Two-scale convergence for locally-periodic microstructures and homogenization of plywood structures

The introduced notion of locally-periodic two-scale convergence allows to average a wider range of microstructures, compared to the periodic one. The compactness theorem for the locally-periodic two-scale convergence and the characterisation of the limit for a sequence bounded in $H^1(\Omega)$ are proven. The underlying analysis comprises the approximation of functions, which periodicity with respect to the fast variable depends on the slow variable, by locally-periodic functions, periodic in subdomains smaller than the considered domain, but larger than the size of microscopic structures. The developed theory is applied to derive macroscopic equations for a linear elasticity problem defined in domains with plywood structures.Comment: 22 pages, 4 figure

Locally periodic unfolding method and two-scale convergence on surfaces of locally periodic microstructures

In this paper we generalize the periodic unfolding method and the notion of two-scale convergence on surfaces of periodic microstructures to locally periodic situations. The methods that we introduce allow us to consider a wide range of non-periodic microstructures, especially to derive macroscopic equations for problems posed in domains with perforations distributed non-periodically. Using the methods of locally periodic two-scale convergence (l-t-s) on oscillating surfaces and the locally periodic (l-p) boundary unfolding operator, we are able to analyze differential equations defined on boundaries of non-periodic microstructures and consider non-homogeneous Neumann conditions on the boundaries of perforations, distributed non-periodically

Red-emitting fluorescent Organic Light emitting Diodes with low sensitivity to self-quenching

International audienceConcentration quenching is a major impediment to efficient organic light-emitting devices. We herein report on Organic Light-Emitting Diodes (OLEDs) based on a fluorescent amorphous red-emitting starbust triarylamine molecule (4-di(4'-tert-butylbiphenyl-4-yl)amino-4'-dicyanovinylbenzene, named FVIN), exhibiting a very small sensitivity to concentration quenching. OLEDs are fabricated with various doping levels of FVIN into Alq3, and show a remarkably stable external quantum efficiency of 1.5% for doping rates ranging from 5% up to 40%, which strongly relaxes the technological constraints on the doping accuracy. An efficiency of 1% is obtained for a pure undoped active region, along with deep red emission (x=0.6; y=0.35 CIE coordinates). A comparison of FVIN with the archetypal DCM dye is presented in an identical multilayer OLED structure

Doped and non-doped organic light-emitting diodes based on a yellow carbazole emitter into a blue-emitting matrix

A new carbazole derivative with a 3,3'-bicarbazyl core 6,6'-substituted by dicyanovinylene groups (6,6'-bis(1-(2,2'-dicyano)vinyl)-N,N'-dioctyl-3,3'-bicarbazyl; named (OcCz2CN)2, was synthesized by carbonyl-methylene Knovenagel condensation, characterized and used as a component of multilayer organic light-emitting diodes (OLEDs). Due to its -donor-acceptor type structure, (OcCz2CN)2 was found to emit a yellow light at max=590 nm (with the CIE coordinates x=0.51; y = 0.47) and was used either as a dopant or as an ultra-thin layer in a blue-emitting matrix of 4,4'-bis(2,2'-diphenylvinyl)-1,1'-biphenyl (DPVBi). DPVBi (OcCz2CN)2-doped structure exhibited, at doping ratio of 1.5 weight %, a yellowish-green light with the CIE coordinates (x = 0.31; y = 0.51), an electroluminescence efficiency EL=1.3 cd/A, an external quantum efficiency ext= 0.4 % and a luminance L= 127 cd/m2 (at 10 mA/cm2) whereas for non-doped devices utilizing the carbazolic fluorophore as a thin neat layer, a warm white with CIE coordinates (x = 0.40; y= 0.43), EL= 2.0 cd/A, ext= 0.7 %, L = 197 cd/m2 (at 10 mA/cm2) and a color rendering index (CRI) of 74, were obtained. Electroluminescence performances of both the doped and non-doped devices were compared with those obtained with 5,6,11,12-tetraphenylnaphtacene (rubrene) taken as a reference of highly efficient yellow emitter

What is the optimal shape of a pipe?

We consider an incompressible fluid in a three-dimensional pipe, following the Navier-Stokes system with classical boundary conditions. We are interested in the following question: is there any optimal shape for the criterion "energy dissipated by the fluid"? Moreover, is the cylinder the optimal shape? We prove that there exists an optimal shape in a reasonable class of admissible domains, but the cylinder is not optimal. For that purpose, we explicit the first order optimality condition, thanks to adjoint state and we prove that it is impossible that the adjoint state be a solution of this over-determined system when the domain is the cylinder. At last, we show some numerical simulations for that problem

Opacity calculation for target physics using the ABAKO/RAPCAL code

Radiative properties of hot dense plasmas remain a subject of current interest since they play an important role in inertial confinement fusion (ICF) research, as well as in studies on stellar physics. In particular, the understanding of ICF plasmas requires emissivities and opacities for both hydro-simulations and diagnostics. Nevertheless, the accurate calculation of these properties is still an open question and continuous efforts are being made to develop new models and numerical codes that can facilitate the evaluation of such properties. In this work the set of atomic models ABAKO/RAPCAL is presented, as well as a series of results for carbon and aluminum to show its capability for modeling the population kinetics of plasmas in both LTE and NLTE regimes. Also, the spectroscopic diagnostics of a laser-produced aluminum plasma using ABAKO/RAPCAL is discussed. Additionally, as an interesting application of these codes, fitting analytical formulas for Rosseland and Planck mean opacities for carbon plasmas are reported. These formulas are useful as input data in hydrodynamic simulation of targets where the computation task is so hard that in line computation with sophisticated opacity codes is prohibitive

Shape optimization for the generalized Graetz problem

We apply shape optimization tools to the generalized Graetz problem which is a convection-diffusion equation. The problem boils down to the optimization of generalized eigen values on a two phases domain. Shape sensitivity analysis is performed with respect to the evolution of the interface between the fluid and solid phase. In particular physical settings, counterexamples where there is no optimal domains are exhibited. Numerical examples of optimal domains with different physical parameters and constraints are presented. Two different numerical methods (level-set and mesh-morphing) are show-cased and compared

Radiative properties of stellar plasmas and open challenges

The lifetime of solar-like stars, the envelope structure of more massive stars, and stellar acoustic frequencies largely depend on the radiative properties of the stellar plasma. Up to now, these complex quantities have been estimated only theoretically. The development of the powerful tools of helio- and astero- seismology has made it possible to gain insights on the interiors of stars. Consequently, increased emphasis is now placed on knowledge of the monochromatic opacity coefficients. Here we review how these radiative properties play a role, and where they are most important. We then concentrate specifically on the envelopes of $\beta$ Cephei variable stars. We discuss the dispersion of eight different theoretical estimates of the monochromatic opacity spectrum and the challenges we need to face to check these calculations experimentally.Comment: 6 pages, 5 figures, in press (conference HEDLA 2010