Affine Dunkl processes

We introduce the analogue of Dunkl processes in the case of an affine root system of type $\widetilde{\text{A}}_1$. The construction of the affine Dunkl process is achieved by a skew-product decomposition by means of its radial part and a jump process on the affine Weyl group, where the radial part of the affine Dunkl process is defined as the unique solution of some stochastic differential equation. We prove that the affine Dunkl process is a c\`adl\`ag Markov process as well as a local martingale, study its jumps, and give a martingale decomposition, which are properties similar to those of the classical Dunkl process

Quantum random walks and minors of Hermitian Brownian motion

Considering quantum random walks, we construct discrete-time approximations of the eigenvalues processes of minors of Hermitian Brownian motion. It has been recently proved by Adler, Nordenstam and van Moerbeke that the process of eigenvalues of two consecutive minors of an Hermitian Brownian motion is a Markov process, whereas if one considers more than two consecutive minors, the Markov property fails. We show that there are analog results in the noncommutative counterpart and establish the Markov property of eigenvalues of some particular submatrices of Hermitian Brownian motion

Combining parameter values or pp-values

We review the methods to combine several measurements, in the form of parameter values or $p$-values.Comment: 15 pages, 4 figure

Hydrodynamics of galaxy mergers with supermassive black holes: is there a last parsec problem ?

We study the formation of a supermassive black hole (SMBH) binary and the shrinking of the separation of the two holes to sub-pc scales starting from a realistic major merger between two gas-rich spiral galaxies with mass comparable to our Milky Way. The simulations, carried out with the Adaptive Mesh Refinement (AMR) code RAMSES, are capable of resolving separations as small as 0.1 pc. The collision of the two galaxies produces a gravo-turbulent rotating nuclear disk with mass (10^9 Msun) and size (60 pc) in excellent agreement with previous SPH simulations with particle splitting that used a similar setup (Mayer et al. 2007) but were limited to separations of a few parsecs. The AMR results confirm that the two black holes sink rapidly as a result of dynamical friction onto the gaseous background, reaching a separation of 1 pc in less than 10^7 yr. We show that the dynamical friction wake is well resolved by our model and we find good agreement with analytical predictions of the drag force as a function of the Mach number. Below 1 pc, black hole pairing slows down significantly, as the relative velocity between the sinking SMBH becomes highly subsonic and the mass contained within their orbit falls below the mass of the binary itself, rendering dynamical friction ineffective. In this final stage, the black holes have not opened a gap as the gaseous background is highly pressurized in the center. Non-axisymmetric gas torques do not arise to restart sinking in absence of efficient dynamical friction, at variance with previous calculations using idealized equilibrium nuclear disk models. (abridged)Comment: Accepted for publication in MNRAS. 10 pages, 6 figure

A possible chiral spin-liquid phase in non-centrosymmetric RRBaCo4_4O7_7

Based on a symmetry approach, we propose a possible explanation of the weak ferromagnetic component recently observed in YBaCo$_3$FeO$_7$ (Valldor et al. Phys Rev B, $\bf {84}$ 224426 (2011)) and other isostructural compounds in the high-temperature spin-liquid phase. Due to the polar nature of their crystal structure, a coupling between time-odd scalar spin chirality which we suggest as the primary order parameter and macroscopic magnetization is possible as follows from the general form of the appropriate free-energy invariant. The deduced pseudoproper coupling between both physical quantities provides a unique possibility to study the critical behaviour of the chiral order parameter

: L'adstrat juridique cinématographique comme soutien pédagogique du document authentique

International audienceThis article proposes to portray the different steps of a learning scenario created for students enrolled in the first year of the Grenoble law school who chose English as a foreign language as part of their curriculum. The court room extract that can be found in the film Vera Drake may be used as resource material to be copied according to the pedagogic strategy which aims at creating authentic tasks for the learner in English for Specific Purposes (ESP). The students are required to perform a task coherent with their professional goal, that is to say, they will be expected to act a prominent scene from a criminal trial. This article will describe how the scenario is led by the necessity to perform meaningful tasks using the target language and also uses an article taken from the Times, law supplement, as a "legal words" tool box and inspiration to create the denunciative context necessary to perform the play.Cet article propose de décrire les activités d'un scénario pédagogique, réalisé pour des étudiants de première année de droit de la faculté de Grenoble dans le cadre de l'apprentissage de l'anglais de spécialité. L'adstrat professionnel juridique que l'on trouve dans le film Vera Drake peut servir de support dans une démarche de pédagogie de projet qui vise l'authenticité de tâches menées par les étudiants, à savoir la mise en scène d'une étape d'un procès au pénal selon le modèle de l'adstrat professionnel. L'article montrera comment le projet, piloté par l'objectif d'appropriation de la langue et culture de spécialité, utilise dans un second temps le document authentique, un article du Times, puisé dans la rubrique " law supplement ", comme outil lexical et de création de contexte énonciatif pour réaliser la tâche finale

Orbital ordering promotes weakly-interacting S=1/2 dimers in the triangular lattice compound Sr3Cr2O8

The weakly interacting S=1/2 dimers system Sr3Cr2O8 has been investigated by powder neutron diffraction and inelastic neutron scattering. Our data reveal a structural phase transition below room temperature corresponding to an antiferro-orbital ordering with nearly 90 degrees arrangement of the occupied 3z^2-r^2 d-orbital. This configuration leads to a drastic reduction of the inter-dimer exchange energies with respect to the high temperature orbital-disorder state, as shown by a spin-dimer analysis of the super-superexchange interactions performed using the Extended Huckel Tight Binding method. Inelastic neutron scattering reveals the presence of a quasi non-dispersive magnetic excitation at 5.4 meV, in agreement with the picture of weakly-interacting dimers