Bridging techniques in a multi-scale modeling of pattern formation

Bridging techniques between microscopic and macroscopic models are discussed in the case of wrinkling analysis. The considered macroscopic models are related to envelope equations of Ginzburg–Landau type, but generally, they are not valid up to the boundary. To this end, a multi-scale approach is considered: the reduced model is implemented in the bulk while the full model is applied near the boundary and these two models are coupled with the Arlequin method (Ben Dhia, 1998). This paper focuses on the definition of the coupling model and the transition between two scales. Especially, a new nonlocal bridging technique is presented and compared with another recent one (Hu et al., 2011). The present method can also be seen as a guide for coupling techniques involving other reduced order models.     

The Role of Hydrogen Bonding and Halogen Bonding in the Polymorphic Structures of 3,5-Dibromo-2,6-diaminopyridinium Bromide

Abstract  

An analysis is made of the supramolecular interactions in the two polymorphic structures of 3,5-dibromo-2,6-diaminopyridinium bromide, with particular emphasis on the roles of hydrogen and halogen bonding. Because of the extensive hydrogen bonding capabilities, hydrogen bonding interactions dominate in both phases. This causes a competition between C–Br···Br–C and C–Br···Br⁻ halogen bonding interactions, with the former dominating in the orthorhombic Pbca phase and the latter in the monoclinic P2₁/c phase. For Pbca phase a = 5.5197(11) ?, b = 15.040(3) ?, c = 23.2555(5) ?, and for P2₁/c phase a = 8.1143(19) ?, b = 14.226(3) ?, c = 8.9005(18) ?, β = 113.18(2)°.     

Estimation and tests of independence in copula models via divergences

We introduce new estimates and tests of independence in copula models with unknown margins using ?-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior point or not. To cite this article: S. Bouzebda, A. Keziou, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Synthesis of pyrazole‐fused azepino[5,4,3‐cd]indoles

The synthesis of some new pyrazolo[3′,4′:6,7]azepino[5,4,3‐cd] indoles (10a‐c) was achieved via regios‐elective cyclization of the respective 3‐(4‐acylaminopyrazol‐5‐yl)indoles (9a‐c) under Bischler‐Napieralski reaction conditions. The latter compounds were obtained by acylation of the corresponding 3‐(4‐aminopyra‐zol‐5‐yl)indoles (8a,b) which, in turn, were prepared by reduction of the 3‐(4‐nitropyrazol‐5‐yl)indoles precursors (7a,b) . The latter synthons were accessible from the reaction of indolylzinc chlorides (5a,b) with 5‐chloro‐1,3‐dimethyl‐4‐nitropyrazole. Ms and nmr spectral data of 10a‐c are in agreement with the assigned azepino‐indole structure as determined for 10a by X‐ray crystal measurements which demonstrate that the azepine ring is almost completely planar with the indole and pyrazole rings.     

Synthesis of heterocyclic and carbocyclic fluoro-olefins by ring-closing metathesis

[reaction: see text] Ring-closing metathesis (RCM) of vinyl fluoride-containing dienes in the presence of ruthenium alkylidene carbene complex 11 proceeded efficiently to give six- and seven-membered cyclic vinyl fluorides. The RCM reaction was used to prepare amine- and sulfamide-linked cyclo-olefins, as well as carbocyclic systems, from a simple commercial fluoro-olefin.     

Characteristics of GaSb growth using various gallium and antimony precursors

We report the epitaxial growth of GaSb using trimethylgallium (TMGa) or triethylgallium (TEGa) with trimethylantimony (TMSb), triethylantimony (TESb), or trisdimethylaminoantimony (TDMASb) in a low-pressure vertical rotating-disk reactor. Growth is kinetically limited for TMGa in the temperature range 560 to 640°C, and is mass-transport limited for TEGa in the range 525 to 640°C. A minimum V/III ratio is necessary to obtain stoichiometric GaSb, and is dependent on the pyrolysis temperature of Ga and Sb precursors. Featureless morphology is achieved for layers grown with TMGa or TEGa and TMSb, while surface defects are observed for layers grown with TEGa and TESb or TDMASb. These observations are consistent with Fourier transform infrared measurements, which indicate interactions between TEGa and TESb or TDMASb. All nominally undoped layers are p-type, with overall superior properties being obtained for layers grown with TEGa and TMSb. However, growth conditions that yield layers with the best electrical properties do not necessarily correspond to the same conditions for highest optical quality.