Branching rules for unitary groups and spectra of invariant differential operators on complex Grassmannians

In this paper, we prove a combinatorial rule describing the restriction of any irreducible representation of U(n+m) to the subgroup U(n)×U(m). We also derive similar rules for the reductions from SU(n+m) to S(U(n)×U(m)), and from SU(n+m) to SU(n)×SU(m). As applications of these representation-theoretic results, we compute the spectra of the Bochner–Laplacian on powers of the determinant bundle over the complex Grassmannian . The spectrum of the Dirac operator acting on the spin Grassmannian is also partially computed. A further application is given by the determination of the spectrum of the Hodge–Laplacian acting on the space of smooth functions on the unit determinant bundle over .     

Polyterephthalates Bearing Bio-based Moieties

Dimethyl terephthalate was reacted with 5,5′-Isopropylidene-bis(ethyl 2-furoate), 1,4:3,6-dianhydrohexitols and ethan-1,2-diol in order to obtain PET incorporating bio-based moieties. Polycondensation was achieved in two steps: (i) the formation of a hydroxyethyl-terminated oligomer by reaction of starting diester mixture with excess ED and, (ii) a polycondensation step with elimination of ED was used to obtain high molar mass copolyesters. Copolymers of various compositions were synthesized and characterized by ¹H-NMR, SEC, DSC and TGA. The resulting materials are amorphous polymers (T _g = 104–127 °C) with good thermal stability.     

Solvation effects and stabilization of multicharged ions: a case study of Ar(m)BeO(q+) complexes

Using first-principle methods, we characterized Ar(m)BeO(q+) (0 ≤ m ≤ 3 and 0 ≤ q ≤ 2) and BeO(q+) (3 ≤ q ≤ 5) multicharged ions (MCIs). This includes their structural parameters, relative stabilities and vibrational wavenumbers. Our calculations confirm the existence of the ArBeO complex. In addition, we found (meta-)stable neutral and ionic complexes such as ArBeO(+), ArBeO(2+), Ar(2)BeO, Ar(2)BeO(+), Ar(2)BeO(2+), Ar(3)BeO, Ar(3)BeO(+) and Ar(3)BeO(2+). The analysis of the structural parameters and of the electron density differences shows that a strong perturbation in the electronic structure of the BeO(q+) (q = 1,2) moiety occurs upon complexation, resulting in a major increase in covalency of these multicharged ions (MCIs). The consequences of solvation of MCIs in argon matrices are pointed out. More generally, the effects on the spectroscopy of MCIs trapped on cold matrices are discussed.     

Full multi grid method for electric field computation in point-to-plane streamer discharge in air at atmospheric pressure

Streamers dynamics are characterized by the fast propagation of ionized shock waves at the nanosecond scale under very sharp space charge variations. The streamer dynamics modelling needs the solution of charged particle transport equations coupled to the elliptic Poisson’s equation. The latter has to be solved at each time step of the streamers evolution in order to follow the propagation of the resulting space charge electric field. In the present paper, a full multi grid (FMG) and a multi grid (MG) methods have been adapted to solve Poisson’s equation for streamer discharge simulations between asymmetric electrodes. The validity of the FMG method for the computation of the potential field is first shown by performing direct comparisons with analytic solution of the Laplacian potential in the case of a point-to-plane geometry. The efficiency of the method is also compared with the classical successive over relaxation method (SOR) and MUltifrontal massively parallel solver (MUMPS). MG method is then applied in the case of the simulation of positive streamer propagation and its efficiency is evaluated from comparisons to SOR and MUMPS methods in the chosen point-to-plane configuration. Very good agreements are obtained between the three methods for all electro-hydrodynamics characteristics of the streamer during its propagation in the inter-electrode gap. However in the case of MG method, the computational time to solve the Poisson’s equation is at least 2 times faster in our simulation conditions.