Spaces of Tilings, Finite Telescopic Approximations and Gap-Labeling

The continuous Hull of a repetitive tiling T in ℝ^d with the Finite Pattern Condition (FPC) inherits a minimal ℝ^d-lamination structure with flat leaves and a transversal which is a Cantor set. This class of tiling includes the Penrose & the Amman Benkker ones in 2D, as well as the icosahedral tilings in 3D. We show that the continuous Hull, with its canonical ℝ^d-action, can be seen as the projective limit of a suitable sequence of branched, oriented and flat compact d-manifolds. As a consequence, the longitudinal cohomology and the K-theory of the corresponding C*-algebra are obtained as direct limits of cohomology and K-theory of ordinary manifolds. Moreover, the space of invariant finite positive measures can be identified with a cone in the d^th homology group canonically associated with the orientation of ℝ^d. At last, the gap labeling theorem holds: given an invariant ergodic probability measure μ on the Hull the corresponding Integrated Density of States (IDS) of any selfadjoint operators affiliated to takes on values on spectral gaps in the ℤ-module generated by the occurrence probabilities of finite patches in the tiling. Accepted in Revised Form: 7 May 2005     

Signatures of short-range many-body effects in the dielectric function of silicon for finite momentum transfer

We present an investigation of the dynamic structure factor and of the dielectric function epsilonM(Q,omega) of the prototypical semiconductor silicon for finite momentum transfer, combining inelastic x-ray scattering experiments and ab initio calculations. In contrast with optical spectra, for finite momentum transfer time-dependent density-functional theory in the adiabatic local-density approximation together with lifetime broadening describes the physics of valence excitations correctly. Major structures in the spectra, governed by short-range crystal and exchange-correlation local-field effects, are strongly influenced by a mixing of transitions of positive and negative energies, in striking difference to spectra for vanishing momentum transfer. This mixing gives rise to a pronounced Fano asymmetry.     

Isolation and characterization of new lignans from the leaves of Cestrum parqui

Three new compounds, a sesquilignans, an oxyneolignan and a norlignan, have been isolated from the aqueous fraction of Cestrum parqui. All of the compounds have been identified on the basis of their spectroscopic properties and tested on the species Lactuca sativa and Lycopersicon esculentum to evaluate their phytotoxic activity.     

Glass-specific behavior in the damping of acousticlike vibrations

High frequency sound is observed in lithium diborate glass, Li2O-2B2O3, using Brillouin scattering of light and x rays. The sound attenuation exhibits a nontrivial dependence on the wave vector, with a remarkably rapid increase towards a Ioffe-Regel crossover as the frequency approaches the boson peak from below. An analysis of literature results reveals that the boson-peak frequency is closely related with a Ioffe-Regel limit for sound in many glasses. We conjecture that this relation, specific to glassy materials, might be rather common among them.     

Toward a DFT-based molecular dynamics description of Co(II) binding in sulfur-rich peptides

In this paper, we investigated the reliability of a Car-Parrinello molecular dynamics (CPMD) approach to characterize the binding of Co(II) metal cation to peptide molecules containing cysteine. To this end, we compared pseudo-potentials and DFT plane wave expansion, which are used as key ingredients in the CPMD method, with standard all-electron Gaussian basis set DFT calculations. The simulations presented here are the first attempts to characterize interactions and dynamics of Co(II) metal with the building blocks of phytochelatin peptide molecules. Benchmark calculations are performed on [Co(Cys-H)]+ and [Co(Glutathione-H)]+ complexes, since they are the main fragments of the Co(II)-Cys and Co(II)-glutathione systems found in gas phase electrospray ionisation mass spectrometry (ESI-MS) experiments done in our laboratory. We also present benchmark calculations on the [Co(H2O)6)]2+ cluster with direct comparisons to highly correlated ab initio calculations and experiments. In particular, we investigated the dissociation path of one water molecule from the first hydration shell of Co(II) with CPMD. Overall, our molecular dynamics simulations shed some light on the nature of the Co(II) interaction and reactivity in Co(II)-phytochelatin building block systems related to the biological and environmental activity of the metal, either in the gas or liquid phase.     

Controllability of quasi-linear Hamiltonian NLS equations

We prove internal controllability in arbitrary time, for small data, for quasi-linear Hamiltonian NLS equations on the circle. We use a procedure of reduction to constant coefficients up to order zero and HUM method to prove the controllability of the linearized problem. Then we apply a Nash–Moser–Hörmander implicit function theorem as a black box.     

Existence and multiplicity of solutions for elliptic equations with jumping nonlinearities

In this paper we are concerned with a semilinear elliptic Dirichlet problem with jumping nonlinearity and, using a completely variational method, we show that the number of solutions may be arbitrarily large provided the number of jumped eigenvalues is large enough. In order to prove this fact, we show that for every positive integer k, when a suitable parameter is large enough, there exists a solution which presents k peaks. Under the assumptions we consider in this paper, new (unexpected) phenomena are observed in the study of this problem and new methods are required to construct the k-peaks solutions and describe their asymptotic behavior (weak limits of the rescaled solutions, localization of the concentration points of the peaks, asymptotic profile of the rescaled peaks, etc.).     

Multigram scale, solventless, and diffusion-controlled route to highly monodisperse PbS nanocrystals

High-quality PbS nanocrystals were produced in multigram-scale quantities through a solventless, heterogeneous, and relatively green route. The heterogeneous nature of this reaction allows one to limit the diffusion in the system, allowing for unprecedented monodispersity and quality of the product demonstrated by a full-width at half-maximum of the photoluminescence peak (PL fwhm) as low as 52 meV, a Stokes shift as low as 10 meV, and a quantum yield (QY) of 40%. The growth of the nanocrystals is interpreted in the framework of a diffusion-controlled Ostwald growth in conditions of strong supersaturation.     

Froc: a new fluorous protective group for peptide and oligosaccharide synthesis

[STRUCTURE: SEE TEXT] The synthesis of a new fluorous protecting group, Froc, is described. This new fluorous tag has been used in peptide and carbohydrate synthesis by our group and readily allows us to fully characterize each product (NMR, MS) and monitor each synthetic step by TLC. Purification of the products is generally performed by standard fluorous solid-phase extraction techniques (e.g., F-SPE), but standard chromatographic purifications are also possible if required.     

Zurek-Kibble mechanism for the spontaneous vortex formation in Nb-Al/Al(ox)/Nb Josephson tunnel junctions: new theory and experiment

New scaling behavior has been both predicted and observed in the spontaneous production of fluxons in quenched Nb-Al/Al(ox)/Nb annular Josephson tunnel junctions (JTJs) as a function of the quench time, tau(Q). The probability f(1) to trap a single defect during the normal-metal-superconductor phase transition clearly follows an allometric dependence on tau(Q) with a scaling exponent sigma = 0.5, as predicted from the Zurek-Kibble mechanism for realistic JTJs formed by strongly coupled superconductors. This definitive experiment replaces one reported by us earlier, in which an idealized model was used that predicted sigma = 0.25, commensurate with the then much poorer data. Our experiment remains the only condensed matter experiment to date to have measured a scaling exponent with any reliability.