Quasiregularity of Hamiltonian chaos is approached using the concept of the type of a chaotic orbit, i.e., the sequence of resonances visited by the orbit. A simple method is introduced for determining the type in the case of kicked-rotor Hamiltonians. First applications of this method are given in the calculation and study of quantities characterizing ‘‘vague tori’’ within resonances, namely, survival probabilities and average dwelling times. Results concerning a newly defined disorder parameter, characterizing quasiregularity, are briefly reported.

We show that a dynamical system of N phase oscillators with global cosine coupling is completely integrable. In particular, we prove that the N-dimensional phase space is foliated by invariant two-dimensional tori, for all N≥3. Explicit expressions are given for the constants of motion, and for the solitary waves that occur in the continuum limit. Our analysis elucidates the origin of the remarkable phase space structure detected in recent numerical studies of globally coupled arrays of Josephson junctions, lasers, and Ginzburg-Landau oscillators.

We find and analyze analytically and numerically two new families of coupled soliton states in nonlinear fiber couplers. The bifurcation diagram for the new types of soliton states is constructed. It is shown that the bifurcation diagram for the fiber coupler is similar to the bifurcation diagram for the stationary waves in a symmetric nonlinear planar waveguide. Physical reasons for this analogy are discussed.

We report experimental results for convection in a thin horizontal layer of a fluid which is heated from below and which undergoes a first-order phase change. For some parameter ranges the denser layer may be stably stratified above the lighter one, as predicted by Busse and Schubert. Over various parameter ranges we observed hexagonal, inverted-hexagonal, and roll flow. Interesting interactions between two-phase convection and Rayleigh-Bénard convection are observed near two codimension-two points.

Narrow, high-power ‘‘spikes’’ can be emitted by a 24-GHz free-electron laser (FEL). Spikes, ∼450 psec long, may occur randomly or in a sequence which is not the mode-locked period of the resonator. The slippage of the FEL is varied by changing the diameter of the drift tube. The slippage is zero when the electron axial speed is the same as the wave group velocity. Spiking was observed with and without slippage. Measurements of the FEL spectrum are reported and we compare the spike width with a solitary-wave theory. The experiment rules out the sideband instability or superradiance as a cause for this spiking.

The anomalous ion thermal transport due to the ion-temperature-gradient driven instability (ITG mode) has been studied in the Columbia Linear Machine. We find that in the presence of the ITG mode, the radial temperature profile relaxes along the direction of a steady state plasma flow parallel to the magnetic field lines. The corresponding local ion thermal conductivity ${\mathrm{\chi }}_{\mathrm{\perp }}$(r), determined from the experimental data, is highly anomalous and shows a strong correlation with the radial profile of the ITG mode.

A new method is developed to study the atomic structure of layered materials by a two-dimensional atomic pair distribution function (2D-PDF) analysis. Using synchrotron x-ray scattering, this method is applied to the study of an ${\mathrm{Al}}_{65}$${\mathrm{Cu}}_{15}$${\mathrm{Co}}_{20}$ single decagonal quasicrystal. The obtained 2D-PDF’s are in excellent agreement with those calculated from a recently proposed structure model based on decagonal cluster packing. However, additional short-range structure is found by analyzing the diffuse scattering intensity. A modification of the model is proposed to explain this short-range structure.

The relaxation mechanism of diblock copolymers above the order-to-disorder transition has been identified. We present the first experimental evidence of the existence of both a local internal breathing relaxation process and a diffusive pattern relaxation mode measured on the same sample for a series of diblock copolymers by applying photon correlation spectroscopy in the polarized geometry. The relaxation characteristics of both modes are modeled in terms of recent theories, with the necessity for a complete theory becoming evident.

The morphology of incommensurately modulated crystals is considered. A surface free energy model is constructed which interprets the stabilization of the incommensurate facets as due to surface pinning of the phase of the modulation wave. The stepped nature of the true crystal surface restricts the stabilization, and thus the surface pinning, to low-index facets. The theory correlates the observed crystal shapes of ${\mathrm{Rb}}_2$${\mathrm{ZnBr}}_4$ and calaverite with the observed, modulated crystal structures of these compounds.

An experimental determination of the superelastic exponent near the percolation threshold is presented. This exponent s’ characterizes the pseudodivergence of the elastic constants of a mixture of very soft material (gel) and a rigid material (alumina and zirconia). From the measurement of the Young’s modulus, s’ is found to be 0.67±0.05. This value is in agreement with previous numerical simulations in 3D, and this indicates that very likely s’ is smaller than the superconductor exponent.

Brillouin light scattering measurements of the elastic properties of a family of polymeric Langmuir-Blodgett films have revealed decreasing elastic constants with increasing monolayer thickness. By treating the rodlike backbone molecules which lie in the plane of the surface and the hydrocarbon side chains as separate constituents of a superlattice, these trends have been interpreted and the elastic properties of the constituent layers evaluated. We find that the anomalously small transverse elastic constants of the films are due to the hydrocarbon side chains.

Starting from 2D experimental observations and using topological arguments, we search for the set of stable positions when a large disk is raised step by step among a 2D array of small monodisperse disks. We show and confirm experimentally that larger disks should move upward continuously via the arching effect whereas smaller disks may only climb up intermittently. We find the critical diameter ratio for a continuous ascent in 2D and 3D. Our model sheds a new light on the decisive role played by vaults in particle size segregation.

We report the first parameter-free calculations of self-diffusion constants in silicon. We have computed diffusion constants for the defect-mediated mechanisms using the local-density approximation in combination with ab initio molecular-dynamics simulations and obtained the diffusion constant for the concerted exchange mechanism from earlier results by Pandey and Kaxiras. We obtain diffusion constants in the range of the experimental values, with the self-interstitial mechanism dominating over the contribution of the other mechanisms.

Using surface laser light scattering spectroscopy, we have observed for the first time the crossover from capillary to Rayleigh (elastic) surface fluctuations on polymer solutions. At low polymer concentrations c<${\mathit{c}}^{\mathrm{*}}$ solutions of polyisobutylene in hexane exhibit ordinary capillary waves on the free surface; at higher concentrations, c>${\mathit{c}}^{\mathrm{*}}$ the capillary mode evolves into a Rayleigh mode. The surface laser light scattering data is quantitatively discussed within the context of recent theory.

The long wavelength hydrodynamics of films with unidirectional translational order adsorbed on fluid surfaces (as in a Langmuir monolayer) is formulated. We find the hydrodynamic frequencies ω(q)∝(± √3 -i)${\mathit{q}}^{14/9}$ ${\cos }^{4/3}$θ ${\sin }^{14/9}$θ where q≡‖q‖ and π/2-θ is the angle between the direction of propagation and the direction of translational order. We also obtain the dynamic structure factor. Our results apply to nematic polymers adsorbed onto a fluid surface and to striped phases of Langmuir monolayers, and provide an experimentally accessible probe of the anomalous elasticity predicted for two-dimensional smectics by Golubović and Wang.

A grazing incidence x-ray diffraction study of ${\mathrm{CH}}_3$(${\mathrm{CH}}_2$${)}_{\mathit{n}\mathrm{-}1}$SH self-assembled on a Au(111) surface shows that self-assembly results in a nonequilibrium state with a specific defect structure. We also explore the global (n,T) phase diagram whose phases are distinguished by the tilt direction and the two-dimensional periodicity. These phases result in distinct long (n>14) and short (n<14) chain-length regimes, and reflect the relative importance of the hydrocarbon and interface interactions in these systems.

The structure of the Cu(110) surface is studied at high temperatures using a combination of lattice-gas Monte Carlo and molecular dynamics methods with identical many-atom interactions derived from the effective-medium theory. A clear roughening transition is found around 1000 K. The rough phase is identified from a logarithmic divergence of the height-height correlation function. The roughening mechanism is connected with the formation of thermally generated diffusive clusters of both adatom and vacancy type.

The appearance of a reversible order-disorder transition at Cu(115) and Cu(117) surfaces has been investigated using perturbed angular correlation spectroscopy. The local atomic arrangement at ${}_{}{}^{111}{}_{}{}^{}\mathrm{In}$ probes is detected via nuclear quadrupole hyperfine interaction. A broadening of the electric field gradient distribution is measured for elevated temperatures due to structural changes around the probes. The onset of disorder on the atomic scale is found to be well above the roughening transition temperatures measured by various scattering techniques.

We show that the 2p core-level line shapes of transition metal (TM) compounds are strongly influenced by the presence of more TM ions. Using calculations of clusters, involving more than one TM ion we explain the double peaked main line of the Ni 2p spectrum of NiO as well as the difference in line shape compared with Ni impurities in MgO and show the sensitivity of the line shape in NiO to surrounding defects. This intersite charge transfer screening also explains the wide asymmetric shape of the main line of the Cu 2p spectrum of CuO and the high-${\mathit{T}}_{\mathit{c}}$ compounds.

Results are presented for the single-particle density of states of the one- and two-dimensional simplified Hubbard and Montorsi-Rasetti model. The former does not exhibit a metal-insulator transition as a function of U. With increasing temperature and for U not too large, the gap closes and spectral weight appears at the chemical potential. The Néel temperature and the temperature range for coexistence of magnetic long-range order and a gapless density of states are determined. The latter model exhibits a metal-insulator transition of the Mott type and does not show magnetic long-range order.