Well-posedness and general decay for Moore–Gibson–Thompson equation in viscoelasticity with delay term

Ricerche di Matematica - The problem of Moore–Gibson–Thompson equation with infinite memory and time delay terms is considered. Under suitable Lyapunov functionals with an appropriate...     

Structure and intercalation behavior of copper II on the layered sodium silicate magadiite material

In this work, the ion-exchange reaction of the sodium silicate Na-magadiite with cupric ions was studied and the mode of interaction of the intercalated Cu²⁺ ions with silicate sheet was investigated. To do this, Na-magadiite was first synthesized using a hydrothermal method and characterized. It is then used to prepare Cu-exchanged magadiite materials with different copper contents by an ion-exchange reaction. The solids obtained were characterized by chemical and thermogravimetric analyses, powder X-ray diffraction, UV–Visible diffuse reflectance and Fourier transform spectroscopy, scanning electron microscopy and transmission electron microscopy. The results show that magadiite has a high affinity to copper ions and that the experimental exchange rate can be easily predicted. They show also that the intercalated Cu²⁺ ions are non-hydrated and are in direct interactions with the terminal interlayer ≡Si–O^? groups, to which they are also probably strongly linked. Furthermore, the interlayer copper oxide species phase formed are in form of small particles homogeneously dispersed. Finally, the introduction of Cu²⁺ ions into the interlayer space does not substantially affect the structure of the Cu-exchanged materials but rather tends to stabilize it by increasing the decomposition temperature of the silanol groups .     

Second-order boundary value problems with integral boundary conditions

In this paper we investigate the existence of positive solutions of nonlocal second-order boundary value problems with integral boundary conditions.     

A dynamic model for milk fouling in a plate heat exchanger

A two-dimensional dynamic fouling model for milk fouling in a plate heat exchanger (PHE) is proposed. Emphasis is placed on fouling prediction based on the hydrodynamic and thermodynamic performances of the PHE. A 12-channel PHE with counter-current flows is used in quantification of the milk deposition developed inside the channels. The aggregation rate of unfolded protein is found to increase exponentially with increasing wall temperature and is accompanied by a substantial reduction in the heat-transfer coefficient.     

Structural and electron charge density studies of a nonlinear optical compound 4,4 di-methyl amino cyano biphenyl

The 4,4 dimethyl amino cyano biphenyl crystal(DMACB) is characterized by its nonlinear activity. The intra molecular charge transfer of this molecule results mainly from the electronic transmission of the electro-acceptor(cyano) and electro-donor(di-methyl-amino) groups. An accurate electron density distribution around the molecule has been calculated based on a high-resolution X-ray diffraction study. The data were collected at 123 K using graphite-monochromated Mo Kα radiation to sin(θ)/λ = 1.24 A 1. The integrated intensities of 13796 reflections were measured and reduced to 6501 independent reflections with I ≥ 3σ(I). The crystal structure was refined using the experimental model of Hansen and Coppens(1978). The crystal structure has been validated and deposited at the Cambridge Crystallographic Data Centre with the deposition number CCDC 876507. In this article, we present the thermal motion and the structural analysis obtained from the least-square refinement based on F2 and the electron density distribution obtained from the multipolar model.     

Curious congruences related to the Bell polynomials

In this paper we give some congruences on the r-derangement polynomials (defined below), Lah polynomials and some versions of Bell numbers and polynomials.     

Asymptotic expansions of the eigenvalues of a 2-D boundary-value problem relative to two cavities linked by a hole of small size

This Note presents the derivation of the 2nd-order asymptotic expansion of the eigenvalues and the eigenfunctions of the operator associated to an interior elliptic equation supplemented by a Dirichlet boundary condition on a domain consisting of two cavities linked by a hole of small size. The asymptotic expansion is carried out with respect to the size of the hole. The main feature of the method is to yield a robust numerical procedure making it possible to compute the eigenvalues without resorting to a refined mesh around the hole. To cite this article: A. Bendali et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Quasi-cyclic codes as codes over rings of matrices

Quasi-cyclic codes over a finite field are viewed as cyclic codes over a noncommutative ring of matrices over a finite field. This point of view permits to generalize some known results about linear recurring sequences and to propose a new construction of some quasi-cyclic codes and self-dual codes.     

Influence of Vertical Vibrations on the Stability of a Binary Mixture in a Horizontal Porous Layer Subjected to a Vertical Heat Flux

Macroscale three-dimensional modeling of fluid flow in a thin porous layer under unsaturated conditions is a challenging task. One major issue is that such layers do not satisfy the representative elementary volume length-scale requirement. Recently, a new approach, called reduced continua model (RCM), has been developed to describe multiphase fluid flow in a stack of thin porous layers. In that approach, flow equations are formulated in terms of thickness-averaged variables and properties. In this work, we have performed a set of experiments, where a wet \(260\hbox {-}\upmu \hbox {m}\)-thin porous layer was placed on top of a dry layer of the same material. We measured the change of average saturation with time using a single-sided low-field nuclear magnetic resonance device known as NMR-MOUSE. We have employed both RCM and the traditional Richards equation-based models to simulate our experimental results. We found that the traditional unsaturated flow model cannot simulate experimental results satisfactorily. Very close agreement was obtained by including the dynamic capillary term as postulated by Hassanizadeh and Gray in the traditional equations. The reduced continua model was found to be in good agreement with the experimental result without adding dynamic capillarity term. Moreover, the computational effort needed for RCM simulations was one order of magnitude less than that of traditional models.     

Adsorption behavior of water and xylene isomers on AlPO-5 zeolite modified by different transition metals

Research on Chemical Intermediates - This work deals with the preparation of MAPO-5 zeolite by a hydrothermal method. In order to study the adsorption properties of this zeolite several transition...