Réduction a priori de modèles thermomécaniquesAn a priori model reduction method for thermomechanical problems

A model reduction method is proposed for finite element models. A previous computation of the state of the structure is not necessary. Residuals defined over the entire time interval and the Karhunen–Loève method provide basis functions. A non-incremental algorithm, from the LATIN method, is used to compute this basis functions. Because of the non-incremental feature, the reduced order model is representative for a large evolution of the state of the structure. To cite this article: D. Ryckelynck, C. R. Mecanique 330 (2002) 499–505.     

Excess Molar Volumes for Binary Mixtures of 1-Alkanol and 1-Alkene. II. The System 1-Alkanol + 1-Octene at 15 and 35°C

Excess molar volumes V ^E measured at 15 and 35°C for the (1-propanol + 1-octene), (1-butanol + 1-octene), (1-octanol + 1-octene), and (1-decanol + 1-decene) systems are reported. These data and the measurements reported before at 25°C for this series of mixtures were used to calculate the excess molar isobaric thermal expansion A _p ^E = ( V ^E/ T)_p at 25°C. In the above series of mixtures the A _p ^E values change from positive over the whole concentration range in the systems formed by 1-propanol and 1-butanol, to positive-negative for longer chain alkanols, the positive values occurring in the alkene-rich region. For systems characterized by the sigmoid shape, the positive region of A _p ^E values decreases with increasing length of the 1-alkanol molecule. The modified model of associated mixtures proposed by Treszczanowicz and Benson predicts qualitatively the changes in the shape of the A _p ^E curves. The model allows interpretation of the above results as a balance between the contributions due to self-association of alkanol, nonspecific interactions, and free volume.     

Ring expansion of a Cp moiety upon CO insertion: Synthesis and characterization of [(η-C6H5OCo)Co3(CO)9]

Reaction of [(CpV)₂(B₂H₆)₂], 1 (Cp = η⁵-C₅H₅) with four equivalents of [Co₂(CO)₈] or [Co₄(CO)₁₂] in hexane at 70 °C leads to the isolation of the tetranuclear carbonyl cluster, [(η⁶-C₆H₅OCo)Co₃(CO)₉], 2 in modest yield. The geometry of 2 is similar to that of [Co₄(CO)₁₂] where all the four Co atoms are arranged in a tetrahedral geometry. The apical cobalt atom in 2 is coordinated to C₆H₅O ring in a η⁶-fashion and the other three cobalt atoms are each coordinated to three carbonyl ligands. Compound 2 has been characterized in solution by IR, ¹H, ¹³C NMR and mass spectrometry and the structural types were unequivocally established by crystallographic analysis.     

A Copper–Formate Framework Showing a Simple to Helical Antiferroelectric Transition with Prominent Dielectric Anomalies and Anisotropic Thermal Expansion,and Antiferromagnetism

We present here the compound [NH₄][Cu(HCOO)₃], a new member of the [NH₄][M(HCOO)₃] family. The Jahn–Teller Cu²⁺ ion leads to a distorted 4⁹?6⁶ chiral Cu–formate framework. In the low‐temperature (LT) orthorhombic phase, the Cu²⁺ is in an elongated octahedron, and the ${{\rm NH}{{+\hfill \atop 4\hfill}}}$ ions in the framework channel are off the channel axis. From 94 to 350 K the ${{\rm NH}{{+\hfill \atop 4\hfill}}}$ ion gradually approaches the channel axis and the related modulation of the framework and the hydrogen‐bond system occurs. The LT phase is simple antiferroelectric (AFE). The material becomes hexagonal above 355 K. In the high‐temperature (HT) phase, the Cu²⁺ octahedron is compressed, and the ${{\rm NH}{{+\hfill \atop 4\hfill}}}$ ions are arranged helically along the channel axis. Therefore, the phase transition is one from LT simple AFE to HT helical AFE. The temperature‐dependent structure evolution is accompanied by significant thermal and dielectric anomalies and anisotropic thermal expansion, due to the different status of the ${{\rm NH}{{+\hfill \atop 4\hfill}}}$ ions and the framework modulations, and the structure–property relationship was established based on the extensive variable‐temperature single‐crystal structures. The material showed long range ordering of antiferromagnetism (AFM), with low dimensional character and a Néel temperature of 2.9 K. Therefore, within the material AFE and AFM orderings coexist in the low‐temperature region.     

Room Temperature Ring Expansion of N‐Heterocyclic Carbenes and BB Bond Cleavage of Diboron(4) Compounds

We report the isolation and detailed structural characterization, by solid‐state and solution NMR spectroscopy, of the neutral mono‐ and bis‐NHC adducts of bis(catecholato)diboron (B₂cat₂). The bis‐NHC adduct undergoes thermally induced rearrangement, forming a six‐membered ‐B?C?N?C?C‐N‐heterocyclic ring via C?N bond cleavage and ring expansion of the NHC, whereas the mono‐NHC adduct is stable. Bis(neopentylglycolato)diboron (B₂neop₂) is much more reactive than B₂cat₂ giving a ring expanded product at room temperature, demonstrating that ring expansion of NHCs can be a very facile process with significant implications for their use in catalysis.     

Thermal expansion of amorphous Zr Al Cu Ni in the vicinity of the glass transition

The thermal expansion of non-crystalline Zr₆₅Al_7.5Cu_17.5 Ni₁₀ has been studied in the range of the glass transition and in the undercooled liquid using a dilatometric device. The measuring technique used permits reliable experimental results up to 40 K above the glass transition temperature. The linear thermal expansion coefficient obtained is almost constant in the glassy state with a value of . It discontinuously increases at the glass transition temperature yielding a value of in the undercooled liquid. The results are compared with specific heat measurements of the amorphous material in this temperature range and are interpreted in the framework of a cluster model. Received 5 March 1999 and received in final form 11 June 1999     

High Péclet number heat exchange between cocurrent streams

Summary  This paper concentrates on the analysis of the heat transfer between two cocurrent laminar flows in parallel channels. For high values of the Péclet number Pe, a boundary layer arises near the wall separating the streams. Matched asymptotic expansions (MAE) are used to obtain approximate solutions. We consider arbitrary inlet temperatures and derive higher-order corrections of the boundary problem. The separating wall is supposed to be sufficiently thin to neglect the heat conduction in it. Analyticity and adiabatic conditions at the outer walls impose restrictions on the inlet temperatures. It turns out, however, that only the inlet temperatures at the wall separating the two fluids enter the leading-order problem. The Nusselt numbers thus calculated are in the leading order proportional to (Pe/x)^1/3, where x is the stream-wise coordinate. An estimate of the thickness of the separating wall to validate the MAE approach is obtained. It is also demonstrated that the MAE analysis is unable to describe the heat exchange of counterflowing fluids. Received 9 June 1999; accepted for publication 17 November 1999