A Remark on the Use of Differential Forms for the Skyrme Problem

We introduce a formulation of the Skyrme problem using differential forms. By means of this formulation, we prove first that the homothetic map between the standard three-sphere of radius R, S³ _r R⁴, and S³ ₁ is the unique minimizer, modulo isometries, of the Skyrme energy in its homotopy class, for any R less than some critical value R₀ (3/2, 2]. We then establish a stability result for this Skyrme-form problem from which we can recover the result of M. Loss and N. S. Manton which states that this homothetic map is stable only up to R = 2.     

Growth by laser ablation of Ti-based oxide films with different valency states

x La_2/3+yTiO_3-δ perovskite (with δ≤0.5) were deposited by the laser ablation technique from Li_0.33La_0.56TiO₃ targets. Their growth onto MgO substrateswas studied as a function of the oxygen pressure. For films grown in vacuum (10^-6 mbar), a La_0.63TiO_2.5 composition was obtained, meaning that Ti³⁺ alone is present in the films, while Li ions are not incorporated under these conditions. This material shows good electric conductivity (ρ=500 mΩ cm). By contrast, insulating films with a Li_0.1La_0.70TiO₃ composition corresponding to the Ti⁴⁺ species were obtained at high oxygen pressures (>0.05 mbar). For all conditions, textured films were grown with different orientations depending on the temperature and the oxygen pressure. Received: 10 September 1997/Accepted: 24 November 1997     

Positive and negative Hanbury-Brown and Twiss correlations in normal metal-superconducting devices

In the light of the recent analogs of the Hanbury-Brown and Twiss experiments [1] in mesoscopic beam splitters, negative current noise correlations are recalled to be the consequence of an exclusion principle. Here, positive (bosonic) correlations are shown to exist in a fermionic system, composed of a superconductor connected to two normal reservoirs. In the Andreev regime, the correlations can either be positive or negative depending on the reflection coefficient of the beam splitter. For biases beyond the gap, the transmission of quasiparticles favors fermionic correlations. The presence of disorder enhances positive noise correlations. Potential experimental applications are discussed. Received 1 June 1999     

Lead Inclusions in Silicon: Structure, Morphology, and Thermal Behavior

Small inclusions of lead have been embedded in pure silicon by rapid quenching. They are topotactic-truncated octahedra with a smaller aspect ratio than the ones found in aluminum. They appear also on single and multiple twins as a bicrystalline unit with a compound morphology. No overheating has been detected, while undercooling is size dependent and can reach 80 K. These results are compared to the structure, morphology and thermal behavior of lead inclusions in aluminum and other cubic matrices.     

Spectral intensities in the ν1 band of carbonyl sulfide and its isotopic species

A tunable diode laser was used to perform measurements of absolute lines intensities in the ν₁ fundamental of carbonyl sulfide. Spectra have also been recorded for the following isotopic species: ¹⁶O¹²C³⁴S, ¹⁶O¹³C³²S and ¹⁶O¹²C³³S. The vibrational band strength S_v⁰ was calculated at 298 K. The absolute intensity for 100% of ¹⁶O¹²C³²S species is found to be S_v⁰ = 29.69 ± 0.15 cm⁻² atm⁻¹ with the uncertainty covering three times the standard deviation. We have tried to determine the α-coefficient involved in the Hermann-Wallis factor F = (1 + αm + )² and the value is found to be negligible (−5 ± 8) × 10⁻⁵. The S_v⁰ value obtained for the other isotopic species is very close to the normal one.     

Self‐doping PPV oligomers – electrochemistry and structure of the self‐doped systems

A novel class of self‐doping conjugated oligomers, E,E‐2‐(sulfoalkoxy)‐5‐alkoxy‐1,4‐bis[2‐(2,4,6‐trimethoxyphenyl) ethenyl]benzenes, is presented. The synthesis and spectroscopic characterisation of five such oligomers are described, and an electrochemical analysis using cyclic voltammetry is performed to determine the anodic peak potentials. A structural study is performed on six self‐doping oligomers in which the structures and energies of the possible mono‐molecular forms of the electrically conducting doped material are described and evaluated using Hirshfeld charges and the Quantum Theory of Atoms In Molecules. Copyright © 2009 John Wiley & Sons, Ltd.     

Towards a monolithic optical cavity for atom detection and manipulation

We study a Fabry-Perot cavity formed from a ridge waveguide on a AlGaAs substrate. We experimentally determined the propagation losses in the waveguide at 780 nm, the wavelength of Rb atoms. We have also made a numerical and analytical estimate of the losses induced by the presence of the gap which would allow the interaction of cold atoms with the cavity field. We found that the intrinsic finesse of the gapped cavity can be on the order of F∼30, which, when one takes into account the losses due to mirror transmission, corresponds to a cooperativity parameter for our system C∼1.     

Quasiperiodicity and randomness in tilings of the plane

We define new tilings of the plane with Robinson triangles, by means of generalized inflation rules, and study their Fourier spectrum. Penrose's matching rules are not obeyed; hence the tilings exhibit new local environments, such as three different bond lengths, as well as new patterns at all length scales. Several kinds of such generalized tilings are considered. A large class of deterministic tilings, including chiral tilings, is strictly quasiperiodic, with a tenfold rotationally symmetric Fourier spectrum. Random tilings, either locally (with extensive entropy) or globally random (without extensive entropy), exhibit a mixed (discrete+continuous) diffraction spectrum, implying a partial perfect long-range order.