Hydrodynamical limit for a drift-diffusion system modeling large-population dynamics

In this paper we study the stability of the following nonlinear drift-diffusion system modeling large population dynamics ∂_tρ+div(ρU−ε∇ρ)=0, divU=±ρ, with respect to the viscosity parameter ε. The sign in the second equation depends on the attractive or repulsive character of the field U. A proof of the compactness and convergence properties in the vanishing viscosity regime is given. The lack of compactness in the attractive case is caused by the blow-up of the solution which depends on the mass and on the space dimension. Our stability result is connected, depending of the character of the potentials, with models in semiconductor theory or in biological population.     

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Two modifications of a five‐coordinate silicon complex

TBPY‐5‐34‐(Butane‐1,4‐diyl)(2‐{[1‐(2‐oxidophenyl)ethylidene‐κO]amino‐κN}ethanolato‐κO)silicon, C₁₄H₁₉NO₂Si, crystallizes in two modifications. The monoclinic form, (IIm), was obtained by crystallization over a period of 2 d at room temperature; the orthorhombic form, (IIo), crystallized overnight at 248 K. The main difference between the two molecular structures involves the angles in the equatorial plane of the trigonal bipyramid around silicon. Form (IIm) has an O—Si—O angle of ca 121° and O—Si—C angles of ca 121 and 116°. In form (IIo), the corresponding angles are ∼123, 124 and 111°. There are also significant differences in the packing: (IIm) shows π stacking, whereas (IIo) does not.     

Conductance in homomorphous solvents: Tetrabutylammonium salts and alkali picrates in butyrolactone-sulfolane mixtures

Conductance measurements are reported for LiPi, NaPi, KPi, RbPi, CsPi, Bu₄NPi, Bu₄NBr, Bu₄NClO₄, Bu₄NNO₃, and Bu₄NBBu₄ at 25°C in -butyrolactone-sulfolane mixtures. In these mixtures of solvents that are practically homomorphous, isodielectic and with comparable dipole moments, the ion pair association and ionic mobilities of large ions conform to the expectations of the primitive model. Electrolytes containing lithium or sodium ions show anomalies indicating that other factors besides shape, dipole moment, and polarizability of the solvent molecules are involved in the association and transport processes of these ions.     

Quecksilber(II)‐chlorid‐ und ‐iodid‐Komplexe von Dithia‐ und Tetrathiakronenethern

Mercury(II) Chloride and Iodide Complexes of Dithia‐ and Tetrathiacrown Ethers The complexes [(HgCl₂)₂((ch)₂30S₄O₆)] ( 1 ), [HgCl₂(mn21S₂O₅)] ( 2 ), [HgCl₂(ch18S₂O₄)] ( 3 ) and [HgI(meb12S₂O₂)]₂[Hg₂I₆] ( 4 ) have been synthesized, characterized and their crystal structures were determined. In [(HgCl₂)₂((ch)₂30S₄O₆)] two HgCl₂ units are discretely bonded within the ligand cavity of the 30‐membered dichinoxaline‐tetrathia‐30‐crown‐10 ((ch)₂30S₄O₆) forming a binuclear complex. HgCl₂ forms 1 : 1 “in‐cavity” complexes with the 21‐membered maleonitrile‐dithia‐21‐crown‐7 (mn21S₂O₅) ligand and the 18‐membered chinoxaline‐dithia‐18‐crown‐6 (ch18S₂O₄) ligand, respectively. The 12‐membered 4‐methyl‐benzo‐dithia‐12‐crown‐4 (meb12S₂O₂) ligand gave with two equivalents HgI₂ the compound [HgI(meb12S₂O₂)]₂[Hg₂I₆]. In the cation [HgI(meb12S₂O₂)]⁺ meb12S₂O₂ forms with the cation HgI⁺ a half‐sandwich complex.     

On the reactivity of benzidinesulfonic acids and their applications in analysis: Reaction of cupric salts with o-benzidinemonosulfonic acid in presence of alkali thiocyanate

In the present work a new method for the detection of coppcr(II) is described. It is based on the reaction of this ion with the alkali salts of o-benzidinemonosulfonic acid, alkali thiocyanate being present. The sensitivity of this test is $\text{1}\text{500,000}$ (l0^-5.7); it ia specific for the Cu⁺² ion and can also be used to distinguish quickly the above-mentioned acid from the benzidine o-o'-disulfonic and benzidine m-m' '-disulfonic acids. It is believed that the mechanism of the reaction can be explained by an oxidation process.     

New [Mo(eta3-allyl)(CO)2L3]+ complexes with monodentate or tridentate nitrogen-donor ligands

Cationic complexes [Mo(eta(3)-allyl)(CO)2L3]+ (L3 = either nitrogen-donor tridentate ligand or three monodentate ligands) were prepared in high yield and under mild conditions using as precursors either the triflato complex [Mo(eta(3)-allyl)(OTf)(CO)2(NCMe)2] or the combination of the chloro complex [Mo(eta(3)-allyl)Cl(CO)2(NCMe)2] and the salt NaBAr'(4)(Ar'= 3,5-bis(trifluoromethyl)phenyl). The tridentate ligands employed were 2,2':6',2'-terpyridine (terpy) and cis,cis-1,3,5-cyclohexanetriamine (CHTA), whereas the monodentate ligands imidazole (im) and 3,5-dimethylpyrazole (dmpz) were chosen. In order to stabilize the labile intermediates, an excess of acetonitrile was used in most of the syntheses. However, the pyrazole complex was prepared through a nitrile-free route to avoid reactions at the coordinated nitrile. The solid state structures of [Mo(eta(3)-methallyl)(CO)2(terpy)]OTf (2), [Mo(eta(3)-methallyl)(CO)2(CHTA)]BAr'4 (3), [Mo(eta(3)-methallyl)(CO)2(NCMe)3]BAr'4 (4), [Mo(eta(3)-allyl)(CO)2(im)3]OTf (5) and [Mo(eta(3)-allyl)(CO)2(dmpz)3]BAr'4 (6) were determined by means of single-crystal X-ray diffraction.