An asymptotic behavior and a posteriori error estimates for the generalized Schwartz method of advection-diffusion equation

In this paper, a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are proved by using the Euler time scheme combined with Galerkin spatial method. Furthermore, an asymptotic behavior in Sobolev norm is deduced using Benssoussan-Lions' algorithm. Finally, the results of some numerical experiments are presented to support the theory.     

Autotandem Catalysis: Inexpensive and Green Access to Functionalized Ketones by Intermolecular Iron-Catalyzed Amidoalkynylation/Hydration Cascade Reaction via N-Acyliminium Ion Chemistry

Iron-based catalysts were applied in cascade-type reactions for the synthesis of different carbonyl compounds. The reactions proceeded by a new iron-catalyzed cascade of alkynylation/hydration by using both the σ- and π-Lewis acid properties of iron salts. The alkynylation reactions of several endo and exocyclic acetoxylactams were achieved with three different catalysts including FeCl₃ ⋅ 6H₂O, FeCl₃, and Fe(OTf)₃ showing the efficiency of σ-Lewis acidity of iron (III) salts in catalyzing the alkynylation reaction. We also demonstrated that the reaction sequence could be shortened by the direct use of hydroxylactams, leading to an environmentally friendly protocol, avoiding the need to perform unnecessary lengthy steps. A combination of the hard/soft iron Lewis acid properties was then used to implement an unprecedented tandem intermolecular alkynylation/intramolecular hydration sequence allowing expedient access to a new carbonyl structures from trivial materials.     

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).     

Experimental quantification of natural convective heat transfer within annulus space filled with a H2O-Cu nanofluid saturated porous medium. Application to electronics cooling

This experimental study deals with cooling electronics contained in a hemispherical cavity whose cupola is maintained isothermal, being its base inclined at an angle varying from 0° (horizontal disc with the cupola oriented upwards) to 135°. The active component is a dome centered on this base. The space between the differentially heated elements of the assembly is filled with a porous medium of high porosity saturated by a water–copper nanofluid whose volume fraction varies between 0% (pure water) and 7%. The Rayleigh number based on the radius of the cupola reaches high values up to 7.29 × 10¹⁰ given the important surface heat flux generated by the device during operation. The ratio between the thermal conductivity of the solid matrix and that of the base fluid ranges between 0 (interstitial volume without porous medium) and 41.4 corresponding to the intended applications. This experimental study done with an industrial prototype at scale 1 quantifies the natural convective heat transfer via the Nusselt number determined for many configurations obtained by varying the solid-fluid thermal conductivity ratio, the inclination angle, the Rayleigh number, and the volume fraction. The study clearly shows that the cooling performance of the Cu-H₂O nanofluid degrades with its age and the number of times it has been used. Analysis of the results reproducibility also proves the irreversibility of the performance. The measured values were compared with those obtained in a recent numerical study based on the volume control method. The observed deviations taking into account the experimental uncertainty margins validate the mathematical model implemented in the numerical approach.     

Experimental confirmation of Kelvin's equilibria

We experimentally corroborate the core analytical deductions of Thomson's 124-year-old theorem, vis-à-vis the stability of a ring of N vortices. Observations made in water vortices produced inside a cylinder via a revolving disk confirm that the regular N-gons are stable for Nor=8. The N相似文献   

Design and characterization of new advanced energetic biopolymers based on surface functionalized cellulosic materials

A new class of energetic biopolymers, which contain nitrate ester (O-NO₂) and nitramine (N-NO₂) as explosophoric groups, was successfully synthesized by surface modification of renewable pristine cellulose (PC) and microcrystalline cellulose (MCC) via epichlorohydrin-mediated amination followed by nitration process to produce new promising energetic aminated and nitrated cellulose and microcrystalline cellulose (APCN and AMCCN). Their structural, thermal, crystallinity and morphological features were examined and compared to those of the common cellulose nitrate. Furthermore, their energetic performances were evaluated by EXPLO5 V6.04 software. Experimental results confirm the successful chemical functionalization process to develop insensitive APCN and AMCCN with outstanding features such as nitrogen content of 15.01% and 15.39%, density of 1.692 g/cm³ and 1.708 g/cm³, and detonation velocity of 7526 m/s and 7752 m/s, respectively, which are significantly higher than those of the nitrated unmodified cellulosic biopolymers. The present investigation provides a suitable pathway to design new insensitive and energy-rich dense cellulosic biopolymers for potential application in high-performance solid propellants and composite explosives.

     

‐error estimates of discontinuous Galerkin methods with theta time discretization scheme for an evolutionary HJB equations

The main purpose of this paper is to analyze the convergence and regularity of our proposed algorithm of the finite element methods coupled with a theta time discretization scheme for evolutionary Hamilton‐Jacobi‐Bellman equations with linear source terms with respect to the Dirichlet boundary conditions (Appl. Math. Comput., 262 (2015), 42.55 ). Also, an optimal error estimate with an asymptotic behavior in uniform norm is given. Copyright © 2017 John Wiley & Sons, Ltd.     

Oxidative Addition of Carbon–Carbon Bonds to Gold

The oxidative addition of strained C? C bonds (biphenylene, benzocyclobutenone) to DPCb (diphosphino‐carborane) gold(I) complexes is reported. The resulting cationic organogold(III) complexes have been isolated and fully characterized. Experimental conditions can be adjusted to obtain selectively acyl gold(III) complexes resulting from oxidative addition of either the C(aryl)? C(O) or C(alkyl)? C(O) bond of benzocyclobutenone. DFT calculations provide mechanistic insight into this unprecedented transformation.     

Transtaganolides A-D: novel metabolites from Thapsia transtagana

Four novel and unusual C-19 compounds from Thapsia transtagana, named transtaganolides A-D, have been isolated. Their structures were established by physical methods, including X-ray analysis of transtaganolides A and B. This is the first time that a 7-methoxy-4,5-dihydro-3H-oxepin-2-one ring has been found in a natural product. [structure: see text]     

Thermal design of a spherical electronic device naturally cooled by means of water–copper nanofluid saturated porous media

Journal of Thermal Analysis and Calorimetry - The present work deals with thermal regulation of a spherical electronic device used in naval navigation techniques. Cooling is achieved by means of...