Homogenization of two-phase flow: high contrast of phase permeabilityHomogénéisation d'écoulement diphasique : grand contraste de perméabilité d'une phase

The steady-state two-phase flow non-linear equation is considered in the case when one of phases has low effective permeability in some periodic set, while on the complementary set it is high; the second phase has no contrast of permeabilities in different zones. A homogenization procedure gives the homogenized model with macroscopic effective permeability of the second phase depending on the gradient and on the second order derivatives of the macroscopic pressure of the first phase. This effect cannot be obtained by classical (one small parameter) homogenization. To cite this article: G.P. Panasenko, G. Virnovsky, C. R. Mecanique 331 (2003).     

An approximate solution to the integral radiative transfer equation in an optically thick slab

We consider the problem of solving the integral form of the radiative transfer equation in an atmosphere with optical thickness τ₀?1. We propose two methods transforming this problem to a finite set of the independent problems of the same type set in an atmosphere with optical thickness much less then τ₀. The error estimates are derived. Copyright © 2007 John Wiley & Sons, Ltd.     

Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Synthesis of a new tricyclic 3-(tetrazol-5-yl)pyridine system from 2-(azidomethyl)nicotinonitriles

2-Methyl-3-cyanopyridines were converted into the corresponding 2-azidomethyl derivatives, which then underwent an intramolecular cycloaddition reaction. A novel heterocyclic system containing a 3-(tetrazol-5-yl)pyridine unit was obtained in this way.     

1, 5-Rearrangement of enol acylates of aryl 1H.-1, 2, 4-triazol-1-ylmethyl ketones

The rearrangement of enol acylates of aryl 1H-1, 2, 4-triazol-1-ylmethyl ketones at 140–150°C in acetic anhydride is studied. The migration of the acyl group to the C(5) atom of the heterocycle is found to be intramolecular. The characteristics of the original and final products are presented. X-ray structural studies of the enol acetates of 2, 4-dichlorophenyl 1H-1, 2, 4-triazol-1-ylmethyl ketone and 2, 4-dichlorophenyl 5-acetyl-1H-1, 2, 4-triazol-1-ylmethyl ketone are carried out.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 560–564, March, 1993.     

Towards supramolecular fixation of NOX gases: encapsulated reagents for nitrosation

The use of simple calix[4]arenes for chemical conversion of NO2/N2O4 gases is demonstrated in solution and in the solid state. Upon reacting with these gases, calixarenes 1 encapsulate nitrosonium (NO+) cations within their cavities with the formation of stable calixarene-NO+ complexes 2. These complexes act as encapsulated nitrosating reagents; cavity effects control their reactivity and selectivity. Complexes 2 were effectively used for nitrosation of secondary amides 5, including chiral derivatives. Unique size-shape selectivity was observed, allowing for exclusive nitrosation of less crowded N-Me amides 5 a-e (up to 95 % yields). Bulkier N-Alk (Alk>Me) substrates 5 did not react due to the hindered approach to the encapsulated NO+ reagents. Robust, silica gel based calixarene material 3 was prepared, which reversibly traps NO2/N2O4 with the formation of NO+-storing silica gel 4. With material 4, similar size-shape selectivity was observed for nitrosation. The N-Me-N-nitroso derivatives 6 d,e were obtained with approximately 30 % yields, while bulkier amides were nitrosated with much lower yields (<8 %). Enantiomerically pure encapsulating reagent 2 d was tested for nitrosation of racemic amide 5 t, showing modest but reproducible stereoselectivity and approximately 15 % ee. Given high affinity to NO+ species, which can be generated by a number of NOX gases, these supramolecular reagents and materials may be useful for NOX entrapment and separation in the environment and biomedical areas.     

1H and13C NMR spectra and structure of 2,3,4-trisubstituted sulfolanes

Conclusions The¹H and¹³C NMR spectra were studied for 2,3,4-trisubstituted sulfolanes and the isomerism of these compounds was determined, The use of chemical shift information is more convenient to determine the isomerism of polysubstituted cyclic compounds by PMR spectroscopy, while use of the direct carbon-proton coupling constants is more convenient for this problem when employing¹³C NMR spectroscopy.Deceased.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2498–2501, November 1984.     

Structural and mechanistic look at the orthoplatination of aryl oximes by dichlorobis(sulfoxide or sulfide)platinum(II) complexes

Structural and mechanistic aspects of orthoplatination of acetophenone and benzaldehyde oximes by the platinum(II) sulfoxide and sulfide complexes [PtCl(2)L(2)] (2, L = SOMe(2) (a), rac-SOMePh (b), R-SOMe(C(6)H(4)Me-4) (c), and SMe(2) (d)) to afford the corresponding platinacycles cis-(C,S)-[Pt(II)(C(6)H(3)-2-CR'=NOH-5-R)Cl(L)] (3, R, R' = H, Me) have been investigated. The reaction of acetophenone oxime with sulfoxide complex 2a in methanol solvent occurs noticeably faster than with sulfide complex 2d due to the fact that the sulfoxide is a much better platinum(II) leaving ligand than the sulfide. Evidence is presented that the orthoplatination is a multistep process. The formation of unreactive dichlorobis(N-oxime)platinum(II) cations accounts for the rate retardation by excess acetophenone oxime and suggests the importance of pseudocoordinatively unsaturated species for the C-H bond activation by Pt(II). A comparative X-ray structural study of dimethyl sulfoxide platinacycle 3b (R = R' = Me) and its sulfide analogue 3e (R = H, R' = Me), as well as of SOMePh complex 3c (R = H, R' = Me), indicated that they are structurally similar and a sulfur ligand is coordinated in the cis position with respect to the sigma-bound phenyl carbon. The differences concern the Pt-S bond distance, which is notably longer in the sulfide complex 3e (2.2677(11) A) as compared to that in sulfoxide complexes 3b (2.201(2)-2.215(2) A) and 3c (2.2196(12) A). Whereas the metal plane is practically a plane of symmetry in 3b due to the H-bonding between the sulfoxide oxygen and the proton at carbon ortho to the Pt-C bond, an S-bonded methyl of SOMePh and SMe(2) is basically in the platinum(II) plane in complexes 3c and 3e, respectively. There are intra- and intermolecular hydrogen bond networks in complex 3b. An interesting structural feature of complex 3c is that the two independent molecules in the asymmetric unit of the crystal reveal an extremely short Pt-Pt contact of 3.337 A.     

Supramolecular fixation of NO2 with calix[4]arenes

Reaction of NO2 with simple calix[4]arenes in chloroform in the presence of a Lewis acid rapidly results in intense coloration caused by the encapsulation of nitrosonium cation.