Anisotropic mesh adaptation: towards user‐independent,mesh‐independent and solver‐independent CFD. Part I: general principles

The present paper is the lead article in a three‐part series on anisotropic mesh adaptation and its applications to structured and unstructured meshes. A flexible approach is proposed and tested on two‐dimensional, inviscid and viscous, finite volume and finite element flow solvers, over a wide range of speeds. The directional properties of an interpolation‐based error estimate, extracted from the Hessian of the solution, are used to control the size and orientation of mesh edges. The approach is encapsulated into an edge‐based anisotropic mesh optimization methodology (MOM), which uses a judicious sequence of four local operations: refinement, coarsening, edge swapping and point movement, to equi‐distribute the error estimate along all edges, without any recourse to remeshing. The mesh adaptation convergence of the MOM loop is carefully studied for a wide variety of test cases. The mesh optimization generic coupling of MOM with finite volume and finite element flow solvers is shown to yield the same final mesh no matter what the starting point is. It is also shown that on such optimized meshes, the need for computational fluid dynamics (CFD) stabilization artifices, such as upwinding or artificial viscosity, are drastically reduced, if not altogether eliminated, in most well‐posed formulations. These two conclusions can be considered significant steps towards mesh‐independent and solver‐independent CFD. The structure of the three‐part series is thus, 1, general principles; 2, methodology and applications to structured and unstructured grids; 3, applications to three‐dimensional flows. Copyright © 2000 John Wiley & Sons, Ltd.     

Stereochemistry of two new polyfunctionalized gem‐dihalo­cyclo­propanes

The two new gem‐dihalogeno­cyclo­propanes (1′S,3R)‐3‐(2′,2′‐di­chloro‐1′‐methyl­cyclo­propyl)‐6‐oxoheptanoic acid, C₁₁H₁₆­Cl₂O₃, (2), and (1′S,3R)‐3‐(2′,2′‐di­bromo‐1′‐methyl­cyclo­propyl)‐6‐oxoheptanoic acid, C₁₁H₁₆Br₂O₃, (3), are isostructural. Both present two stereogenic centers at C1′ and C3. The absolute configuration was determined by X‐ray methods. The cyclo­propyl rings are unsymmetrical, the shortest bond being distal with respect to the alkyl‐substituted C atom.     

Catalytic oxidation of α-pinene by transition metal using t-butyl hydroperoxide and hydrogen peroxide

The allylic oxidation of α-pinene 1 was investigated using various catalytic systems. By a proper choice of the latter, the reaction can be directed toward the selective synthesis of verbenol 2 or verbenone 3. High yield into verbenone was achieved under mild conditions with copper salts as catalysts and t-butyl hydroperoxide (TBHP) as oxidant. On the other hand, when Pd(acac)₂ was used with hydrogen peroxide, verbenol was obtained as the main product.     

Microtubule‐Binding R3 Fragment from Tau Self‐Assembles into Giant Multistranded Amyloid Ribbons

Tau protein and its fragments self‐assemble into amyloid fibrils in the presence of polyanions, such as heparin. By combining microscopy, scattering, and spectroscopy techniques, we studied the aggregation of the 26‐mer Tau‐derived peptide alone, Tau_306–327, the third repeat fragment (R3) of the microtubule‐binding domain. We show that: i) the sole Tau_306–327 can self‐assemble into amyloid fibrils without the need of aggregation‐promoting polyanions; ii) the resulting structures consist of surprisingly large, well‐ordered 2D laminated flat ribbons, with a log‐normal distribution of the lateral width, reaching the unprecedented lateral size of 350 nm and/or 45 individual protofilaments, that is, the largest amyloid laminated structures ever observed for Tau or any other amyloidogenic sequence. Our results provide insight into the molecular determinants of Tau aggregation and open new perspectives in the understanding of the assembly of amyloid fibrils and β‐sheet‐based biomaterials.     

Pricing Occupation-Time Options in a Mixed-Exponential Jump-Diffusion Model

In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of intervals.     

Convergence in law for certain additive functionals of symmetric stable processes under strong topology

We give some limit theorems of certain additive functionals for symmetric stable process of index $1<\alpha ?2$ in anisotropic Besov space. These results generalize those obtained by Eisenbaum (1997) and by Csaki et al. (2002). To cite this article: M. Ait Ouahra, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Preferential oxidation of CO in H2 over highly loaded Au/ZrO2 catalysts obtained by direct oxidation of bulk alloy

The intimate mixture of a skeletal gold structure with ZrO2 nanoparticles obtained simply by oxidation of Au(0.5)Zr(0.5) alloy at room temperature turns out to be an efficient catalyst for the selective oxidation of CO in the presence of hydrogen.     

Cationic dyes adsorption onto high surface area ‘almond shell’ activated carbon: Kinetics,equilibrium isotherms and surface statistical modeling

Almond shell agricultural biomass was used to prepare high surface area activated carbon using potassium hydroxide as activating agent. The activated carbon (AC) was characterized using X-Ray photoelectron spectroscopy, X-Ray diffraction, Thermogravimetric and differential thermal analyses, Scanning electron microscopy, Fourier transform infrared, Brunauer–Emmett–Teller surface area and Raman spectroscopy. The AC was found to have a high surface area of 2054 m² g^?1. The influence of various key parameters was evaluated on the adsorption process including contact time, adsorbent dose and solution pH. Isotherm data were modeled using Langmuir and Freundlich models. Langmuir isotherm model presented the best fit to experimental data suggesting homogeneous distribution of adsorption sites. The adsorbent demonstrated high monolayer adsorption capacity of 833.33 and 625.0 mg/g for Methylene Blue and Crystal Violet, respectively. The efficiency of the adsorption process was linked to the micro-mesoporous structure and to the availability of the surface adsorption sites. Response surface methodology was used to optimize the removal efficiency from aqueous solution.