Surface-tension-driven instabilities of a pure liquid layer evaporating into an inert gas

A theoretical model of the evaporation of a pure liquid layer is developed. We focus on the influence of an inert gaseous component, in addition to vapor, on surface-tension-driven Bénard instabilities. It is assumed that the gas phase is perfectly mixed at some distance from the liquid-gas interface (given composition, pressure, and temperature). If this distance is not much larger than the liquid layer thickness, it is shown that a reduction of the full two-layer problem to a one-layer problem is possible, provided the evaporation rate is not too large. An analytical expression is given for the corresponding dimensionless heat transfer coefficient (a generalized, wavenumber-dependent Biot number) at the evaporating interface. The approach is validated through a comparison with a direct numerical resolution of the full two-layer problem.     

An improved procedure for the conversion of indolines into indoles

The addition of a sacrificial enamine (such as indole), or of a vinyl ether (like dihydropyran) to an indoline during dehydrogenation by phenylseleninic anhydride dramatically improves the yield of the corresponding indole. This is due to scavenging of Se¹¹ phenylselenenating species.     

Favorskii-Reaktion von enolisierbaren Cyclobutanonen: Abhängigkeit der Stereoselektivität von der Abgangsgruppe,der Temperatur und dem Lösungsmittel

Dependence of the Stereoselectivity on the Leaving Group, the Temperature and the Solvent in the Favorskii-Reaction of Enolisable Cyclobutanones The base-induced contraction of enolisable 2-halocyclobutanones is often not stereoselectiv. The cis/trans-isomer ratio in the cyclopropanecarboxylic acid 9 derived from 2,4-cis-substituted cyclobutanones 7 depends on the nature of the leaving group. In addition, the choice of the base, the temperature and the solvent can profoundly affect the stereoselectivity of the Favorskii-reaction. The use of the p-bromophenylsulphonyloxy group as leaving group and an inhomogenous reaction medium leads exclusively to cis-carboxylic acid 9 .     

Crystal growth and electrical properties of lithium,rubidium, and cesium molybdenum oxide bronzes

Crystals of Li_0.33 MoO₃ (blue), Rb_0.23MoO₃ (blue) and Cs_0.31MoO₃ (red) were grown by electrolysis from MoO₃M₂MoO₄ melts (M =alkali metal) with composition 70–77 mole% MoO₃. Melts richer in M₂MoO₄ produced MoO₂ only. Correlation is made between bronze formation and the coordination of Mo in the melt and in the equilibrium solid phase M₂Mo₄O₁₃. Li_0.33MoO₃ and Cs_0.31MoO₃ are semiconductors with high-temperature-range activation energies 0.16 and 0.12 eV. Rb_0.23MoO₃ has an electrical behavior similar to that of blue K_xMoO₃ with a semiconductor-metal transition at (170 ± 5) K. ESR spectra observed in Li_0.33MoO₃ and Rb_0.23MoO₃ single crystals at 4.2 K show extensive delocalization of the 4d¹ electron associated with Mo(V) centers. Attempts to grow molybdenum bronzes containing Ca or Y were unsuccessful.     

Face Selectivity of the Diels-Alder Reaction of 5,6-Bis((D)methylidene)-2-bicyclo[2.2.2]octene

The face selectivity (endo-face vs. exo-face attack onto the exocyclic s-cis-butadiene moiety) of the [4+2]cycloadditions of 5,6-bis((D)methylidene)-2-bicyclo-[2.2.2]octene ( 11 ) to strong dienophiles has been determined in benzene at 25°. It is ca. 95/5, 75/5, 70/30, 60/40 and 50/50 for N-phenyltriazolinedione (NPTAD), tetracyanoethylene (TCE), dimethyl acetylenedicarboxylate (DMAD), maleic anhydride (MA) and singlet oxygen (¹O₂), respectively. The endo-face preference is probably due to a participation of the homoconjugated double bond at C(2), C(3) which makes the etheno bridge more polarizable than the ethano bridge in 11. The absence of face selectivity with ¹O₂ is consistent with an entropy-controlled mechanism involving the intermediacy of an exciplex.     

Mise en evidence de la formation de R2MMR2 a partir de disila-1,2 et digerma-1,2 cyclohexenes-4

Intermediates with π-bonded Si or Ge are generated during gas phase pyrolysis of 1,2-disila- or 1,2-digerma-cyclohex-4-enes.Compounds such as R₂MMR₂ are successfully trapped by addition or [2 + 2] and [4 + 2] cycloadditions. These results were proved by mass spectrometry.     

Study of the ternary system FeCrTe around the composition FeCr2Te4

The system FeCrTe was investigated around the composition FeCr₂Te₄. FeCr₂Te₄ is a metastable compound. Single crystals with Fe_0·93Cr_1·76Te₄ composition were grown by vapor transport or the Bridgman method. These crystals are metallic and anisotropic ferromagnets.     

Independence versus indetermination: basis of two canonical clustering criteria

Advances in Data Analysis and Classification - This paper aims at comparing two coupling approaches as basic layers for building clustering criteria, suited for modularizing and clustering very...     

Gibbs states of the Hopfield model with extensively many patterns

We consider the Hopfield model withM(N)=N patterns, whereN is the number of neurons. We show that if is sufficiently small and the temperature sufficiently low, then there exist disjoint Gibbs states for each of the stored patterns, almost surely with respect to the distribution of the random patterns. This solves a provlem left open in previous work. The key new ingredient is a self-averaging result on the free energy functional. This result has considerable additional interest and some consequences are discussed. A similar result for the free energy of the Sherrington-Kirkpatrick model is also given.