Hydrodynamic stability of the spherical front of a reaction accompanied by a strong increase in viscosity

The hydrodynamic stability of the steady spherical front of a reaction accompanied by a strong increase in viscosity taking place in a radial, centrally symmetric flow of condensed reaction medium is considered. The flow is assumed to be bounded by two permeable concentric spherical surfaces. The stability is investigated in the linear approximation with respect to small perturbations. A relation is obtained for the dependence of the perturbation growth rate on the parameters of the problem: the viscosity ratio of the medium at the front, the ratio of the boundary surface radii to the radius of the front, and the dimensionless hydrodynamic resistances of the boundary surfaces. It is shown that the front is stable over almost the entire physical region of variation of the parameters and that instability occurs only in the case of a low hydrodynamic resistance of the outer boundary surface as the front approaches.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 46–53, May–June, 1988.     

Benchmark solutions for the incompressible Navier–Stokes equations in general co-ordinates on staggered grids

Benchmark problems are solved with the steady incompressible Navier–Stokes equations discretized with a finite volume method in general curvilinear co-ordinates on a staggered grid. The problems solved are skewed driven cavity problems, recently proposed as non-orthogonal grid benchmark problems. The system of discretized equations is solved efficiently with a non-linear multigrid algorithm, in which a robust line smoother is implemented. Furthermore, another benchmark problem is introduced and solved in which a 90° change in grid line direction occurs.     

Silyl modification of biologically active compounds. 12. Silyl group as true incentive to antitumour and antibacterial action of choline and colamine analogues

A series of triorganylsilyl(β‐dialkylaminoethoxy)silanes was prepared and characterized by elemental analysis, ¹H, ¹³C, ²⁹Si NMR and mass spectroscopy. Comparative study of ²⁹Si resonance of newly synthesized compounds showed correlation between its value and substituent nature at the silicon atom, and is shifted upfield for β‐triorganyl(N,N‐dialkylaminoethoxy)silanes in comparison with corresponding methiodides, revealing weak N^…Si interaction for proper silanes. In vitro antitumour and antimicrobial properties were investigated. The biological activity data exhibited a marked enhancement of inhibitory activity on trialkylsilylation against tumour cell lines and all the test bacterial/fungal strains. Copyright © 2006 John Wiley & Sons, Ltd.     

Theoretical calculation of the potential curves of the states of HF below 14 eV

Potential energy curves obtained through extensive ab initio configuration interaction calculations are reported for the states of HF below 14 eV as well as that for the ground state of HF⁺. Agreement with ultraviolet absorption data is obtained to within 0.2 eV. The disagreement between the reported UV absorption and electron scattering data is examined.     

Variations on polynomial subgroup growth

A groupG hasweak polynomial subgroup growth (wPSG) of degree ≤α if each finite quotient Ḡ ofG contains at most │Ḡ│ ^a subgroups. The main result is that wPSG of degree α implies polynomial subgroup growth (PSG) of degree at mostf(α). It follows that wPSG is equivalent to PSG. A corollary is that if, in a profinite groupG, thek-generator subgroups have positive “density” δ, thenG is finitely generated (the number of generators being bounded by a function ofk and δ).