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

Large-eddy simulation of the lid-driven cubic cavity flow by the spectral element method

This paper presents the large-eddy simulation of the lid-driven cubic cavity flow by the spectral element method (SEM) using the dynamic model. Two spectral filtering techniques suitable for these simulations have been implemented. Numerical results for Reynolds number $\text{Re}=12'000$ are showing very good agreement with other experimental and DNS results found in the literature

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 ≤

Unsymmetrical Triphenylamine-Oligothiophene Hybrid Conjugated Systems as Donor Materials for High-Voltage Solution-Processed Organic Solar Cells

The synthesis of unsymmetrical triphenylamine-oligothiophene hybrid conjugated systems bearing dicyanovinyl electron acceptor end-groups is presented. When used as molecular donor materials in solution-processed bulk heteroj­unction solar cells, these compounds lead to efficient devices with very high open-circuit voltages

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

Tristhienylphenylamine - extended dithiafulvene hybrids as bifunctional electroactive species

Extended hybrid conjugated systems based on a trithienylphenylamine core with 1, 2 and 3 peripheral dithiafulvenyl units have been synthesized and studied by cyclic voltammetry and UV-Vis. absorption spectroscopy. Theoretical calculations have also been undergone. The behaviour of these derivatives which depends on the number of dithiafulvene moieties grafted of the central core is cleared up. One polymer, obtained from derivative 3 presents polyelectrochromic properties

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

Segregated anatomical input to sub-regions of the rodent superior colliculus associated with approach and defense

The superior colliculus (SC) is responsible for sensorimotor transformations required to direct gaze toward or away from unexpected, biologically salient events. Significant changes in the external world are signaled to SC through primary multisensory afferents, spatially organized according to a retinotopic topography. For animals, where an unexpected event could indicate the presence of either predator or prey, early decisions to approach or avoid are particularly important. Rodents’ ecology dictates predators are most often detected initially as movements in upper visual field (mapped in medial SC), while appetitive stimuli are normally found in lower visual field (mapped in lateral SC). Our purpose was to exploit this functional segregation to reveal neural sites that can bias or modulate initial approach or avoidance responses. Small injections of Fluoro-Gold were made into medial or lateral sub-regions of intermediate and deep layers of SC (SCm/SCl). A remarkable segregation of input to these two functionally defined areas was found. (i) There were structures that projected only to SCm (e.g., specific cortical areas, lateral geniculate and suprageniculate thalamic nuclei, ventromedial and premammillary hypothalamic nuclei, and several brainstem areas) or SCl (e.g., primary somatosensory cortex representing upper body parts and vibrissae and parvicellular reticular nucleus in the brainstem). (ii) Other structures projected to both SCm and SCl but from topographically segregated populations of neurons (e.g., zona incerta and substantia nigra pars reticulata). (iii) There were a few brainstem areas in which retrogradely labeled neurons were spatially overlapping (e.g., pedunculopontine nucleus and locus coeruleus). These results indicate significantly more structures across the rat neuraxis are in a position to modulate defense responses evoked from SCm, and that neural mechanisms modulating SC-mediated defense or appetitive behavior are almost entirely segregated