A tight-binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of “quantized” bands of orbits. New bands appear when renormalized Harper parameters exceed integer multiples of $\pi /2$. Orbits with frequencies commensurate with the kicking frequency are shown to correlate with classical accelerator modes in the original kicked problem. Signatures of this superdiffusive and, in our view, resonant transport are seen in both classical and quantum behavior. An important feature of our analysis is the emergence of a natural scaling relating classical and quantum couplings which is necessary for establishing correspondence.

We simulate size segregation in granular mixtures which are almost completely packed in a rotating drum. Instead of a 3D drum, we simulate a 2D thin rotating box which is almost completely packed with granular mixtures. The phase inversion of a radially segregated pattern which was found in a 3D experiment is qualitatively reproduced with this simulation. A global convection appears after a radial segregation pattern is formed, and this convection induces an axially segregated pattern.

We investigate the stabilization mechanisms due to viscous forces in the invasion front during drainage displacement in two-dimensional porous media using a network simulator. We find that in horizontal displacement the capillary pressure difference between two different points along the front varies almost linearly as a function of height separation in the direction of the displacement. The numerical result supports arguments taking into account the loopless displacement pattern where nonwetting fluid flows in separate strands (paths). As a consequence, we show that existing theories developed for viscous stabilization are not compatible with drainage when loopless strands dominate the displacement process.

A theory is presented for propagation of waves in bounded media near the mobility edge, based on the self-consistent theory for localization. It predicts a spatially inhomogeneous diffusion constant that leads to scale dependence in enhanced backscattering and transmission.

Using a streak camera we have measured the three Stokes polarization parameters during a polarization switch of a vertical-cavity semiconductor laser. The switch occurs along a corkscrew path on the Poincaré sphere and takes on average a few nanoseconds; this value agrees with a theoretical treatment based upon the Fokker-Planck equation.

Quantum electrodynamics of atom spontaneous emission from a three-dimensional photonic crystal is studied in a full vectorial framework. The electromagnetic fields are quantized via solving the eigenproblem of photonic crystals with use of a plane-wave expansion method. It is found that the photon density of states and local density of states (LDOS) with a full band gap vary slowly near the edge of band gap, in significant contrast to the singular character predicted by the previous isotropic model. Therefore, the spontaneous emission can be solved by conventional Weisskopf-Wigner approximate theory, which yields a pure exponentially decaying behavior with a rate proportional to the LDOS.

We report on the fabrication of what we believe is the first example of a two-dimensional (2D) nonlinear photonic crystal [Berger, Phys. Rev. Lett. 81, 4136 (1998)], where the refractive index is constant but where the 2nd order nonlinear susceptibility is spatially periodic. Such crystals allow for efficient quasi-phase-matched 2nd harmonic generation using multiple reciprocal lattice vectors. External 2nd harmonic conversion efficiencies $>60\mathrm{}\%$ were measured with picosecond pulses. The fabrication technique is extremely versatile and should allow for the fabrication of a broad range of 2D crystals including quasicrystals.

We study elastic band gaps in nonhomogeneous periodic finite media. The finite-difference time-domain method is used for the first time in the field of elastic band-gap materials. It is used to interpret experimental data for two-dimensional systems consisting of cylinders of fluids (Hg, air, and oil) inserted periodically in a finite slab of aluminum host. The method provides good convergence, can be applied to realistic finite composite slabs, even to composites with a huge contrast in the elastic parameters of their components, and describes well the experiments.

A varicose-profile, thin layer of heavy gas ( ${\mathrm{SF}}_6$) in lighter gas (air) is impulsively accelerated by a planar, Mach 1.2 shock, producing the Richtmyer-Meshkov instability. We present the first measurements of the circulation in the curtain during the vortex-dominated, nonlinear stage of the instability evolution. These measurements, based on particle image velocimetry data, are employed to validate an idealized model of the nonlinear perturbation growth.

We present measurements of the Nusselt number $N$ as a function of the Rayleigh number $R$ in cylindrical cells with aspect ratios $0.5\le \Gamma \equiv D/d\le 12.8$ ( $D$ is the diameter and $d$ is the height). We used acetone with a Prandtl number $\sigma =4.0\mathrm{}$ for ${10}^5\lesssim R\lesssim 4\times {10}^{10}$. A fit of a power law $N=N_0{R}^{{\gamma }_{\mathrm{eff}}}$ over limited ranges of $R$ yielded values of ${\gamma }_{\mathrm{eff}}$ from 0.275 near ${R=10\mathrm{}}^7$ to 0.300 near ${R=10\mathrm{}}^{10}$. The data are inconsistent with a single power law for $N\left(R\right)$. For $R>\mathrm{}{10}^7$ they are consistent with $N=a{\sigma }^{-1\mathrm{}/12}{R}^{1/4}+b{\sigma }^{-1\mathrm{}/7}{R}^{3/7}$ as proposed by Grossmann and Lohse for $\sigma \gtrsim 2$.

A free-floating plate is introduced in a Bénard convection cell with an open surface. It partially covers the cell and distorts the local heat flux, inducing a coherent flow that in turn moves the plate. Remarkably, the plate can be driven to a periodic motion even under the action of a turbulent fluid. The period of the oscillation depends on the coverage ratio, and on the Rayleigh number of the convective system. The plate oscillatory behavior observed in this experiment may be related to a geological model, in which continents drift in a quasiperiodic fashion.

In a closed volume of molten sodium an intense single-vortex-like helical flow has been produced by an outside powered propeller. At a flow rate of $0.67{\mathrm{m}}^3/\mathrm{s}$ a slowly growing magnetic field eigenmode was detected. For a slightly lower flow, additional measurements showed a slow decay of this mode. The measured results correspond satisfactorily with numerical predictions for the growth rates and frequencies.

The distribution of tunneling rates in the presence of classical chaos is derived. We use classical information about tunneling trajectories plus random matrix theory arguments about wave function overlaps. The distribution depends on the stability of a specific tunneling orbit and is not universal, though it does reduce to the universal Porter-Thomas form when the orbit is very unstable. For some situations there may be systematic deviations due to scarring of real periodic orbits. The theory is tested in a model problem and possible experimental realizations are discussed.

We study the time dependence of the ionization probability of Rydberg atoms driven by a microwave field, both in classical and in quantum mechanics. The quantum survival probability follows the classical one up to the Heisenberg time and then decays algebraically as $P\left(t\right)\propto 1/t$. This decay law derives from the exponentially long times required to escape from some region of the phase space, due to tunneling and localization effects. We also provide parameter values which should allow one to observe such decay in laboratory experiments.

We discuss how nonstationarity in observed time series data due to pronounced fluctuations of system parameters can be resolved by making use of embedding techniques for scalar data. If a $D$-dimensional deterministic system is driven by $P$ slowly time dependent parameters, a $(D+P)$-dimensional manifold has to be reconstructed from the scalar time series, which is done by an $m>\mathrm{}2\mathrm{}(D+P)$-dimensional time delay embedding. We show that in this space essential aspects of determinism are restored. We demonstrate the validity of the idea heuristically, for numerical examples and for human speech data.

We present new types of solitary wave solutions for the higher order nonlinear Schrödinger (HNLS) equation describing propagation of femtosecond light pulses in an optical fiber under certain parametric conditions. Unlike the reported solitary wave solutions of the HNLS equation, the novel ones can describe bright and dark solitary wave properties in the same expressions and their amplitude may approach nonzero when the time variable approaches infinity. In addition, such solutions cannot exist in the nonlinear Schrödinger equation. Furthermore, we investigate the stability of these solitary waves under some initial pertubations by employing the numerical simulation methods.

We present an experimental study of the thermal response to a positive temperature quench in two-phase fluid ${\mathrm{SF}}_6$ in low gravity for temperature ranging from $10.1$ to $0.1$ K from the critical temperature. The temperature was measured simultaneously in the gas, the liquid, and the cell wall by thermistors and the density distribution was observed by interferometry. During the quench the gas temperature considerably exceeded the temperature of the heating walls (overheating up to $23\%$). This striking observation is discussed in the light of the adiabatic heat transfer in this highly compressible fluid while the key role of the localization in low gravity of the gas and liquid phases is revealed.

We report on a new type of interaction between solitary current density spots observed in an ac-driven gas discharge system. These spots behave as independent particles as long as they are far apart from each other. Upon collision, in most cases one of the spots is extinguished. However, we also observe the formation of stable bound pairs of spots that move rather fast. We argue that both the rapid motion and the binding itself are due to a pronounced symmetry breaking with respect to size and breakdown phase of the individual spots. Basic features of pairs of spots traveling due to a true two-spot mechanism are discussed.

New experimental results demonstrate that chaos control can be accomplished using controllers that are very simple relative to the system being controlled. Chaotic dynamics in a driven pendulum and a double scroll circuit are controlled using an adjustable, passive limiter—a weight for the pendulum and a diode for the circuit. For both experiments, multiple unstable periodic orbits are selectively controlled using minimal perturbations. These physical examples suggest that chaos control can be practically applied to a much wider array of important problems than initially thought possible.