation. The spectrum is steeper than the Kolmogorov-Zakharov spectrum of wave turbulence.

Experiments by several groups during the past decade have shown that a molten polymer nanofilm subject to a large transverse thermal gradient undergoes spontaneous formation of periodic nanopillar arrays. The prevailing explanation is that coherent reflections of acoustic phonons within the film cause a periodic modulation of the radiation pressure which enhances pillar growth. By exploring a deformational instability of particular relevance to nanofilms, we demonstrate that thermocapillary forces play a crucial role in the formation process. Analytic and numerical predictions show good agreement with the pillar spacings obtained in experiment. Simulations of the interface equation further determine the rate of pillar growth of importance to technological applications.

A new cloaking method is presented for 2D quasistatics and the 2D Helmholtz equation that we speculate extends to other linear wave equations. For 2D quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is close to 1 in a disk and close to 0 in another disk, and such a polynomial is constructed. For the 2D Helmholtz equation it is numerically shown that three exterior cloaking devices placed around the object suffice to hide it.

In this Letter, we study slow-light transport in photonic-crystal waveguides in the presence of structural imperfections. In contrast with previous theoretical works that rely on perturbation theories, the present formalism takes into account multiple scattering and localization effects. It allows for a quantitative prediction of the main statistical transport coefficients, including averaged values as well as probability distributions. In particular, we evidence that, as the group velocity decreases, the attenuation probability distribution exhibits a rapid broadening that one should consider for designing slow-light devices.

We demonstrate that metamaterials with anisotropic properties can be used to develop a new class of periodic structures that has been named radial wave crystals. They can be sonic or photonic, and wave propagation along the radial directions is obtained through Bloch states like in usual sonic or photonic crystals. The band structure of the proposed structures can be tailored in a large amount to get exciting novel wave phenomena. For example, it is shown that acoustical cavities based on radial sonic crystals can be employed as passive devices for beam forming or dynamically orientated antennas for sound localization.

We present new experimental results on the transition from coherent-phase to random-phase three-wave interactions in capillary waves under parametric excitation. Above the excitation threshold, coherent wave harmonics spectrally broaden. An increase in the pumping amplitude increases spectral widths of wave harmonics and eventually causes a strong decrease in the degree of the three-wave phase coupling. The results point to the modulation instability of capillary waves, which leads to breaking of continuous waves into ensembles of short-lived wavelets or envelope solitons, as the reason for the phase randomization of three-wave interactions.

Surface spontaneous parametric down-conversion is predicted as a consequence of continuity requirements for electric- and magnetic-field amplitudes at a discontinuity of ${\chi }^{(2)}$ nonlinearity. A generalization of the usual two-photon spectral amplitude is suggested to describe this effect. Examples of nonlinear layered structures and periodically poled nonlinear crystals show that surface contributions to spontaneous down-conversion can be important.

A droplet placed in a liquid-liquid solution is expected to grow, or shrink, in time as $\sim t^{1/2}$. In this Letter, we report experimental evidence that when the composition in the interface is far from thermodynamic equilibrium due to the nonideality of the mixture, a droplet shrinks as $\sim t$. This scaling is due to the coupling between mass and momentum transfer known as Korteweg forces as a result of which the droplet self-propels around. The consequent hydrodynamic convection greatly enhances the mass transfer between the droplet and the bulk phase. Thus, the combined effect of nonideality and nonequilibrium modifies the dynamical behavior of the dissolving droplet.

Recent research on second-harmonic generation in left-handed materials has shown a light localization mechanism that originates from an all-angle phase-matching condition between counterpropagating electromagnetic modes at fundamental and double frequencies. By combining these properties with negative refraction, we propose in this Letter an original approach to the design of a second-harmonic lens. Numerical simulations demonstrate that feasible metamaterials can be tailored to operate in the visible range of frequency. These nonlinear lenses open an attractive solution for the biphotonic microscopy technique by imaging passive biological structures.

We measure the complex scattering amplitudes of a flat microwave cavity (a “chaotic billiard”). Time-reversal ($\mathcal{T}$) invariance is partially broken by a magnetized ferrite placed within the cavity. We extend the random-matrix approach to $\mathcal{T}$ violation in scattering, determine the parameters from some properties of the scattering amplitudes, and successfully predict others. Our work constitutes the most precise test of the random-matrix theoretical approach to $\mathcal{T}$ violation so far available.

We introduce a new approach for measuring both the effective medium and the transport properties of light propagation in heterogeneous media. Our method utilizes the conceptual equivalence of frequency variation with a change in the effective index of refraction. Experimentally, we measure intensity correlations via spectrally resolved refractive index tuning, controlling the latter via changes in the ambient pressure. Our experimental results perfectly match a generalized transport theory that incorporates the effective medium and predicts a precise value for the diffusion constant. Thus, we directly confirm the applicability of the effective medium concept in strongly scattering materials.

A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an integrable structure permits us to calculate the joint distribution of eigenvalues for these matrices analytically. Spectral statistics of these ensembles are quite unusual and in many cases give rigorously new examples of intermediate statistics.

Direct numerical simulation of transitional pipe flow is carried out in a long computational domain in order to characterize the dynamics within the saddle region of phase space that separates laminar flow from turbulent intermittency. For Reynolds numbers ranging from $\mathrm{Re}=1800$ to 2800, a shoot and bisection method is used to compute critical trajectories. The chaotic saddle or edge state approached by these trajectories is studied in detail. For $\mathrm{Re}\le 2000$ the edge state and the corresponding intermittent puff are shown to share similar averaged global properties. For $\mathrm{Re}\ge 2200$, the puff length grows unboundedly whereas the edge state varies only little with Re. In this regime, transition is shown to proceed in two steps: first the energy grows to produce a localized turbulent patch, which then, during the second stage, spreads out to fill the pipe.

We introduce a new phase space representation for open quantum systems. This is a very powerful tool to help advance in the study of the morphology of their eigenstates. We apply it to two different versions of a paradigmatic model, the baker map. This allows us to show that the long-lived resonances are strongly scarred along the shortest periodic orbits that belong to the classical repeller. Moreover, the shape of the short-lived eigenstates is also analyzed. Finally, we apply an antiunitary symmetry measure to the resonances that allows us to quantify their localization on the repeller.

Typical microresonators exhibit a large frequency spacing between resonances and a limited tunability. This impedes their use in a large class of applications which require a resonance of the microresonator to coincide with a predetermined frequency. Here, we experimentally overcome this limitation with highly prolate-shaped whispering-gallery-mode “bottle microresonators” fabricated from standard optical glass fibers. Our resonators combine an ultrahigh quality factor of $3.6\times {10}^8$, a small mode volume, and near-lossless fiber coupling, characteristic of whispering-gallery-mode resonators, with a simple and customizable mode structure enabling full tunability.

The Cotton-Mouton (Voigt) and Faraday effects induce adjustable linear and circular birefringence in optical media with external magnetic fields. We consider these effects as a technique for magneto-optical control of the transmission of bimodal light beams through Kerr-nonlinear crystals. Numerical analysis suggests that a properly applied magnetic field may accelerate, delay, or arrest the collapse of $(2+1)\mathrm{D}$ beams. Experimentally, the magnetic collapse acceleration is demonstrated in a bulk yttrium iron garnet (YIG) crystal.