We have investigated the self-diffusion in a stable gas-fluidized bed of fine powder. Two regimes have been observed: for gas velocities $v_g$ above the minimum fluidization velocity $v_m$ and below a critical gas velocity $v_c$ smaller than the minimum bubbling velocity $v_b$ the powder does not mix. Experimental measurements show the existence of yield stresses in this regime which are responsible for the static behavior of the bed. For $v_g>v_c$ the yield stress vanishes; the bed behaves like a fluid and displays a diffusive dynamics. In this region we have found that the diffusion coefficient $D$ increases with gas velocity until the bed expansion approaches its maximum value.

After the dynamo experiment in November 1999 [A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000)] had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed.

We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the output function evaluation (OFE) method. We show analytically that the OFE method is much more efficient than the uncertainty method for boundaries with $D<\mathrm{}0.5\mathrm{}$, where $D$ is the dimension of the intersection of the boundary with a one-dimensional manifold. We apply the OFE method to a scattering system, and compare it to the uncertainty method. We use the OFE method to study the behavior of the fractal dimension as the system's dynamics undergoes a topological transition.

The synchronization of chatoic semiconductor lasers with optical feedback is studied numerically in a one-way coupling configuration, in which a small amount of the intensity of one laser (master laser) is injected coherently into the other (slave laser). A regime of anticipated synchronization is found, in which the intensity of the slave laser is synchronized to the future chaotic intensity of the master laser. Anticipation is robust to small noise and parameter mismatches, but in this case the synchronization is not complete. It is also shown that anticipated synchronization occurs in coupled time-delay systems, when the coupling has a delay that is less than the delay of the systems.

We have measured the photon number probability distribution of a laser in which the inversion is not slaved to the field. For the experiments, we have used a ${\mathrm{Nd}}^{3+}:{\mathrm{YVO}}_4$ laser which has a sufficiently slow inversion to allow measurement of the photon fluctuations at a time scale much shorter than that of the relaxation oscillations. The photon distribution function becomes highly nonstandard (i.e., non-Poissonian) in such a laser; this is consistent with available theoretical work. We point out the relevance of our results for the case of the semiconductor microlaser.

We consider inertial particles suspended in an incompressible turbulent flow. Because of particles' inertia their flow is compressible, which leads to fluctuations of concentration significant for heavy particles. We show that the statistics of these fluctuations is independent of details of the velocity statistics, which allows us to predict that the particles cluster on the viscous scale of turbulence and describe the probability distribution of concentration fluctuations. We discuss the possible role of the clustering in the physics of atmospheric aerosols, in particular, in cloud formation.

We report the first measurement of a reduction in the conductivity of liquid sodium due to turbulence in a spherical flow (the $\beta$ effect). The sodium is contained in a 0.15 m diameter sphere, typical flow speeds are about 1 m/s, and magnetic Reynold's numbers range from 1 to 8. We find a reduction from the molecular value of the conductivity of about $4\%$. Results are in rough agreement with simple predictions from mean-field electrodynamics.

A comprehensive derivation is presented of normal form maps for grazing bifurcations in piecewise smooth models of physical processes. This links grazings with border-collisions in nonsmooth maps. Contrary to previous literature, piecewise linear maps correspond only to nonsmooth discontinuity boundaries. All other maps have either square-root or $\left(3/2\right)$-type singularities.

The onset of the wave resistance, via generation of capillary-gravity waves of a small object moving with velocity $V$, is investigated experimentally. Because of the existence of a minimum phase velocity $V_c$ for surface waves, the problem is similar to the generation of rotons in superfluid helium near their minimum. In both cases waves or rotons are produced at $V>\mathrm{}{V}_c$ due to Cherenkov radiation. We find that the transition to the wave drag state is continuous: in the vicinity of the bifurcation the wave resistance force is proportional to $\sqrt{{V-V}_c}$ for various fluids.

Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices. These transients are caused by the presence of chaotic saddles, and they are a common phenomenon in higher dimensional dynamical systems. For many physical systems, chaotic saddles have a big impact on laboratory measurements, but there has been no way to observe these chaotic saddles directly. We present the first general method to locate and visualize chaotic saddles in higher dimensions.

Delayed feedback control of chaos is well known as an effective method for stabilizing unstable periodic orbits embedded in chaotic attractors. However, it had been shown that the method works only for a certain class of periodic orbits characterized by a finite torsion. Modification based on an unstable delayed feedback controller is proposed in order to overcome this topological limitation. An efficiency of the modified scheme is demonstrated for an unstable fixed point of a simple dynamic model as well as for an unstable periodic orbit of the Lorenz system.

The dynamics of Rydberg states of a hydrogen atom subjected simultaneously to uniform static electric field and two microwave fields with commensurate frequencies is considered in the range of small field amplitudes. In the certain range of the parameters of the system the classical secular motion of the electronic ellipse reveals chaotic behavior. Quantum mechanically, when the fine structure of the atom is taken into account, the energy level statistics obey predictions appropriate for the symplectic Gaussian random matrix ensemble.

Directed collective motion in a circular array of unidirectionally coupled oscillators with symmetric potential is obtained numerically in the absence of external bias. This striking feature is interpreted as the effect of the spontaneous breaking of temporal symmetry of the coupling. It is revealed that a proper match of various control parameters is important in generating an optimal coherent global transport. Noise-sustained directed transport is also observed, and the related stochastic resonance in an autonomous system is identified.

A coherent x-ray generation scheme is proposed which involves characteristics of free electron lasers and atomic high harmonic generation schemes. A thin solid layer or any other periodic atomic structure with limited dimensions is exposed to a short, superintense laser pulse. The electrons are extracted from the layer due to the extreme force and penetrate periodically through the ionic structure. Consequently, thousands of harmonics of the laser radiation field are shown to coherently amplify along the interaction length. The small signal gain of the generated x-ray radiation exceeds that arising from the multiphoton Compton process in plasmas and is competitive with that in the leading x-ray free electron lasers.

Incoherent optical spatial solitons require noninstantaneous nonlinearity, i.e., the local intensity fluctuation of the solitons must be faster than the medium can respond. Observing partially incoherent bicomponent solitons, we find that there exists a threshold speed. When the fluctuation of the soliton intensity, resulting from the time-varying interference of its constituent modes, is below the threshold, the soliton beam and its induced waveguide oscillate violently. Just above the threshold, the soliton-induced waveguide is observed to be dragged by the soliton beam.

All-optical angular control of the molecular alignment in liquid-crystal films is demonstrated using a laser beam having an elliptically shaped intensity profile. The material birefringence is unimportant, as proven by the fact that good alignment is obtained with unpolarized light. This raises the possibility of achieving optical angular control of transparent isotropic bodies. A general theoretical approach, based on light and matter angular momentum conservation, shows that the optical alignment is due to the internal compensation between the transfer of the orbital and the spin part of angular momentum of the incident photons to the material.

The transmittance spectrum for an air-bridge type of AlGaAs photonic crystal (PC) slabs successfully fabricated was measured. It is found that the observed spectrum is consistent with both the theoretical band structure and the calculated one. Moreover, the transmittance due to the modes below the light line is found to be almost $100\%$, indicating that the guided modes should exist. The respective stop bands are observed in the $\Gamma -\mathrm{M}$ direction for TM-like and TE-like modes, implying that a photonic band gap should exist for the TE-like guided modes. The present PC is very suited for controlling the radiation field.

Long liquid capillary bridges are normally unstable because of the growth of a mode where one end becomes slender while the other becomes rotund. This Rayleigh-Plateau instability was suppressed for weightless bridges on NASA's KC-135 aircraft by placing the bridge in an acoustic standing wave. With an appropriate acoustic wavelength and amplitude the radiation pressure automatically squeezes more on the rotund portion of the bridge so as to suppress the growth of the relevant capillary mode. Stabilization is a natural consequence of the interaction with the steady sound field.

We present new heat-conduction equations, named ballistic-diffusive equations, which are derived from the Boltzmann equation. We show that the new equations are a better approximation than the Fourier law and the Cattaneo equation for heat conduction at the scales when the device characteristic length, such as film thickness, is comparable to the heat-carrier mean free path and/or the characteristic time, such as laser-pulse width, is comparable to the heat-carrier relaxation time.