The flow pattern induced by a swarm of bubbles rising in a liquid layer is studied numerically. The fluid motion is described by spatially filtered Navier-Stokes equations forced by the presence of the bubbles. When the volume fraction and the residence time of the bubbles increase, a Rayleigh-Taylor-type instability develops. After transient stages, the flow reaches an equilibrium state made of counterrotating cellular structures. The simulations suggest that no wavelength selection mechanism exists in the present situation, making a striking difference with thermal convection.

We develop a classical model for the decay of homogeneous and isotropic turbulence that takes into account the growth of the energy containing length scale and its saturation when it reaches the size of the containing vessel. The model describes our data on the decay of grid turbulence in helium II through 4 orders of magnitude in vorticity, as well as classical experiments on decaying turbulence.

We observe coherent resonant coupling of optical whispering-gallery modes in fluorescence from dye doped polymer bispheres with diameters ranging from 2 to $5\mu \mathrm{m}$. By monitoring the frequencies of fluorescence peaks of individual spheres, we sort out two spheres with appropriate size matching and bring them into contact. Wave optics calculation also gives good agreement with the experiment. By taking into account harmonic coupling of the whispering-gallery modes, the obtained features of normal mode splitting are well explained by the tight-binding photon picture.

Twelvefold quasiperiodic structures are observed in an autonomous optical pattern forming system with continuous rotational symmetry. These quasipatterns arise from a primary hexagonal structure. In dependence on the experimental parameters the bifurcation can be sub- or supercritical. In the supercritical case, the transition is mediated by a new kind of patterns with different amplitudes in its fundamental modes. It is proven by an optical Fourier filtering technique that the observed quasipatterns can exist only in the presence of harmonics of the fundamental unstable modes.

We report the experimental formation of optical spatiotemporal solitons. Intense femtosecond-duration pulses experience a saturable self-focusing nonlinearity due to the cascading of quadratic nonlinear processes. Strong coupling of the interacting fundamental and harmonic waves produces solitons that overcome diffraction in one spatial dimension as well as group-velocity dispersion to reach constant beam size and pulse duration, both compressed with respect to the input values. Spatiotemporal solitons are observed both with nearly zero and with large group-velocity mismatch between fundamental and harmonic pulses.

We present results on the onset of convective behavior of ${}^3\mathrm{He}$ along the critical isochore where the fluid compressibility diverges as $T\to T_c$, the critical temperature. The aspect ratio of the Rayleigh-Bénard cell was 57. The “adiabatic temperature gradient” that stabilizes the fluid layer was observed and agreed with predictions. This is the first systematic study of the convection onset in the compressibility-dominated stability regime. The initial slope of the convection current versus the reduced Rayleigh number was found to be independent of compressibility and to be the same as in experiments with a similar aspect ratio in liquid ${}^3\mathrm{He}$, ${}^4\mathrm{He}$, and water.

We find that circular kinks form on the surface of granular material when the axis of rotation is tilted more than the angle of internal friction of the material. Radius of the kinks is measured as a function of the spinning speed and the tilting angle. Stability consideration of the surface results in an explanation that the kink is a boundary between the inner unstable and outer stable regions. A simple cellular automata model also displays kinks at the stability boundary.

We propose a continuum description for the axial separation of granular materials in a long rotating drum. The model, operating with two local variables, concentration difference and the dynamic angle of repose, describes both initial transient traveling wave dynamics and long-term segregation of the binary mixture. Segregation proceeds through ultraslow logarithmic coarsening.

Experimental and theoretical results for the axially, stably stratified Taylor-Couette flow are presented. The primary instability is a direct Hopf bifurcation. It leads the system into an oscillatory state of confined internal waves, in good agreement with linear stability analysis. The secondary bifurcation, which leads the system to a pattern of drifting nonaxisymmetric vortices, is a subcritical Hopf bifurcation. This first experimental evidence of a global bifurcation is thought to be generic to dynamical systems with one destabilizing and one stabilizing control parameter.

We consider the effect of microscopic external noise on the collective motion of a globally coupled map in fully desynchronized states. Without the external noise a macroscopic variable shows high-dimensional chaos distinguishable from random motions. With the increase of external noise intensity, the collective motion is successively simplified. The number of effective degrees of freedom in the collective motion is found to decrease as $-\log {\sigma }^2$ with the external noise variance ${\sigma }^2$. It is shown how the microscopic noise can suppress the number of degrees of freedom at a macroscopic level.

We show that the well-known instability in actively mode-locked lasers with detuning between the resonator round-trip time and the modulator period exhibits a transition to turbulence analogous to fluid flow. We derive a universal normalized detuning of the laser that plays the same role as Reynolds number in fluid flow. This is the first time that the recently proposed theory for the onset of turbulence in hydrodynamics is verified in a system outside of hydrodynamics.

We propose a method for timing optical solitons through an intermittent injection of cw light pulses. By changing amplitude, frequency, and width of a cw light pulse, we demonstrate that a free parametric control of time shift of a soliton is possible. An analytic formula is also provided which agrees well with numerical results.

We study the pattern formation in a chemical two-layer system, placed in a Hele-Shaw cell. The upper layer is an organic solvent in which a carboxylic acid is dissolved. The lower layer consists of water containing an inorganic base. We report on a novel instability type which is driven by an exothermic neutralization reaction in vicinity to the interface. This instability combines plume and finger regimes and gives rise to a self-sustained dynamics.

It is shown by perturbation techniques and numerical simulations that the inverse cascade of kink-antikink annihilations, characteristic of the Kolmogorov flow in the slightly supercritical Reynolds number regime, is halted by the dispersive action of Rossby waves in the $\beta$-plane approximation. For $\beta \to 0$, the largest excited scale is $\propto \ln 1/\beta$ and differs strongly from what is predicted by standard dimensional phenomenology which ignores the depletion of nonlinearity.

We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out on samples whose sizes are large compared to the localization length (localized regime). The case of small samples is also discussed (ballistic regime). We provide a physical argument which explains in a quantitative way the origin of the exponential divergence of the moments. The occurrence of a log-normal tail for finite size systems is analyzed. Finally, we present exact results in the low energy limit which clearly show a departure from the universal behavior.

We study quantum chaos in a non-KAM system exemplified by a particle in an infinite potential well subject to a periodic kicking force. For a small perturbation $K$, the classical phase space displays a stochastic web structure, and the diffusion coefficient scales as $D\propto K^{2.5}$. However, in the large $K$ regime, $D\propto K^2$. Quantum mechanically, we observe that the level spacing statistics of the quasieigenenergies changes from Poisson to Wigner distribution as $K$ increases. The quasieigenstates are power-law localized for small $K$ and extended for large $K$. Possible experimental realization of this model is also discussed.

In periodically driven chaotic dynamical systems with a broad distribution of intrinsic time scales, perfect phase synchronization cannot be reached. Long segments of evolution during which the phase of a chaotic variable follows the phase of the driving force are interrupted by short segments of phase drift. We demonstrate that this drift is another short-lived synchronized state; its onset is caused by the passage near the long unstable periodic orbits whose frequencies are locked by external force in ratios different from 1:1.

We present an experimental study of forced drainage through a soap foam, where a constant liquid flux at the top of a dry foam produces a downwards traveling wave with a constant velocity and uniform liquid content. The results are not consistent with existing models and we propose a new model, based upon relaxing the condition of wall rigidity throughout the network and emphasizing the importance of viscous damping in the nodes where Plateau borders meet. This model agrees well with the experimentally measured (power-law) scaling behavior of the drainage velocity, and the width of the propagating liquid front, on the imposed flow rate and bubble size.

Ultrafast laser pulses with complex envelopes (amplitude and frequency modulated) are used to excite an optically dense column of rubidium vapor. Pulse reshaping, stimulated emission dynamics, and residual electronic excitation in the Rb vapor are all shown to depend strongly on the laser pulse shape. Pulses that produce adiabatic passage in the optically thin limit exhibit more complex behavior in optically thick samples, including an unexpected dependence on the sign of the frequency sweep. Numerical solutions of the Maxwell-Bloch equations are shown to account for our results.

We observe polarization-locked vector solitons in a mode-locked fiber laser. Temporal vector solitons have components along both birefringent axes. Despite different phase velocities due to linear birefringence, the relative phase of the components is locked at $\pm \pi /2\mathrm{}$. The value of $\pm \pi /2\mathrm{}$ and component magnitudes agree with a simple analysis of the Kerr nonlinearity. These fragile phase-locked vector solitons have been the subject of much theoretical conjecture, but have previously eluded experimental observation.