Asymptotic solvers for ordinary differential equations with multiple frequencies

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focusing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question. Numerical examples illustrate the effectiveness of the method

On phenomenon of scattering on resonances associated with discretisation of systems with fast rotating phase

Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of system with one fast rotating phase lead to a situation of such kind: numerical solution demonstrate phenomenon of scattering on resonances that is absent in the original system.Comment: 10 pages, 5 figure

Thick films of YSZ electrolytes by dip-coating process

Yttria stabilized zirconia (YSZ, 8% Y2O3) thick films were coated on porous Ni-YSZ substrates using the dip-coating process and a suspension with a new formulation. The suspension was obtained by addition of a polymeric matrix in a stable suspension of a commercial YSZ (Tosoh) powders dispersed in an azeotropic MEK-EtOH mixture. The green layers were densified after an optimization of the suspension composition. YSZ Tosoh particles encapsulated by a zirconium alkoxide sol and added with colloidal alkoxide precursor are used to load the suspension. The in situ growth of these colloids increases significantly the layers density after an appropriated heat treatment. The obtained films are continuous, homogeneous and 20 μm thick. Different microstructures are obtained depending on the synthesis parameters of the suspension

A micropillar for cavity optomechanics

We present a new micromechanical resonator designed for cavity optomechanics. We have used a micropillar geometry to obtain a high-frequency mechanical resonance with a low effective mass and a very high quality factor. We have coated a 60-$\mu$m diameter low-loss dielectric mirror on top of the pillar and are planning to use this micromirror as part of a high-finesse Fabry-Perot cavity, to laser cool the resonator down to its quantum ground state and to monitor its quantum position fluctuations by quantum-limited optical interferometry

piRNAs and Aubergine cooperate with Wispy poly(A) polymerase to stabilize mRNAs in the germ plasm

Piwi-interacting RNAs (piRNAs) and PIWI proteins play a crucial role in germ cells by repressing transposable elements and regulating gene expression. In Drosophila, maternal piRNAs are loaded into the embryo mostly bound to the PIWI protein Aubergine (Aub). Aub targets maternal mRNAs through incomplete base-pairing with piRNAs and can induce their destabilization in the somatic part of the embryo. Paradoxically, these Aub-dependent unstable mRNAs encode germ cell determinants that are selectively stabilized in the germ plasm. Here we show that piRNAs and Aub actively protect germ cell mRNAs in the germ plasm. Aub directly interacts with the germline-specific poly(A) polymerase Wispy, thus leading to mRNA polyadenylation and stabilization in the germ plasm. These results reveal a role for piRNAs in mRNA stabilization and identify Aub as an interactor of Wispy for mRNA polyadenylation. They further highlight the role of Aub and piRNAs in embryonic patterning through two opposite functions

Evidence of Brillouin scattering in an ytterbium-doped double-clad fiber laser

We have designed and performed an experiment that permitted direct observation of Brillouin backscattering in an Yb-doped double-clad fiber laser. Fifteen Brillouin-shifted frequencies were observed for the first time to our knowledge. We clearly demonstrate that stimulated Brillouin scattering is directly responsible for both fast transient dynamics of the laser and reduction of the laser’s pulse width

Preparation of Ni–YSZ thin and thick films on metallic interconnects as cell supports. Applications as anode for SOFC

In this work, we propose the preparation of a duplex anodic layer composed of both a thin (100 nm) and a thick film (10 lm) with Ni–YSZ material. The support of this anode is a metallic substrate, which is the interconnect of the SOFC unit cell. The metallic support limits the temperature of thermal treatment at 800 C to keep a good interconnect mechanical behaviour and to reduce corrosion. We have chosen to elaborate anodic coatings by sol–gel route coupled with dip-coating process, which are low cost techniques and allow working with moderate temperatures. Thin films are obtained by dipping interconnect substrate into a sol, and thick films into an optimized slurry. After thermal treatment at only 800 C, anodic coatings are adherent and homogeneous. Thin films have compact microstructures that confer ceramic protective barrier on metal surface. Further coatings of 10 lm thick are porous and constitute the active anodic material

Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property