A posteriori error analysis using the constitutive law for the Crouzeix–Raviart element

In this work, we study the error in the approximation of the solution of elliptic partial differential equations obtained with the nonconforming finite elements method; we adopt the error in a constitutive law approach.     

Statistical properties of turbidity, oxygen and pH fluctuations in the Seine river estuary (France)

We consider here, the fluctuations of turbidity, oxygen and pH time series recorded from the MAREL system (Ifremer, France), which is based on the deployment of data buoys equipped with water analysis capabilities in an automated mode. We perform a spectral analysis (from 10 min to years) of these time series, and we estimate their probability density functions. Oxygen, turbidity and pH are important quantities for ecosystem studies and physics-biology couplings, and their fluctuations reveal the possible influence of environmental factors such as tides and turbulence. Turbidity variability is highly complex and does not appear to be directly coupled to turbulence, since no clear range is visible. On the other hand, oxygen percentage of saturation and pH data show remarkably nice scaling ranges, indicating an important coupling with turbulence, but also biological or chemical activity, since the statistics differ markedly from passive scalars. Several possible sources of this variability are discussed.     

Upper Bound of the Constant in Strengthened C.B.S. Inequality for Systems of Linear Partial Differential Equations

The constant in the strengthened Cauchy–Bunyakowski–Schwarz (C.B.S.) inequality plays a crucial role in the convergence rate of multilevel iterative methods as well as in the efficiency of a posteriori error estimators, that is the framework of finite element approximations of systems of partial differential equations. We consider an approximation of general systems of linear partial differential equations in R ³. Concerning a multilevel convergence rate corresponding to nested general tetrahedral meshes of size h and 2h, we give an estimate of this constant for general three-dimensional cases.     

Diffusion of vanadium in GaAs

The diffusion of Vanadium has been studied in V-doped GaAs layers (GaAs:V) grown by Metal-Organic Chemical Vapour Deposition (MOCVD) using secondary ion mass spectroscopy (SIMS). The vanadium (V) concentration profiles of sandwiched structures made of alternatively undoped and V doped GaAs layers have shown a concentration independent diffusion coefficient (D_V) for varying V doping levels from 10¹⁸ to 10¹⁹ cm⁻³. Measurements of D_V at 550, 615 and 680 °C indicate that the temperature dependence of D_V can be represented by the Arrhenius equation:  cm² s⁻¹. It is suggested that V diffuses via interstitial sites.     

An atomistic level description of guest molecule effect on the formation of hydrate crystal nuclei by <Emphasis Type="Italic">ab initio</Emphasis> calculations

In the present study, we report the results of a systematic investigation of cage-like water structures using the first-principles calculations. These results show that, in the case of methane hydrate, the following nucleation mechanism can be revealed. The formation of small water cavities filled with methane is the first step of the formation of methane hydrate. It is not necessary to occupy all dodecahedral cages by guest molecules. After that small cavities start to form the H-bonding network with surrounding water molecules and a small number of water molecules is enough for the formation of a stable hydrogen-bonding network. The structural information contained in such nuclei is conserved in the forming crystal. Moreover, the presence of a methane molecule between small cages is also important to prevent the adhesion of cavities. It found that the ozone molecule can also stabilize the small cage since the value of the interaction energy between the ozone guest and the water host framework is very close to that obtained for the methane case. However, ozone affects the structure of large cavities and hence, the second guest is necessary to stabilize the hydrate structure.     

A posteriori error estimates for subgrid viscosity stabilized approximations of convection–diffusion equations

We derive a posteriori error estimates for subgrid viscosity stabilized finite element approximations of convection–diffusion equations in the high Péclet number regime. Two estimators are analyzed: an asymptotically robust one and a fully robust one with respect to the Péclet number. Numerical results on test cases with boundary layers or internal layers show that the asymptotically robust estimator can be used to construct adaptive meshes.     

Miscibility and Thermal Behaviour of Poly(styrene-co-itaconic acid)/Poly(butyl methacrylate-co-4-vinylpyridine) Mixtures. Accessibility and Self-Association Effects

Summary: The miscibility and thermal behaviour of binary mixtures of poly(styrene-co-itaconic acid) containing 11 or 27 mol % of itaconic acid (PSIA-11 or PSIA27) with poly(butyl methacrylate) (PBMA)or poly(butyl methacrylate-co-4-vinylpyridine) containing 10 or 26 mol% of 4-vinylpyridine (PBM4VP-10, PBM4V-P26) were investigated by differential scanning calorimetry, scanning electron microscopy, FTIR spectroscopy and thermogravimetry. The results showed that 11 mol % of itaconic acid and 10 mol % of 4-vinylpyridine respectively introduced within the polystyrene and poly(butyl methacrylate) matrices induced the miscibility of this pair of polymers due to specific interactions of hydrogen bonding type with partial pyridine protonation that occurred between the two copolymers as evidenced by FTIR from the appearance of two new bands at 1607 cm⁻¹ and 1640 cm⁻¹. Increasing itaconic acid content from 11 to 27 mol % led to a decrease of the intensity of the specific interactions within PSIA-27/PBM4VP blends and is attributed to both accessibility and self association effects as evidenced by DSC from the change of the shape of the Tg- composition curves and by FTIR spectroscopy. As shown from the thermogravimetric study, the presence of these specific interactions delayed the anhydride formation and improved the thermal stability of the blends.     

The Hermitian Jacobi Process: A Simplified Formula for the Moments and Application to Optical Fiber MIMO Channels

Functional Analysis and Its Applications - Using a change of basis in the algebra of symmetric functions, we compute the moments of the Hermitian Jacobi process. After a careful arrangement of...