Application of the wavelet transform for a channel flow in a mixed convection phenomenon

The aim of this paper is to investigate laminar-turbulent transition in a mixed convection phenomenon occurring in a horizontal rectangular duct. Indeed, laminar-turbulent transition is well known in the case of forced convection but the presence of secondary flow induced by natural convection on this transition is not well highlighted. In this study, we will not be concerned by determining a critical threshold value of a Reynolds number of transition but only to estimate the degree of turbulence in the transition regime, i.e. weak turbulence in the case of a mixed convection phenomenon. This is possible thanks to the application of the wavelet transform. The calculation of the Hölder exponent, associated with the maximum value of the singularity spectrum for various experimental conditions allows the degree of turbulence to be measured. The variation of the Hölder exponent versus heat flux and Reynolds number enables us to show that there are two ways to go towards turbulence: thermal by increasing heat flux and hydrodynamic by increasing fluid velocity.     

A posteriori error estimation for the Stokes–Darcy coupled problem on anisotropic discretization

This paper presents an a posteriori error analysis for the stationary Stokes–Darcy coupled problem approximated by finite element methods on anisotropic meshes in or 3. Korn's inequality for piecewise linear vector fields on anisotropic meshes is established and is applied to non‐conforming finite element method. Then the existence and uniqueness of the approximation solution are deduced for non‐conforming case. With the obtained finite element solutions, the error estimators are constructed and based on the residual of model equations plus the stabilization terms. The lower error bound is proved by means of bubble functions and the corresponding anisotropic inverse inequalities. In order to prove the upper error bound, it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration. To measure this correspondence, a so‐called matching function is defined, and its discussion shows it to be useful tool. With its help, the upper error bound is shown by means of the corresponding anisotropic interpolation estimates and a special Helmholtz decomposition in both media. Copyright © 2016 John Wiley & Sons, Ltd.     

Sur la compacité des multimesures (I)On compactness of set-valued measures (I)

Let $\text{M}{}_{\mathrm{+}}\text{(T,}\text{K}\text{,}\text{ck}\text{(E))}$ be the space of positive $\text{K}$-regular set-valued measures defined on a σ-algebra $\text{B}$ with values in the space of all compact non empty convex subsets of a Banach space E. We characterize the compact subsets of $\text{M}{}_{\mathrm{+}}\text{(T,}\text{K}\text{,}\text{ck}\text{(E))}$ endowed with the weakest topology for which all mappings M→M(A), $\text{A∈}\text{B}$ are continuous. The case of real nonnegative measures has been investigated by Topsøe [6], Grothendieck [3] and others. To cite this article: K.K. Siggini, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 949–952.     

A linear backward Euler scheme for the saturation equation: Regularity results and consistency

We consider a linearization of a numerical scheme for the saturation equation (or porous medium equation) , through first order expansions of the fractional function f and the inverse of the function , after a regularization of the porous medium equation. We establish a regularity result for the Continuous Galerkin Method and a regularity result for the linearized scheme analogous to the corresponding nonlinear scheme. We then show that the linearized scheme is consistent with the nonlinear scheme analyzed in a previous work.     

Enzymatic membranes for the selective transport of neutral molecules by electrophoresis

The active and selective transport of glucose and glycerol was carried out using electrophoresis and artificial enzymatic membranes. These positively charged composite membranes carry, on the face adjacent to the donor compartment of an electrophoresis module, a specific kinase (hexokinase or glycerokinase) and, on the opposite face, an alkaline phosphatase (ALP). Phosphorylation of the neutral substrate (glucose or glycerol) on the donor side by the kinase generates a negatively charged phosphorylated substrate, whose transmembrane migration is promoted by an electric field and by the membrane's positive charge. Dephosphorylation of the phosphorylated substrate by ALP on the opposite face regenerates the neutral substrate, which accumulates in the receiver compartment of the electrophoresis module. Using an electrophoresis module specifically designed for this study, our experiments were carried out enabling glucose and glycerol to be concentrated approximately eight- and twelve-fold, respectively, in 8 h.     

Synthesis,Single Crystal Growth and Crystal Structure of Ta7Cu10Ga34 – a 8 × 4 × 2 Super Structure of CsCl

Single crystals of Ta₇Cu₁₀Ga₃₄ were grown from the elements in a Cu/Ga melt. Ta₇Cu₁₀Ga₃₄ represents the first ternary compound of the system Ta/Cu/Ga. The crystal structure (Cmmm, oC102, Z = 2, a = 23.803(1), b = 12.2087(4), c = 5.7487(2) Å, 1291 refl. 78 parameters, R₁ = 0.037, wR₂ = 0.070). The crystal structure is characterized by rods of pentagonal prisms MGa₁₀, which are alternatingly occupied by Ta and Cu. Four of these rods are connected to columns running in direction (001). These columns are linked by cubic units TaGa₈, CuGa₈, and GaGa₈. According to the characteristic structural elements and the size of the unit cell Ta₇Cu₁₀Ga₃₄ represents a 8 × 4 × 2 super structure of CsCl or bcc. With respect to the underlying CsCl structure the formula can be written as [Ta₇Cu₁₀Ga₂□₁₃]Ga₃₂, i.e. a cubic primitive packing of 32 Ga atoms with Ta, Cu, and Ga in cubic voids and 13 vacancies. The pentagonal‐prismatic coordination of Ta and Cu can formally be obtained from the cubic primitive packing of Ga atoms by a 45° rotation of a part of the Ga₈ cubes. There is a close similarity to the binary compounds Ta₈Ga₄₁ and Ta_2–xGa_5+x. The first one is also related to a CsCl‐like structure, the latter one contains rods of pentagonal prisms, which form the same columns. There are also relations to the ternaries V₂Cu₃Ga₈ and V₁₁Cu₉Ga₄₆, whose cubic structures are more or less complex variants of CsCl.     

Contact analysis in the presence of an ellipsoidal inhomogeneity within a half space

Many materials contain inhomogeneities or inclusions that may greatly affect their mechanical properties. Such inhomogeneities are for example encountered in the case of composite materials or materials containing precipitates. This paper presents an analysis of contact pressure and subsurface stress field for contact problems in the presence of anisotropic elastic inhomogeneities of ellipsoidal shape. Accounting for any orientation and material properties of the inhomogeneities are the major novelties of this work. The semi-analytical method proposed to solve the contact problem is based on Eshelby’s formalism and uses 2D and 3D Fast Fourier Transforms to speed up the computation. The time and memory necessary are greatly reduced in comparison with the classical finite element method. The model can be seen as an enrichment technique where the enrichment fields from the heterogeneous solution are superimposed to the homogeneous problem. The definition of complex geometries made by combination of inclusions can easily be achieved. A parametric analysis on the effect of elastic properties and geometrical features of the inhomogeneity (size, depth and orientation) is proposed. The model allows to obtain the contact pressure distribution – disturbed by the presence of inhomogeneities – as well as subsurface and matrix/inhomogeneity interface stresses. It is shown that the presence of an inclusion below the contact surface affects significantly the contact pressure and subsurfaces stress distributions when located at a depth lower than 0.7 times the contact radius. The anisotropy directions and material data are also key elements that strongly affect the elastic contact solution. In the case of normal contact between a spherical indenter and an elastic half space containing a single inhomogeneity whose center is located straight below the contact center, the normal stress at the inhomogeneity/matrix interface is mostly compressive. Finally when the axes of the ellipsoidal inclusion do not coincide with the contact problem axes, the pressure distribution is not symmetrical.     

On existence and uniqueness for a coupled system modeling immiscible flow through a porous medium

We consider a system of nonlinear coupled partial differential equations that models immiscible two-phase flow through a porous medium. A primary difficulty with this problem is its degenerate nature. Under reasonable assumptions on the data, and for appropriate boundary and initial conditions, we prove the existence of a weak solution to the problem, in a certain sense, using a compactness argument. This is accomplished by regularizing the problem and proving that the regularized problem has a unique solution which is bounded independently of the regularization parameter. We also establish a priori estimates for uniqueness of a solution.