We show that Manning's empirical formula for the mean velocity of turbulent flows in channels represents the power-law asymptotic behavior of a flow of incomplete similarity in the relative roughness. We then derive the formula based on the phenomenological theory of turbulence. Our derivation yields the correct similarity exponent; it justifies Manning's use of a single parameter, the hydraulic radius, to characterize the geometry of the cross section; and it affords insight into the mechanism of momentum transfer.

We study the nucleation and the growth of avalanches in a model experimental system consisting of a bidimensional packing of noncohesive grains positioned in a rotating drum. We show that the avalanche mass increases linearly in time, and that the growth rate is governed by the velocities of the two up and down fronts. The upper front is shown to propagate upwards with a velocity which is equal to the averaged velocity of the flowing grains, whereas the velocity of the downslope propagating front is approximately equal to twice the avalanche velocity. We describe simple mechanisms which quantitatively account for the observed dynamical properties.

We give quantitative experimental evidence of the influence of cavity detuning in determining the pattern selection in a one-dimensional large Fresnel number optical oscillator. The issues of the selection of the transverse mode close to threshold and the value of the pump parameter at threshold are addressed. Competition between right and left traveling waves, resulting in a winner takes all dynamics, is also reported. Experimental results are in quantitative agreement with the theoretical predictions formulated for a broad class of systems comparable to the one here considered.

We report on numerical and experimental observations of islands of stability induced in a Bunimovich stadium atom-optics billiard by a soft wall repulsive potential. A deviation from exponential decay of the survival probability of atoms in an open billiard is observed, and explained by the presence of these stable islands and a sticky region surrounding them. We also investigate islands in dispersing billiards with soft walls, and predict a new mechanism for their formation.

We present experimental results on the robustness of acoustic time-reversal focusing in a multiple scattering medium undergoing perturbations. Time reversal in such a medium can be viewed as a correlation technique, analogous to diffusive wave spectroscopy. Moreover, the recent introduction of telecommunication techniques based on time reversal in changeable media naturally raises the question of sensitivity to a perturbation of the medium. We consider the situation where the reversibility of an acoustic wave generated by a linelike source is gradually destroyed when a perturbation is added, either locally (by removing scatterers) or globally (by changing the temperature) to the multiple scattering medium.

Here we report a simple microfluidics phenomenon which allows the efficient mass production of micron size gas bubbles with a perfectly monodisperse and controllable diameter. It resorts on a self-excited breakup phenomenon (which locks at a certain frequency) of a short gas microligament coflowing in a focused liquid stream. In this work, we describe the physics of the phenomenon and obtain closed expressions for the bubble diameter as a function of the liquid and gas properties, geometry, and flow parameters, from a large set of experimental results.

A paradoxical symmetry breaking—development of a unidirectional flow via thermal instability—is predicted by an analytical solution for compressible convection near a point source of both heat and gravity. Such a flow can propel a cosmic hot body (e.g., a protostar) in a molecular cloud. This convection emerges at the critical Rayleigh number $\mathrm{Ra}=l(l+1\mathrm{})\left[2l\right(l+1\mathrm{})+1+3\mathrm{}{\mu }_V/2\mathrm{}]\gamma /(\gamma -1\mathrm{})$, where $l$ is the number of flow cells, ${\mu }_V$ is the second-to-first viscosity ratio, and $\gamma$ is the specific heat ratio.

The reconstruction of Fokker-Planck equations from observed time series data suffers strongly from finite sampling rates. We show that previously published results are degraded considerably by such effects. We present correction terms which yield a robust estimation of the diffusion terms, together with a novel method for one-dimensional problems. We apply these methods to time series data of local surface wind velocities, where the dependence of the diffusion constant on the state variable shows a different behavior than previously suggested.

We reveal experimentally waveguiding characteristics and group-velocity dispersion of line defects in photonic crystal slabs as a function of defect widths. The defects have waveguiding modes with two types of cutoff within the photonic band gap. Interference measurements show that they exhibit extraordinarily large group dispersion, and we found waveguiding modes whose traveling speed is 2 orders of magnitude slower than that in air. These characteristics can be tuned by controlling the defect width, and the results agree well with theoretical calculations, indicating that we can design light paths with made-to-order dispersion.

Motivated by recent experimental observations of anomalous diffraction in linear waveguide array, we propose a novel model governing the propagation of an optical beam in a diffraction managed nonlinear waveguide array. This model supports discrete spatial solitons whose beamwidth and peak amplitude evolve periodically. A nonlocal integral equation governing the slow evolution of the soliton amplitude is derived and its stationary soliton solutions are obtained.

We observe powder “droplets” forming when tapping repeatedly a horizontal flat plate initially covered with a monolayer of fine powder particles. Starting from a simple model involving both the air flow through the porous cake and avalanche properties, we set up an analytical model which satisfactorily fits the experimental results. We observe a close analogy between the governing equations of the phenomenon and the basic physics of wetting liquids, including the equivalent of the Laplace law and the surface tension parameter leading to the well known Rayleigh-Taylor instability.

We study the process by which a perturbed granular medium of millimetric-size particles reaches a “frozen” static configuration by decreasing perturbation intensity. The granular system is perturbed by isolated taps or by continuous vibrations. The granular process is observed by an immersed oscillator, which is used as a low-frequency “thermometer.” A diffusive noise is seen until well below the fluidization limit, and the approach to the frozen configuration arises according to a modified Vogel-Fulcher-Tammann (VFT) behavior. As a function of an empirical control parameter with unit of time one recovers a standard VFT form.

For a simple class of quasiperiodically forced dynamical systems, we present a rigorous result supporting the idea that the attractors for this class of systems, although nonchaotic, are strange in the sense that their box-counting dimension is two while their information dimension is one. Furthermore, this result is stable to changes of the system, suggesting that the basic features leading to it may be present in typical quasiperiodically forced systems.

It is shown using three series of Rayleigh number simulations of varying aspect ratio AR and Prandtl number Pr that the normalized dissipation at the wall, while significantly greater than 1, approaches a constant dependent upon AR and Pr. It is also found that the peak velocity, not the mean square velocity, obeys the experimental scaling of $\mathrm{Ra}{}^{0.5}$. The scaling of the mean square velocity is closer to $\mathrm{Ra}{}^{0.46}$, which is shown to be consistent with experimental measurements and the numerical results for the scaling of Nu and the temperature if there are strong correlations between the velocity and temperature.

We study theoretically the polarization state of light in multiple scattering media in the limit of low contrast in the refractive index. Linearly polarized photons are randomly rotated due to the Berry phase associated with the scattering path. For circularly polarized light independent speckle patterns are found for the two helical states. The statistics of the geometric phase is related to the writhe distribution of semiflexible polymers such as DNA.

We present a study of the influence of interparticle cohesive forces on the packing of spheres. This is achieved by changing the external magnetic field on iron spheres in the millimeter size range. The force of cohesion between two spheres is measured by opposing magnetic and gravitational force. The void fraction of the bed resulting from many spheres being poured into a container at a given magnetic field is measured. The void fraction of the packed spheres as a function of interparticle force is thus established. We find that the void fraction is determined only by the ratio of interparticle force to particle weight, regardless of particle size. This is shown to be a universal effect, not limited to magnetic systems.

We study experimentally and numerically the secondary instability corresponding to the destabilization of stationary transverse roll patterns appearing in a 1D liquid crystal layer subjected to optical feedback. This dynamical instability appears as roll dislocations in the spatiotemporal diagrams. We show that it originates from the Gaussian spatial transverse dependence of a control parameter and that its corresponding mechanism is the selection of a local unstable wave number. This instability is the optical counterpart of the ramp-induced Eckhaus instability observed in hydrodynamics.

High-order harmonics were coherently controlled using chirped femtosecond laser pulses for the production of sharp and strong harmonics. As the laser intensity was increased above the saturation intensity for optical-field ionization, the laser chirp needed to suppress harmonic chirp in the plateau region changed from positive to negative. We showed that the modification of a laser chirp condition in a rapidly ionizing medium should be included for the proper coherent control of high-order harmonics, necessitating the integral treatment of the interaction between atoms and a driving laser pulse.

We give experimental and numerical evidence for a new dynamical regime in the operation of semiconductor lasers subject to delayed optical feedback occurring for short delay times. This short cavity regime is dominated by a striking dynamical phenomenon: regular pulse packages forming a robust low-frequency state with underlying fast, regular intensity pulsations. We demonstrate that these regular pulse packages correspond to trajectories moving on global orbits comprising several destabilized fixed points within the complicated phase space structure of this delay system.

The measured distribution of the single-channel delay time of localized microwave radiation and its correlation with intensity differ sharply from the behavior of diffusive waves. The delay time is found to increase with intensity, while its variance is inversely proportional to the fourth root of the intensity. The distribution of the delay time weighted by the intensity is found to be a double-sided stretched exponential to the 1/3 power centered at zero. The correlation between dwell time and intensity provides a dynamical test of photon localization.