Existence and stability of multisite breathers in honeycomb and hexagonal lattices

We study the existence and stability of multisite discrete breathers in two prototypical non-square Klein-Gordon lattices, namely a honeycomb and a hexagonal one. In the honeycomb case we consider six-site configurations and find that for soft potential and positive coupling the out-of-phase breather configuration and the charge-two vortex breather are linearly stable, while the in-phase and charge-one vortex states are unstable. In the hexagonal lattice, we first consider three-site configurations. In the case of soft potential and positive coupling, the in-phase configuration is unstable and the charge-one vortex is linearly stable. The out-of-phase configuration here is found to always be linearly unstable. We then turn to six-site configurations in the hexagonal lattice. The stability results in this case are the same as in the six-site configurations in the honeycomb lattice. For all configurations in both lattices, the stability results are reversed in the setting of either hard potential or negative coupling. The study is complemented by numerical simulations which are in very good agreement with the theoretical predictions. Since neither the form of the on-site potential nor the sign of the coupling parameter involved have been prescribed, this description can accommodate inverse-dispersive systems (e. g. supporting backward waves) such as transverse dust-lattice oscillations in dusty plasma (Debye) crystals or analogous modes in molecular chains.

Nonlinear excitations in strongly-coupled plasma lattices: envelope solitons, kinks and intrinsic localized modes

Ensembles of charged particles (plasmas) are a highly complex form of matter, most often modeled as a many-body system characterized by weak inter-particle interactions (electrostatic coupling). However, strongly-coupled plasma configurations have recently been produced in laboratory, either by creating ultra-cold plasmas confined in a trap or by manipulating dusty plasmas in discharge experiments. In this paper, the nonlinear aspects involved in the motion of charged dust grains in a one-dimensional plasma monolayer (crystal) are discussed. Different types of collective excitations are reviewed, and characteristics and conditions for their occurrence in dusty plasma crystals are discussed, in a quasi-continuum approximation. Dust crystals are shown to support nonlinear kink-shaped supersonic solitary longitudinal excitations, as well as modulated envelope localized modes associated with longitudinal and transverse vibrations. Furthermore, the possibility for intrinsic localized modes (ILMs) — Discrete Breathers (DBs) — to occur is investigated, from first principles. The effect of mode-coupling is also briefly considered. The relation to previous results on atomic chains, and also to experimental results on strongly-coupled dust layers in gas discharge plasmas, is briefly discussed.

Nonlinear Dynamics of Rotating Multi-Component Pair Plasmas and e-p-i Plasmas

The propagation of small amplitude stationary profile nonlinear electrostatic excitations in a pair plasma is investigated, mainly drawing inspiration from experiments on fullerene pair-ion plasmas. Two distinct pair ion species are considered of opposite polarity and same mass, in addition to a massive charged background species, which is assumed to be stationary, given the frequency scale of interest. In the pair-ion context, the third species is thought of as a background defect (e.g. charged dust) component. On the other hand, the model also applies formally to electron-positron-ion (e-p-i) plasmas, if one neglects electron-positron annihilation. A two-fluid plasma model is employed, incorporating both Lorentz and Coriolis forces, thus taking into account the interplay between the gyroscopic (Larmor) frequency ?c and the (intrinsic) plasma rotation frequency O0. By employing a multi-dimensional reductive perturbation technique, a Zakharov-Kuznetsov (ZK) type equation is derived for the evolution of the electric potential perturbation. Assuming an arbitrary direction of propagation, with respect to the magnetic field, we derive the exact form of nonlinear solutions, and study their characteristics. A parametric analysis is carried out, as regards the effect of the dusty plasma composition (background number density), species temperature(s) and the relative strength of rotation to Larmor frequencies. It is shown that the Larmor and mechanical rotation affect the pulse dynamics via a parallel-to-transverse mode coupling diffusion term, which in fact diverges at ?c ? ±2O0. Pulses collapse at this limit, as nonlinearity fails to balance dispersion. The analysis is complemented by investigating critical plasma compositions, in fact near-symmetric (T- ˜ T+) “pure” (n- ˜ n+) pair plasmas, i.e. when the concentration of the 3rd background species is negligible, case in which the (quadratic) nonlinearity vanishes, so one needs to resort to higher order nonlinear theory. A modified ZK equation is derived and analyzed. Our results are of relevance in pair-ion (fullerene) experiments and also potentially in astrophysical environments, e.g. in pulsars.

Transport, atom blockade and output coupling in a Tonks-Girardeau gas

Recent landmark experiments have demonstrated how quantum mechanical impurities can be created within strongly correlated quantum gases and used to probe the coherence properties of these systems. Here we present a theoretical model to simulate such an output coupler for a Tonks- Girardeau gas that shows excellent agreement with the experimental results for atom transport and output coupling. The solid theoretical basis our model provides allows us to explore non-equilibrium transport phenomena in ultra-cold quantum gases and leads us to predict a regime of atom blockade, where the impurity component becomes localised in the parent cloud despite the presence of gravity. We show that this provides a stable mixed-species quantum gas in the strongly correlated limit.

Temperature-dependent gap edge in strong-coupling superconductors determined using the Eliashberg-Nambu formalism

Using the theory of Eliashberg and Nambu for strong-coupling superconductors, we have calculated the gap function for a model superconductor and a selection of real superconductors includong the elements Al, Sn, Tl, Nb, In, Pb and Hg and one alloy, Bi2Tl. We have determined thetemperature-dependent gap edge in each and found that in materials with weak electron-phonon ($\lambda 1.20$), not only is the gap edge double valued but it also departs significantly from the BCS form and develops a shoulderlike structure which may, in some cases, denote a gap edge exceeding the $T = 0$ value. These computational results support the insights obtained by Leavens in an analytic consideration of the general problem. Both the shoulder and double value arise from a common origin seated in the form of the gap function in strong coupled materials at finite temperatures. From the calculated gap function, we can determine the densities of states in the materials and the form of the tunneling current-voltage characteristics for junctions with these materials as electroddes. By way of illustration, results are shown for the contrasting cases of Sn ($\lambda=0.74$) and Hg ($\lambad=1.63$). The reported results are distinct in several ways from BCS predictions and provide an incentive determinative experimental studies with techniques such as tunneling and far infrared absorption.

Long-range electronic coupling in bis(cyclometalated) ruthenium complexes

Symmetrical and unsymmetrical ligands containing terpyridyl coordinating units (N, N, N) or a cyclometalating equivalent (N, C, N), connected back-to-back either directly or via a p-terphenylene or 1,3-phenylene spacer, have been used to construct new diruthenium complexes. These compounds incorporate various terdentate chelates as capping ligands, to allow a double control of the electronic properties of each subcomplex and of the ensemble: via the terminal ligand or through the bridging fragment. Electronic coupling was studied from the intervalence transitions observed in several bimetallic ruthenium complexes of the bis-(cyclometalated) type differing by the substitution of a nitrogen atom by carbon in the terminal terpyridyl unit. The largest metal-metal interaction was found in complexes for which the terminal complexing unit is of the 1,3-di-2-pyridylbenzene type, i.e., with the carbon atom located on the metal-metal C-2 axis of the molecule. Investigations of the mechanism of interaction by extended Huckel calculations showed that the replacement of nitrogen by carbon raises the filled ligand levels, increasing the mixing with ligand orbitals and thus the metal-metal coupling. Finally, the intervalence transition was still observed for a bridging ligand containing three phenylene units as spacers, corresponding to a 24-Angstrom metal-metal distance.

New Cu-Based Catalysts Supported on TiO2 Films for Ullmann SNAr-Type C-O Coupling Reactions

New routes for the preparation of highly active TiO2-supported Cu and CuZn catalysts have been developed for C-O coupling reactions. Slurries of a titania precursor were dip-coated onto glass beads to obtain either structured mesoporous or non-porous titania thin films. The Cu and CuZn nanoparticles, synthesized using a reduction by solvent method, were deposited onto calcined films to obtain a Cu loading of 2 wt%. The catalysts were characterized by inductively coupled plasma (ICP) spectroscopy, temperature-programmed oxidation/reduction (TPO/TPR) techniques, Cu-63 nuclear magnetic resonance (NMR) spectroscopy, X-ray diffraction (XRD), scanning and transmission electron microscopy (S/TEM-EDX) and X-ray photo-electron spectroscopy (XPS). The activity and stability of the catalysts obtained have been studied in the C-O Ullmann coupling of 4-chloropyridine and potassium phenolate. The titania-supported nanoparticles retained catalyst activity for up to 12 h. However, catalyst deactivation was observed for longer operation times due to oxidation of the Cu nanoparticles. The oxidation rate could be significantly reduced over the CuZn/TiO2 catalytic films due to the presence of Zn. The 4-phenoxypyridine yield was 64% on the Cu/nonporous TiO2 at 120 degrees C. The highest product yield of 84% was obtained on the Cu/mesoporous TiO2 at 140 degrees C, corresponding to an initial reaction rate of 104 mmol g(cat)(-1) s(-1). The activation energy on the Cu/mesoporous TiO2 catalyst was found to be (144 +/- 5) kJ mol(-1), which is close to the value obtained for the reaction over unsupported CuZn nanoparticles (123 +/- 3 kJ mol(-1)) and almost twice the value observed over the catalysts deposited onto the non-porous TiO2 support (75 +/- 2 kJ mol(-1)).

Transverse Oscillations in Chromospheric Mottles

A number of recent investigations have revealed that transverse waves are ubiquitous in the solar chromosphere. The vast majority of these have been reported in limb spicules and active region fibrils. We investigate long-lived, quiet-Sun, on-disk features such as chromospheric mottles (jet-like features located at the boundaries of supergranular cells) and their transverse motions. The observations were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope. The data set is comprised of simultaneous imaging in the Ha core, Ca II K, and G band of an on-disk quiet-Sun region. Time-distance techniques are used to study the characteristics of the transverse oscillations. We detect over 40 transverse oscillations in both bright and dark mottles, with periods ranging from 70 to 280 s, with the most frequent occurrence at ~165 s. The velocity amplitudes and transverse displacements exhibit characteristics similar to limb spicules. Neighboring mottles oscillating in-phase are also observed. The transverse oscillations of individual mottles are interpreted in terms of magnetohydrodynamic kink waves. Their estimated periods and damping times are consistent with phase mixing and resonant mode conversion.

PRELIMINARY STUDIES OF RADIATION COUPLING BETWEEN REMOTE SOFT-X-RAY LASER-AMPLIFIERS

Coupling of a soft X-ray laser beam with a relaying concave mirror in a sequentially pumped amplifier geometry using the Ne-like Ge system has been studied experimentally. Preliminary observations indicate an increase in the spatial coherence of the amplified relayed beam. In addition, near-field imaging of one of the amplifier plasmas shows a double-lobed intensity pattern of the emergent beam indicating refractive guiding of the amplified beam with components both normal and tangential to the target surface.