We study internal wave generation in a laboratory model of oscillating tidal flow on a continental margin. Waves are found to be generated only in a near-critical region where the slope of the bottom topography matches that of internal waves. Fluid motion with a velocity an order of magnitude larger than that of the forcing occurs within a thin boundary layer above the bottom surface. The resonant wave is unstable because of strong shear; Kelvin-Helmholtz billows precede wave breaking. This work provides a new explanation for the intense boundary flows on continental slopes.

We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic orbit can be continued even when it is unstable. This is demonstrated with the continuation of initially stable rotations of a vertically forced pendulum experiment through a fold bifurcation to find the unstable part of the branch.

Local convective heat flux $\mathbf{J}(\mathbf{r})$ in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in a cylindrical cell filled with water. The measured $\mathbf{J}(\mathbf{r})$ in the bulk region shows a different scaling behavior with varying Rayleigh numbers compared with that measured in the plume-dominated regions near the sidewall and near the lower conducting plate. The local transport measurements thus allow us to disentangle boundary and bulk contributions to the total heat flux and directly check their respective scaling behavior against the theoretical predictions.

We consider the deposition of a film of viscous liquid on a flat plate being withdrawn from a bath, experimentally and theoretically. For any plate speed $U$, there is a range of “thick” film solutions whose thickness scales like $U^{1/2}$ for small $U$. These solutions are realized for a partially wetting liquid, while for a perfectly wetting liquid the classical Landau-Levich-Derjaguin film is observed, whose thickness scales like $U^{2/3}$. The thick film is distinguished from the Landau-Levich-Derjaguin film by a dip in its spatial profile at the transition to the bath. We calculate the phase diagram for the existence of stationary film solutions as well as the film profiles and find excellent agreement with experiment.

We investigate the dynamics of a thermally convecting fluid as it interacts with freely moving solid objects. This is a previously unexplored paradigm of interactions between many free bodies mediated by thermal convection, which gives rise to surprising robust oscillations between different large-scale circulations. Once begun, this process repeats cyclically, with the collection of objects (solid spheres) entrained and packed from one side of the convection cell to the other. The cyclic frequency is highest when the spheres occupy about half of the cell bottom and their size coincides with the thickness of the thermal boundary layer. Our work shows that a deformable mass stimulates a thermally convecting fluid into oscillation, a collective behavior that may be found in nature.

We realize an absolute position control of drifting dissipative optical solitons by injecting an incoherent amplitude parameter gradient onto the nonlinear optical system. This allows for two-dimensional, arbitrary control patterns. The control of the soliton drift velocity is studied applying a periodic, hexagonally shaped modulation. The guiding of dissipative solitons by one- and two-dimensional parameter modulations is demonstrated. Furthermore, one-dimensional, line-shaped parameter modulations are designed to act as barriers for dissipative solitons, allowing implementations of position selectors for solitons. The interaction of dissipative optical solitons with barriers is studied for different barrier parameters.

Quantum accelerator modes have been experimentally observed, and theoretically explained, in the dynamics of kicked cold atoms in the presence of gravity, when the kicking period is close to a half-integer multiple of the Talbot time. We generalize the theory to the case when the kicking period is sufficiently close to any rational multiple of the Talbot time, and thus predict new rich families of experimentally observable quantum accelerator modes.

The nonlinear interaction of waves in a driven medium may lead to wave turbulence, a state such that energy is transferred from large to small length scales. Here, wave turbulence is observed in experiments on a vibrating plate. The frequency power spectra of the normal velocity of the plate may be rescaled on a single curve, with power-law behaviors that are incompatible with the weak turbulence theory of Düring et al. [Phys. Rev. Lett. 97, 025503 (2006)]. Alternative scenarios are suggested to account for this discrepancy—in particular the occurrence of wave breaking at high frequencies. Finally, the statistics of velocity increments do not display an intermittent behavior.

An thin elastic steel plate is excited with a vibrator and its local velocity displays a turbulentlike Fourier spectrum. This system is believed to develop elastic wave turbulence. We analyze here the motion of the plate with a two-point measurement in order to check, in our real system, a few hypotheses required for the Zakharov theory of weak turbulence to apply. We show that the motion of the plate is indeed a superposition of bending waves following the theoretical dispersion relation of the linear wave equation. The nonlinearities seem to efficiently break the coherence of the waves so that no modal structure is observed. Several hypotheses of the weak turbulence theory seem to be verified, but nevertheless the theoretical predictions for the wave spectrum are not verified experimentally.

Experimental results for the evolution of the probability distribution function (PDF) of a scalar mixed by a turbulent flow in a channel are presented. The sequence of PDF from an initial skewed distribution to a sharp Gaussian is found to be nonuniversal. The route toward homogeneization depends on the ratio between the cross sections of the dye injector and the channel. In connection with this observation, advantages, shortcomings, and applicability of models for the PDF evolution based on a self-convolution mechanism are discussed.

We propose a design of coupling for stable synchronization and antisynchronization in chaotic systems under parameter mismatch. The antisynchronization is independent of the specific symmetry (reflection symmetry, axial symmetry, or other) of a dynamical system. In the synchronization regimes, we achieve amplification (attenuation) of a chaotic driver in a response oscillator. Numerical examples of a Lorenz system, Rössler oscillator, and Sprott system are presented. Experimental evidence is shown using an electronic version of the Sprott system.

We perform high-resolution numerical simulations of homogenous and isotropic compressible turbulence, with an average 3D Mach number close to 0.3. We study the statistical properties of intermittency for velocity, density, and entropy. For the velocity field, which is the only quantity that can be compared to the isotropic incompressible case, we find no statistical differences in its behavior in the inertial range due either to the slight compressibility or to the different dissipative mechanism. For the density field, we find evidence of “frontlike” structures, although no shocks are produced by the simulation.

When a liquid drop contacts a wettable surface, the liquid spreads over the solid to minimize the total surface energy. The first moments of spreading tend to be rapid. For example, a millimeter-sized water droplet will wet an area having the same diameter as the drop within a millisecond. For perfectly wetting systems, this spreading is inertially dominated. Here we identify that even in the presence of a contact line, the initial wetting is dominated by inertia rather than viscosity. We find that the spreading radius follows a power-law scaling in time where the exponent depends on the equilibrium contact angle. We propose a model, consistent with the experimental results, in which the surface spreading is regulated by the generation of capillary waves.

We report an experimental study of the dynamics of thermal fluctuations in a 4.86 mm thick layer of ${\mathrm{CS}}_2$ heated from above. Stabilizing gradients ranged from 10.3 to $61.7\mathrm{K}/\mathrm{cm}$. Power spectral measurements were made over the wave vector range $9{\mathrm{cm}}^{-1}<q<100{\mathrm{cm}}^{-1}$, using a shadowgraph apparatus. Over this range, the spectra change from having a well-resolved oscillatory mode at low $q$ to monotonic decay at higher $q$. For the smallest gradient, the results for the power spectra compare very well with theory, but slight deviations are seen for larger gradients.

We propose a new measure (phase-slope index) to estimate the direction of information flux in multivariate time series. This measure (a) is insensitive to mixtures of independent sources, (b) gives meaningful results even if the phase spectrum is not linear, and (c) properly weights contributions from different frequencies. These properties are shown in extended simulations and contrasted to Granger causality which yields highly significant false detections for mixtures of independent sources. An application to electroencephalography data (eyes-closed condition) reveals a clear front-to-back information flow.

We report observations of the Schawlow-Townes noise limit in a cryogenic sapphire secondary frequency standard. The effect causes a fundamental limit to the frequency stability, and was measured through the novel excitation of a bimodal maser oscillation of a Whispering Gallery doublet at 12.04 GHz. The beat frequency of 10 kHz between the oscillations enabled a sensitive probe for this measurement of fractional frequency instability of ${10}^{-14}{\tau }^{-1/2}$ with only 0.5 pW of output power.

We consider the classical dynamics of a particle in a ($d=2,3$)-dimensional space-periodic potential under the influence of time-periodic external fields with zero mean. We perform a general time-space symmetry analysis and identify conditions, when the particle will generate a nonzero averaged translational and vortex currents. We perform computational studies of the equations of motion and of corresponding Fokker-Planck equations, which confirm the symmetry predictions. We address the experimentally important issue of current control. Cold atoms in optical potentials and magnetic traps are among possible candidates to observe these findings experimentally.

It has been shown that the spectral fluctuations of different quantum systems are characterized by $1/f^{\alpha }$ noise, with $1\le \alpha \le 2$, in the transition from integrability to chaos. This result is not well understood. We show that chaos-assisted tunneling gives rise to this power-law behavior. We develop a random matrix model for intermediate quantum systems, based on chaos-assisted tunneling, and we discuss under which conditions it displays $1/f^{\alpha }$ noise in the transition from integrability to chaos. We conclude that the variance of the elements that connect regular with chaotic states must decay with the difference of energy between them. We compare the characteristics of the transition modeled in this way with what is obtained for the Robnik billiard.

We experimentally investigate the transition to synchronization in a population of photochemical oscillators with weak global coupling. Above a critical coupling strength the oscillators join a one-phase group or two-phase clusters. The number of oscillators in each cluster depends on the initial phase distribution, and irregular switching of oscillators between clusters is observed. The fully synchronized state emerges above a second critical coupling strength. In agreement with earlier theory, the experiments demonstrate the importance of population heterogeneity in cluster multistability.

The polarization of highly divergent modes of broad-area square vertical-cavity surface-emitting lasers is shown to be only marginally affected by material anisotropies but determined by an interplay of the polarization properties of the Bragg cavity mirrors and of the transverse boundary conditions. This leads to a locking of the polarization direction to the boundaries and its indeterminacy for wave vectors oriented along the diagonal. We point out a non-Poissonian character of nearest-neighbor frequency spacing distribution and the impossibility of single-wave number solutions.