Linearly repetitive Delone sets are rectifiable

We show that every linearly repetitive Delone set in the Euclidean d  -space R^d${\mathbb{R}}^d$, with d?2$d?2$, is equivalent, up to a bi-Lipschitz homeomorphism, to the integer lattice Z^d${\mathbb{Z}}^d$. In the particular case when the Delone set X   in R^d${\mathbb{R}}^d$ comes from a primitive substitution tiling of R^d${\mathbb{R}}^d$, we give a condition on the eigenvalues of the substitution matrix which ensures the existence of a homeomorphism with bounded displacement from X   to the lattice βZ^d$\beta {\mathbb{Z}}^d$ for some positive β. This condition includes primitive Pisot substitution tilings but also concerns a much broader set of substitution tilings.     

Ads Manifolds With Particles and Earthquakes on Singular Surfaces

We prove two related results. The first is an “earthquake theorem” for closed hyperbolic surfaces with cone singularities where the total angle is less than π: any two such metrics in are connected by a unique left earthquake. The second result is that the space of “globally hyperbolic” AdS manifolds with “particles” – cone singularities (of given angle) along time-like lines – is parametrized by the product of two copies of the Teichmüller space with some marked points (corresponding to the cone singularities). The two statements are proved together. F.B. was partially supported by the A.N.R. project GEODYCOS. J.-M.S. was partially supported by the A.N.R. programs RepSurf, 2006-09, ANR-06-BLAN-0311, GeomEinstein, 2006-09, 06-BLAN-0154, and FOG, 2007-10, ANR-07-BLAN-0251-01.     

Spectral distributions for long range perturbations

We study distributions which generalize the concept of spectral shift function, for pseudo-differential operators on . We call such distributions spectral distributions. Relations between relative scattering determinants and spectral distributions are established; they lead to the definition of regularized scattering phase. These relations are analogous to the usual one for the standard spectral shift function. We give several asymptotic properties in the high energy and semiclassical limits where both nontrapping and trapping cases are considered. In particular, we prove Breit-Wigner formulae for the regularized scattering phases, for semiclassical Schrödinger operators with long-range potentials.     

Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a multidimensional central limit theorem for this estimator are established. Similar results are obtained for a refinement of the generalized quadratic variations (QV) estimator. The example of the multifractional Brownian motion is studied in detail. A simulation study is included showing that the IR-estimator is more accurate than the QV-estimator.     

Electronic properties of 2D and 3D hybrid organic/inorganic perovskites for optoelectronic and photovoltaic applications

We herein investigate theoretically both 2D and 3D Hybrid Organic/inorganic perovskite crystal structures based on density functional theory (DFT) calculations and symmetry analyses. Our findings reveal the universal features of the electronic band structure for the class of lead-halide hybrids (R-NH \(_{3})_{n}\hbox {PbX}_{m}\) , where \((\mathrm{{n}}, \mathrm{{m}})=(2,4)\) and (1,3) respectively for 2D and 3D structures. Among those, the large spin-orbit coupling acting on the conduction band is shown to play a major role on the band gap of these materials. Moreover, this approach can easily be generalized to related layered and 3D hybrids, thus providing a clear-sighted inside in their electronic and optical properties.     

Milliwatt-peak-power pulse characterization at 1.55 microm by wavelength-conversion frequency-resolved optical gating

A novel wavelength-conversion configuration based on four-wave mixing in an optical fiber has been used to generate a frequency-resolved optical gating (FROG) trace identical to that obtained from second-harmonic generation (SHG). The use of an optical fiber waveguide permits enhanced measurement sensitivity compared with that of conventional SHG-FROG and has been used for complete characterization of 1-mW peak-power picosecond pulses at 1.55 microm from an unamplified semiconductor laser diode gain switched at 10 GHz.     

Pd–H and Ni–H phase diagrams using cluster variation method and Monte Carlo simulation

This work focuses on interstitial solid solutions of hydrogen in the face-centred cubic (fcc) host lattice of palladium and nickel, using a first-principles based approach. Cluster Variation Method (CVM) and Monte Carlo simulation algorithms were especially designed, allowing a coupled use of both techniques, to study hydrogen–vacancy interactions inside an fcc metallic host lattice. First-principles calculations provided the H–Vac interaction energies by structure inversion method. The phase diagrams and thermodynamic properties were computed using only theoretical inputs. The mechanisms leading to the formation of the miscibility gaps observed for both Pd–H and Ni–H systems and the hydrogen ordering on palladium interstitial lattice were reproduced without any empirical term.