Homogenized model of reaction–diffusion in a porous mediumUn modèle homogénéisé de réaction–diffusion dans un milieu poreux

We study the initial boundary value problem for the reaction–diffusion equation,

$\text{?}{}_{\mathrm{t}}\text{u}{}^{\mathrm{\epsilon }}\text{??·(a}{}^{\mathrm{\epsilon }}\text{?u}{}^{\mathrm{\epsilon }}\text{)+g(u}{}^{\mathrm{\epsilon }}\text{)=h}{}^{\mathrm{\epsilon }}$

in a bounded domain $\text{Ω}$ with periodic microstructure $\text{F}{}^{\mathrm{(\epsilon )}}\text{∪}\text{M}{}^{\mathrm{(\epsilon )}}$, where a^ε(x) is of order 1 in $\text{F}{}^{\mathrm{(\epsilon )}}$ and κ(ε) in $\text{M}{}^{\mathrm{(\epsilon )}}$ with κ(ε)→0 as ε→0. Combining the method of two-scale convergence and the variational homogenization we obtain effective models which depend on the parameter θ=lim_ε→0κ(ε)/ε². In the case of strictly positive finite θ the effective problem is nonlocal in time that corresponds to the memory effect. To cite this article: L. Pankratov et al., C. R. Mecanique 331 (2003).     

A novel implicit method for coastal hydrodynamics modeling: application to the Arcachon lagoon

The present Note reports on numerical modeling of shallow flows in coastal areas. Successful numerical simulations of such flows should be able to cope with strong irregularities of the bathymetry and to reproduce the covering/uncovering (wetting/drying) of tidal flats due to the tidal oscillations of the free surface. Also, adoption of large time steps is necessary to simulate phenomena which last actually several days or months. In the present study, a new numerical model based on an implicit resolution of the shallow water equations is proposed. A penalty method has been employed for numerical treatment of dry zones emerging during the wetting and drying processes. The capability of the present model has been verified by comparison with standard test cases. Further applications and comparisons have been also carried out to simulate the tidal propagation in the Arcachon lagoon. To cite this article: A. Le Dissez et al., C. R. Mecanique 333 (2005).     

Processus de réorientation des variantes de martensite dans un monocristal de Cu–Al–NiReorientation process of martensite variants in a Cu–Al–Ni monocrystal

On the one hand, Chu (Thesis, Minnesota, 1993), Abeyaratne et al. (Philos. Mag. A 73 (2) (1996) 457–497) performed biaxial tensile tests on a single crystal Cu–Al–Ni plate, in order to analyze the reorientation process of martensite variants.On the other hand, use is made of a constitutive model with n+1 internal variables (the volume fractions of austenite and of the n martensite variants) specific to the thermomechanical behavior of SMA single crystals in order to simulate the martensite variant reorientation.The comparison between experimental results and model prediction is fairly good. To cite this article: P. Blanc, C. Lexcellent, C. R. Mecanique 331 (2003).     

煤层倾角与覆岩变形破裂分带

地下采煤中三带(冒落带、裂隙带、弯曲带)高度的判断是预测采空引起地表变形破坏程度的依据。在诸多的影响因素中, 煤层倾角是控制“三带”高度的最主要因素。建立在实测统计基础上的经验范围值用于“三带”高度的判断带有一定的人为性。急倾斜煤层中冒落带和裂隙带高度随煤层倾角变化的规律已被褐示[7].通过弹塑性岩石材料的非线性有限元模拟, 本文提出了利用应力重分布图判断中、缓倾角煤层采空区覆岩“三带”高度的方法, 并应用于实际工程。     

Phenomenological nonlinear modelling of glassy polymers

Compared with the numerous works into the constitutive equations for the mechanical behaviour of metals, very little attention has been devoted to those of polymers. However, a model is required to describe both the complex shape of the stress–strain curves and strain rate sensitivity of glassy polymers. In this Note, a unified viscoelastic-viscoplastic model is presented in which the nonlinear pre-yield behaviour, the strain softening and the strain hardening are described by internal variables, in analogy with the models developed for metals. In order to check the predictive capability of the model, the numerical results are compared with the experimental data (monotone, creep and relaxation tests) of a typical amorphous glassy polymer. To cite this article: F. Zaïri et al., C. R. Mecanique 333 (2005).     

Un algorithme efficace d'intégration plastique pour un matériau obéissant au critère anisotrope de HillAn efficient algorithm for plastic integration of material satisfying the Hill's anisotropic yield criterion.

This Note deals with an efficient algorithm to carry out the plastic integration and compute the stresses due to large strains for materials satisfying the Hill's anisotropic yield criterion. The classical algorithm of plastic integration such as ‘Return Mapping Method’ is largely used for nonlinear analyses of structures and numerical simulations of forming processes, but it requires an iterative schema and may have convergence problems. A new direct algorithm based on a scalar method is developed which allows us to directly obtain the plastic multiplier without an iteration procedure; thus the computation time is largely reduced and the numerical problems are avoided. To cite this article: I. Titeux et al., C. R. Mecanique 332 (2004).     

Large Eddy Simulation of Premixed Turbulent Combustion Using Ξ Flame Surface Wrinkling Model

One commonly-used method for deriving the RANS equations for multicomponent flow is the technique of conditional averaging. In this paper the concept is extended to LES, by introducing the operations of conditional filtering and surface filtering. Properties of the filtered indicator function are investigated mathematically and computationally. These techniques are then used to derive conditionally filtered versions of the Navier–Stokes equations which are appropriate for simulating multicomponent flow in LES. Transport equations for the favre-averaged indicator function and the unresolved interface properties (the wrinkling and the surface area per unit volume) are also derived. Since the paper is directed towards modelling premixed combustion in the flamelet regime, closure of the equations is achieved by introducing physical models based on the picture of the flame as a wrinkled surface separating burnt and unburnt components of the fluid. This leads to a set of models for premixed turbulent combustion of varying complexity. The results of applying one of this set of models to propagation of a spherical flame in isotropic homogeneous turbulence are analysed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bisimido Molybdenum Complexes of the Extremely Bulky Pr* Framework

Synthesis and characterization of molybdenum bisimido complexes featuring the extremely bulky Pr* framework [Pr* = 2,6‐bis(diphenylmethyl)‐4‐methylphenyl] are reported. The octahedral halide complex [Mo(NPr*)₂Cl₂(THF)₂] ( 1 ) is readily available from ammonium dimolybdate and the amine Pr*NH₂, and features two THF molecules in the coordination sphere of molybdenum. The chloride ligands in 1 may be exchanged with methyl or benzyl groups using Grignard reagents. The resulting complexes [Mo(NPr*)₂Me₂] ( 2 ) and [Mo(NPr*)₂Bz₂] ( 3 ) are monomeric and, in contrast to 1 , do not coordinate further neutral two‐electron donor ligands in neither the solid state nor in solution.     

雷诺实验的计算机仿真模拟

雷诺实验是学生学习流体理论、判定流型必不可少的实验。为了促进实验教学,用Lab VIEW等制作雷诺实验仿真模拟软件,改善教学条件,提高实验效果和学生动手及计算机应用能力。通过对开发软件的应用,强化了学生的实验技能训练,很好地辅助了教学,并收到良好的教学效果。     

On-line preconcentration of weak electrolytes by electrokinetic accumulation in CE: experiment and simulation

A new on-line preconcentration technique was developed that makes possible to determine nanomolar concentrations of weak acidic analytes in CE. The method consists of long-running electrokinetic sample injection and stacking (electrokinetic immobilization) of the analytes at a boundary of two electrolytes with different pH values (pH 9.5 and 2.5) and consequent mobilization of the stacked uncharged analytes in a micellar system (containing SDS micelles). Several factors including buffer concentration, pH, applied voltage, time of preconcentration, and SDS concentration were tested to optimize the analysis method. An about 4600-fold increase of the sample concentration (in comparison with the standard CZE) can be achieved during the preconcentration step. Two preservatives applied in food industry -- benzoic acid and sorbic acid were used as model samples. The applicability of the proposed method in food analysis was demonstrated by determination of nanomolar concentrations of benzoic acid in sunflower oil. An extended version of the computer program Simul was used for modeling both the preconcentration and mobilization processes taking place in the capillary.