Spectral discretization of Darcy’s equations with pressure dependent porosity

We consider the flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with boundary conditions on the pressure around a circular well. When the boundary pressure presents high variations, the permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a spectral discretization of the resulting system of equations which takes into account the axisymmetry of the domain and of the flow. We prove optimal error estimates and present some numerical experiments which confirm the interest of the discretization.     

Spectral discretization of the vorticity, velocity and pressure formulation of the Navier–Stokes equations

We consider the Navier–Stokes equations in a two- or three-dimensional domain provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns, the vorticity, the velocity and the pressure, and prove the existence of a solution for this problem. Next we propose a discretization by spectral methods which relies on this formulation. In the two-dimensional case, we prove quasi-optimal error estimates for the three unknowns. We conclude with some numerical experiments.

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Résumé Nous considérons les équations de Navier–Stokes dans un domaine biou tri-dimensionnel, munies de conditions aux limites non usuelles portant sur la composante normale de la vitesse et la ou les composantes tangentielles du tourbillon. Nous écrivons une formulation variationnelle de ce problème qui comporte trois inconnues indépendantes: le tourbillon, la vitesse et la pression. Nous prouvons que ce problème admet au moins une solution. Nous proposons une discrétisation par méthodes spectrales construite à partir de cette formulation. Dans le cas bidimensionnel, nous établissons des majorations quasi-optimales de l'erreur pour les trois inconnues. Nous concluons par quelques expériences numériques.

     

Monomiale Ideale und mengentheoretische vollständige Durchschnitte

Ohne Zusammenfassung     

Fast and accurate algorithm for cavities reconstruction in an elasticity problem

The aim of this work is to reconstruct the location and geometry of a cavity embedded in a linear isotropic material Ω via an exterior boundary measurement of the displacement field. The considered problem is governed by the linear elasticity system. This inverse problem of geometry reconstruction (ie, location and shape) is formulated as a topology optimization one and solved by minimizing a Kohn‐Vogelius type functional with the help of the topological sensitivity method. Some numerical results are presented using a noniterative geometric algorithm.     

Local order in aqueous NaCl solutions and pure water: X-ray scattering and molecular dynamics simulations study

The microstructures of pure water and aqueous NaCl solutions over a wide range of salt concentrations (0-4 m) under ambient conditions are characterized by X-ray scattering and molecular dynamics (MD) simulations. MD simulations are performed with the rigid SPC water model as a solvent, while the ions are treated as charged Lennard-Jones particles. Simulated data show that the first peaks in the O...O and O...H pair correlation functions clearly decrease in height with increasing salt concentration. Simultaneously, the location of the second O...O peak, the signature of the so-called tetrahedral structure of water, gradually disappears. Consequently, the degree of hydrogen bonding in liquid water decreases when compared to pure fluid. MD results also show that the hydration number around the cation decreases as the salt concentration increases, which is most likely because some water molecules in the first hydration shell are occasionally substituted by chlorine. In addition, the fraction of contact ion pairs increases and that of solvent-separated ion pairs decreases. Experimental data are analyzed to deduce the structure factors and the pair correlation functions of each system. X-ray results clearly show a perturbation of the association structure of the solvent and highlight the appearance of new interactions between ions and water. A model of intermolecular arrangement via MD results is then proposed to describe the local order in each system, as deduced from X-ray scattering data.     

Ring extensions with some finiteness conditions on the set of intermediate rings

A ring extension R ⊆ S is said to be FO if it has only finitely many intermediate rings. R ⊆ S is said to be FC if each chain of distinct intermediate rings in this extension is finite. We establish several necessary and sufficient conditions for the ring extension R ⊆ S to be FO or FC together with several other finiteness conditions on the set of intermediate rings. As a corollary we show that each integrally closed ring extension with finite length chains of intermediate rings is necessarily a normal pair with only finitely many intermediate rings. We also obtain as a corollary several new and old characterizations of Prüfer and integral domains satisfying the corresponding finiteness conditions.     

Investigation of the electrical properties of a new PPV derivative-based on a sandwich structure for opto-electronic applications

The opto-electronic properties of native poly(p-phenylene vinylene) (PPV) were tuned by the confinement of the π-conjugation and the incorporation of a sulphur group as a spacer in order to obtain a blue-green emitting polymer (PPVS). The energy band gap of the PPVS thin film has been measured by UV-vis absorption spectroscopy and evaluated to 2.87 eV. Current-voltage characteristics and impedance spectroscopy measurements performed on sandwich structures [ITO/PPVS/Al] are used to elucidate the conduction mechanisms. The static electrical characterisations showed a space charge limited conduction (SCLC) and a conductivity with low power frequency behaviour characteristic of a hopping transport in disordered materials. The impedance spectra can be discussed in terms of an equivalent circuit model designed as a parallel resistor R_P and capacitor C_P network in series with a resistor R_S. We extract numerical values of these parameters by fitting experimental data. Their evolution with bias voltages has shown that the SCLC mechanism is characterised by an exponential trap distribution.     

Selective Detection of Dopamine in Presence of Ascorbic Acid by Use of Glassy‐Carbon Electrode Modified with Amino‐β‐Cyclodextrin and Carbon Nanotubes

A glassy carbon electrode modified with per‐6‐amino‐β‐cyclodextrin (β‐CDNH₂) and functionalized single‐walled carbon nanotubes (SWCNT‐COOH) was elaborated. This structure was investigated for the detection of dopamine acid (DA) in presence of ascorbic acid (AA). The sensor behavior was studied by cyclic voltammetry, square wave voltammetry and electrochemical impedance spectroscopy. The analysis results show that the electrode modification with CD derivative improves the sensitivity and selectivity of the DA recognition; the electrochemical response was further improved by introduction of SWCNT‐COOH. The sensor shows good and reversible linear response toward DA within the concentration range of 7×10^?7–10^?4 M with a detection limit of 5×10^?7 M.