Fundamental Stokes eigenmodes in the square: which expansion is more accurate, Chebyshev or Reid-Harris?

The well-known Reid-Harris expansions, applied to the stream function formulation, and the projection-diffusion Chebyshev Stokes solver, in primitive variables, are used to compute the fundamental Stokes eigenmodes of each of the symmetry families characterizing the Stokes solutions in the square. The numerical accuracy of both methods, applied with several discretizations, are compared, for both the eigenvalues and the main features of the corresponding eigenmodes. The Chebyshev approach is by far the most efficient, even though the associated solver does not provide a divergence free velocity but asymptoticall

Vector potential-vorticity relationship for the Stokes flows: application to the Stokes eigenmodes in 2D/3D closed domain

The unsteady dynamics of the Stokes flows, where $$\vec{\nabla}^{2} \left(\frac{p}{\rho}\right) =0$$ , is shown to verify the vector potential-vorticity ( $$\vec{\psi},\,\vec{\omega}$$ ) correlation $$\frac{\partial\vec{\psi}}{\partial t}+\nu\,\vec{\omega}+\vec{\Pi}=0$$ , where the field $$\vec{\Pi}$$ is the pressure-gradient vector potential defined by $$\vec{\nabla} \left(\frac{p}{\rho}\right)=\vec{\nabla}\times\vec{\Pi}$$ . This correlation is analyzed for the Stokes eigenmodes, $$\frac{\partial\vec{\psi}}{\partial t}=\lambda\,\vec{\psi}$$ , subjected to no-slip boundary conditions on any two-dimensional (2D) closed contour or three-dimensional (3D) surface. It is established that an asymptotic linear relationship appears, verified in the core part of the domain, between the vector potential and vorticity, $$\nu\,\left(\vec{\omega}-\vec{\omega}_0\right)=-\lambda\,\vec{\psi}$$ , where $$\vec{\omega}_0$$ is a constant offset field, possibly zer

Numerical Evaluation of the Accuracy and Stability Properties of High-order Direct Stokes Solvers with or without Temporal Splitting

The temporal stability and effective order of two different direct high-order Stokes solvers are examined. Both solvers start from the primitive variables formulation of the Stokes problem, but are distinct by the numerical uncoupling they apply on the Stokes operator. One of these solvers introduces an intermediate divergence free velocity for performing a temporal splitting (J. Comput. Phys. [1991] 97, 414-443) while the other treats the whole Stokes problem through the evaluation of a divergence free acceleration field (C.R. Acad. Sci. Paris [1994] 319 Serie I, 1455-1461; SIAM J. Scient. Comput. [2000] 22(4), 1386-1410). The second uncoupling is known to be consistent with the harmonicity of the pressure field (SIAM J. Scient. Comput. [2000] 22(4), 1386-1410). Both solvers proceed by two steps, a pressure evaluation based on an extrapolated in time (of theoretical order Je) Neumann condition, and a time implicit (of theoretical order Ji) diffusion step for the final velocity. These solvers are implemented with a Chebyshev mono-domain and a Legendre spectral element collocation schemes. The numerical stability of these four options is investigated for the sixteen combinations of (Je,Ji), 1 ≤ Je, Ji ≤

Identification Model of the Object Oriented Technology risks, for Avionics Certification

International audienceThe introduction of any new technology in an existing industrial process has a dual effect: on the one hand, it is expected to bring some well-identified benefits, but on the other hand, it also brings a certain number of new risks. It is the role and responsibility of decision makers, designers, and developers to estimate and balance these two aspects, taking into account the very specific characteristics of their industrial domain. In the domain of software systems, for instance, object-oriented technologies have been demonstrated to increase software quality and productivity, but they simultaneously bring some specific risks that must be carefully characterized and handled, especially when they are integrated in the development of software applications for critical systems. In the avionics domain, the OOTiA document proposes a first and informal identification of some of these risks. However this identification process misses the formal background that would guarantee its consistency and completeness. In this paper, we suggest to fill this gap by considering the management of software risk as a specific case of industrial risk management. To achieve this goal, we propose a generic model for the identification of software risks. This model provides the information required by the subsequent phases of risk management: risk estimation, risk acceptance, and risk mitigation

Scavenging of aerosol particles by rain in a cloud resolving model

International audienceWe describe a below-cloud scavenging module of aerosol particles by raindrops for use in a three-dimensional mesoscale cloud resolving model. The rate of particle removal is computed by integrating the scavenging efficiency over the aerosol particle and the drop size distributions. Here the numerical integration is performed accurately with a Gauss quadrature algorithm. The efficiency of the scavenging module is partially confirmed with experimental data. More interestingly, it is illustrated by two numerical experiments: the simulation of a forced convective circulation in a tropical cloudy boundary layer and a two-dimensional simulation of an African squall line. The results show a very selective wet removal of the aerosol particles which clearly depends on the mode radius, the width and the vertical profile of concentration. Furthermore, the squall line case shows the importance of resolving internal circulations to redistribute layers of aerosol particles in order to improve estimates of particle removal by below-cloud scavenging

Organic dye for dye-sensitized solar cells

Organic dye for a dye-sensitized solar cell (DSSC) comprising at least one electron-acceptor unit and at least one π-conjugated unit. Said organic dye is particularly useful in a dye-sensitized photoelectric transformation element which, in its turn, can be used in a dye-sensitized solar cell (DSSC)

3,4-Vinylenedioxythiophene (VDOT): a new building block for thiophene-based π-conjugated systems

The synthesis of the title compound and its use as a building block in π-conjugated systems are presented

Bilayer Hybrid Solar Cells Based on Triphenylamine−Thienylenevinylene Dye and TiO2

Photoinduced energy conversion from multilayers of organic dye on dense TiO2 films was investigated in bilayer hybrid solar cells. Dye layers of varying thicknesses were prepared by spin-casting the star-shaped dye [tris(dicyano-vinyl-2-thienyl)phenyl]amine (1) from solutions onto dense TiO2 on conducting glass substrates. A spin-cast layer of poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) and graphite powder was used for contacting the devices. Excitons generated in the dye multilayer contribute to the power conversion efficiency, reaching a maximum of ca. 0.3% at a dye layer thickness of ca. 8 nm for the devices described herein. For dye layers exceeding 5 nm, the cell performance becomes limited by the exciton diffusion length LED and the hole mobility in the organic layer. Using dye multilayers is a viable way to increase light harvesting in solid-state dye-sensitized solar cells

Exciton enhanced dye sensitized solar cells

Date du colloque&nbsp;: 05/2009</p

Calibration and First light of the Diabolo photometer at the Millimetre and Infrared Testa Grigia Observatory

We have designed and built a large-throughput dual channel photometer, Diabolo. This photometer is dedicated to the observation of millimetre continuum diffuse sources, and in particular, of the Sunyaev-Zel'dovich effect and of anisotropies of the 3K background. We describe the optical layout and filtering system of the instrument, which uses two bolometric detectors for simultaneous observations in two frequency channels at 1.2 and 2.1 mm. The bolometers are cooled to a working temperature of 0.1 K provided by a compact dilution cryostat. The photometric and angular responses of the instrument are measured in the laboratory. First astronomical light was detected in March 1995 at the focus of the new Millimetre and Infrared Testa Grigia Observatory (MITO) Telescope. The established sensitivity of the system is of 7 mK_RJ s^1/2$. For a typical map of at least 10 beams, with one hour of integration per beam, one can achieve the rms values of y_SZ ~ 7 10^-5 and the 3K background anisotropy Delta T/T ~ 7 10^-5, in winter conditions. We also report on a novel bolometer AC readout circuit which allows for the first time total power measurements on the sky. This technique alleviates (but does not forbid) the use of chopping with a secondary mirror. This technique and the dilution fridge concept will be used in future scan--modulated space instrument like the ESA Planck mission project.Comment: 10 pages, LaTeX, 12 figures, accepted for publication in Astronomy and Astrophysics Supplement Serie