Many-Polaron States in the Holstein–Hubbard Model

A variational approach is proposed to study some properties of the adiabatic Holstein–Hubbard model which describes an assembly of fermionic charges interacting with a static atomic lattice. The sum of the electronic energy and the lattice elastic energy is proved to have minima with a many-polaron structure in a certain domain of model parameters. Our analytical work consists in expanding these energy minima from the zero electronic transfer limit which remarkably holds for a finite amplitude of the onsite Hubbard repulsion and for an unbounded lattice size.     

Analytical and numerical prediction of harmonic sound power in the inlet of aero-engines with emphasis on transonic rotation speeds

Tone noise radiated through the inlet of a turbofan is mainly due to rotor-stator interactions at subsonic regimes (approach flight), and to the shock waves attached to each blade at supersonic helical tip speeds (takeoff). The axial compressor of a helicopter turboshaft engine is transonic as well and can be studied like turbofans at takeoff. The objective of the paper is to predict the sound power at the inlet radiating into the free field, with a focus on transonic conditions because sound levels are much higher. Direct numerical computation of tone acoustic power is based on a RANS (Reynolds averaged Navier–Stokes) solver followed by an integration of acoustic intensity over specified inlet cross-sections, derived from Cantrell and Hart equations (valid in irrotational flows). In transonic regimes, sound power decreases along the intake because of nonlinear propagation, which must be discriminated from numerical dissipation. This is one of the reasons why an analytical approach is also suggested. It is based on three steps: (i) appraisal of the initial pressure jump of the shock waves; (ii) 2D nonlinear propagation model of Morfey and Fisher; (iii) calculation of the sound power of the 3D ducted acoustic field. In this model, all the blades are assumed to be identical such that only the blade passing frequency and its harmonics are predicted (like in the present numerical simulations). However, transfer from blade passing frequency to multiple pure tones can be evaluated in a fourth step through a statistical analysis of irregularities between blades. Interest of the analytical method is to provide a good estimate of nonlinear acoustic propagation in the upstream duct while being easy and fast to compute. The various methods are applied to two turbofan models, respectively in approach (subsonic) and takeoff (transonic) conditions, and to a Turbomeca turboshaft engine (transonic case). The analytical method in transonic appears to be quite reliable by comparison with the numerical solution and with available experimental data.     

Production of large quantities of “Janus” nanoparticles using wax-in-water emulsions

For the first time, large amount of Janus silica particles as small as 100 nm in diameter were prepared through a simple method based on the elaboration of Pickering emulsions of wax-in-water. Controlling the kinetic stabilization of wax droplets allows the fabrication of gram-sized quantities of regular asymmetric inorganic particles with high yield. In fact, our method is based on a limited coalescence process, which allows one to predict the quantity of interface which is produced when working with a known mass of wax, and thus to be sure that all introduced silica particles are adsorbed on the wax surface. To this end, the hydrophilic surface of the silica particles was made partially hydrophobic by adsorbing a known amount of surfactant: cetyltrimethylammonium bromide (CTAB). Varying the concentration in surfactant results in tuning the penetration rate of the particles in the wax droplets, leading to various dimension of the modified area. The broken spherical symmetry of the particle surface was thereafter revealed by the selective adsorption of gold nanoparticles on the amino-modified surface.     

La densité de la loi-limite d'un processus en cascade expansif

Sans résumé     

Non-quasi-stationary state pyrolysis of ethane

An induction period has been observed in the pyrolysis of ethane in a continuous-flow stirred tank reactor at 530°C. The rate constants of the initiation, determining propagation and termination steps, have been determined.     

Inductive (direct) limits in the categories of heterogeneous algebras and of abstract automata

In our preceding paper [2], we have studied the fundamental properties of the heterogeneous algebras, and constructed the projective limits in the category of these algebras and in the category of abstract automata. The present article is devoted to the study ofdirect limits in the same categories.     

Anisotropy profiles of optical fibers and preforms

An experimental method to measure the optical anisotropy profiles of optical fibers and preforms is presented. The local values of n_z?n_r and n_z?n_?, (r,?,z) being a cylindrical coordinate system associated with the fiber or preform, are obtained.