Three-dimensional dynamics of thin Newtonian liquid films subjected to long-range van der Waals forces on a horizontal coated solid surface is numerically studied in the framework of the long-wave theory. The dynamics of nonvolatile films results in the emergence of an isolated steady drop standing on a practically flat film, while volatile films uniformly disappear on the macroscale. In both cases the evolution of the initial small-amplitude noise spans over the stages of self-organization, fast thinning of the depressions, formation and expansion of the “holes,” emergence of the polygonal network of liquid ridges, and its breakup, as seen in the experiments.

In the free surface flow of dense suspensions in confined domains, spontaneous particle enrichment occurs in the region adjacent to the free surface with an attendant increase in the effective viscosity. We present experimental evidence that this particle accretion introduces stability considerations that would otherwise not exist if the suspension remained uniform. For conditions favoring global stability, a local fingering instability can occur in the accretion band. For conditions favoring global instability, accretion can suppress the global growth of viscous fingers at the interface.

Spiral surface waves emitted from a vertical vortex are studied experimentally. It is found that, similar to what occurs in the scattered wave of electrons for the Aharonov-Bohm effect, the number of arms of these waves is linked to circulation flux and therefore to the number of dislocations in the wave front.

We describe several mechanisms that prevent equipartition of energy in mechanical systems. In certain regimes, we present a quantitative prediction of the relative abundance of orbits exhibiting these mechanisms. This quantitative prediction is confirmed in numerical experiments.

By using the diffraction properties of waveguide arrays, we propose a scheme to produce structures with designed diffraction. We fabricated arrays with reduced, canceled, and even reversed diffraction. Results of experiments with such waveguides are presented and compared with the predictions made by coupled-mode theory.

We show that a hybridization of the optical and material nonlinearities takes place near the threshold of the subharmonic generation in photorefractive crystals. It results in a critical (with a singularity) enhancement of the rate of spatial amplification of light waves and leads to a variety of new optical critical phenomena.

We present experimental and numerical observations of transverse instability in quadratic media under conditions that emphasize the inherently spatiotemporal and multidimensional nature of the wave propagation. Intensity-dependent beam filamentation is shown to be closely connected to the periodic evolution of quadratic solitons, and implications for the generation of three-dimensional spatiotemporal solitons are discussed.

We propose that the photonic band structure (PBS) of semiconductor-based photonic crystals (PCs) can be made tunable if the free-carrier density is sufficiently high. In this case, the dielectric constant of the semiconductor, modeled as $\varepsilon \left(\omega \right)={\varepsilon }_0(1-{\omega }_p^2/{\omega }^2)$, depends on the temperature $T$ and on the impurity concentration $N$ through the plasma frequency ${\omega }_p$. Then the PBS is strongly $T$ and $N$ dependent; it is even possible to obliterate a photonic band gap. This is shown by calculating the 2D PBS for PCs that incorporate either intrinsic InSb or extrinsic Ge.

We report experimental results which show that the stimulated Brillouin scattering (SBS) spectrum in an optical fiber is inhomogeneous, exhibiting spectral broadening and hole burning under cw monochromatic laser excitation. This phenomenon arises from the waveguide interaction of the pump and Stokes signals and is a fundamental property of SBS in waveguiding systems due to their ability to confine a fan of radiation wave vector directions.

We report observation of a new mixture-separation process: an insonified mixture of helium and argon in a narrow duct spatially separates along the acoustic-propagation axis. We measure mole-fraction differences across the ends of the duct as large as $7\%$. We measure initial separation flux densities as high as ${10}^{-3\mathrm{}}{\mathrm{M}}^{2}c$, where M is the acoustic Mach number and $c$ is the sound speed. This initial separation flux, as a function of both the amplitudes and the relative phasing of the pressure and velocity oscillations in the duct, agrees well with a recent theory involving oscillating thermal diffusion in the acoustic boundary layer.

We investigate the behavior of spiral waves in a quasi-two-dimensional spatial open reactor using Belousov-Zhabotinsky reaction. The goal of this study is to answer two questions raised recently: Can a system sustain a stable long-wavelength modulated spiral? What causes the transition from spiral to defect-mediated turbulence? Our experimental results show that in a certain range of control parameters, a sustained long-wavelength modulated spiral is stable. The amplitude and the wavelength of modulations increase with the control parameter. As the latter is increased to across a threshold, defects are generated far away from the spiral center as a result of the neighboring two wave fronts being too close.

We consider chaotic billiards in $d$ dimensions, and study the matrix elements $M_{\mathrm{nm}}$ corresponding to general deformations of the boundary. We analyze the dependence of $|M_{\mathrm{nm}}{|}^2$ on $\omega =\left(E_n{-E}_m\right)/ħ$ using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency $\omega$. We show that, for dilations and translations of the boundary, $|M_{\mathrm{nm}}{|}^2$ vanishes like ${\omega }^4$ as $\omega \to 0$, for rotations such as ${\omega }^2$, whereas for generic deformations it goes to a constant. Such special cases lead to quasiorthogonality of the eigenstates on the boundary.

We show that the two point intensity correlation in the near field of the scattered light is directly related to the two point density correlation $g\left(r\right)$. Preliminary measurements on two sets of calibrated random pinholes of 140 and $300\mu \mathrm{m}$ diameters, and on aqueous solutions of latex spheres of $5$, $10$, and $40\mu \mathrm{m}$ are reported. A discussion on the desirability of the technique as a simple and powerful alternative to low angle scattering will be presented.

We report the realization of the spatial counterpart of the Dicke superradiance. The new process is revealed by the realization of the spatial quantum partition statistics within the detection of photons emitted in sub-Poissonian regime by an active microcavity excited by ultrashort pulses. The superradiant enhancement of the time decay of the dipole excitation has also been investigated.

We report on the first experimental observation of a novel type of optical vector soliton, a dipole-mode soliton, recently predicted theoretically. We show that these vector solitons can be generated in a photorefractive medium employing two different processes: a phase imprinting, and a symmetry-breaking instability of a vortex-mode vector soliton. The experimental results display remarkable agreement with the theory, and confirm the robust nature of these radially asymmetric two-component solitary waves.

The particle dynamics and shear forces of granular matter in a Couette geometry are determined experimentally. The normalized tangential velocity $V\left(y\right)$ declines strongly with distance $y$ from the moving wall, independent of the shear rate and of the shear dynamics. Local rms velocity fluctuations $\delta V\left(y\right)$ scale with the local velocity gradient to the power $0.4\pm 0.05$. These results agree with a locally Newtonian, continuum model, where the granular medium is assumed to behave as a liquid with a local temperature $\left[\delta V\right(y){]}^2$ and density dependent viscosity.

We investigated experimentally the morphological evolution of thin polydimethylsiloxane films sandwiched between a silicon wafer and different bounding liquids with interfacial tensions varying by 2 orders of magnitude. It is shown that increasing the compatibility between film and bounding liquid by adding a few surfactant molecules results in a faster instability of shorter characteristic wavelength. Inversely, based on the characteristic parameters describing the instability we determined extremely small interfacial tensions with a remarkable accuracy.

Motivated by recent experimental and numerical results, a simple unifying picture of intermittency in turbulent shear flows is suggested. Integral structure functions (ISF), taking into account explicitly the shear intensity, are introduced on phenomenological grounds. ISF can exhibit a universal scaling behavior, independent of the shear intensity. This picture is in satisfactory agreement with both experimental and numerical data. Possible extension to convective turbulence and implication on closure conditions for large-eddy simulation of nonhomogeneous flows are briefly discussed.

In mixed systems, besides regular and chaotic states, there are states supported by the chaotic region mainly living in the vicinity of the hierarchy of regular islands. We show that the fraction of these hierarchical states scales as ${ħ}^{\alpha }$ and we relate the exponent $\alpha =1-1\mathrm{}/\gamma$ to the decay of the classical staying probability $P\left(t\right)\sim t^{-\gamma }$. This is numerically confirmed for the kicked rotor by studying the influence of hierarchical states on eigenfunction and level statistics.

We apply sum rules to answer the question: What is the largest off-resonance electronic nonlinear susceptibility allowed by quantum mechanics? The sum-rule-restricted three-level model shows that the two-level limit yields the absolute maximum susceptibility, which is found to depend only on the first excited state transition energy and number of electrons—in agreement with a large set of second- and third-order susceptibility data from the literature. As such, the sum rules provide a target for the maximum possible off-resonant susceptibilities.