A minimal composite theory for stability of non-parallel compressible boundary-layer flow

A new minimal composite theory that extends the approach of Govindarajan and Narasimha [1] is proposed here for 2D non-parallel compressible boundary-layer stability subject to 3D disturbances. The mean profiles are obtained from Hortons analysis, which provides a good approximation for a large range of Prandtl numbers at non-zero pressure gradients. In the lowest order, all effects of order lower than O(R^-2/3) anywhere in the boundary-layer are included, R being the local boundary-layer Reynolds number; the resulting non-parallel formulation yields a set of four ordinary differential equations, as compared to the five coupled equations of classical parallel flow theory of Mack [2]. The largest effect on stability of flow non-parallelism is found to be due to the wall-normal advection of velocity and temperature disturbance quantities by the mean flow. The present theory shows that the bulk viscosity, invariably included in compressible stability theories, is irrelevant at the lowest order. In comparison with the full [O(R^-1)] non-parallel theory, the present theory is marginally better than the parallel flow theory. PACS 03.50.De, 04.20-q, 42.65-k     

Crystal structure refinement and bonding patterns of CrB4: a boron-rich boride with a framework of tetrahedrally coordinated B atoms

Crystals of chromium tetraboride, a recently proposed candidate superhard material, have been grown for the first time to allow for a first structure refinement of the compound [orthorhombic, space group Immm (No. 71), a = 474.82(8) pm, b = 548.56(8) pm, and c = 287.17(4) pm, R value (all data) = 0.018]. The previously proposed structure model is confirmed, and accurate interatomic distances are presented for the first time. First-principles electronic structure calculations emphasize the unique framework of three-dimensionally linked B atoms that are tetrahedrally coordinated and carry a slightly negative charge. All B-B bonding is of the 2-center 2-electron type. CrB(4) is metallic with a pseudogap at the Fermi level.     

Synthesis of benzo-furan derivatives-I Karanj ketone, karanjin and pongapin

A new method of preparing benzo-furan derivatives using substituted allyl phenols has been worked out. Ozonolysis of the allyl derivatives and subsequent ring closure of the resulting o-hydroxy-acetaldehydes by means of o-phosphoric acid give good yields of karanj ketone, karanjin, pongapin and the corresponding 2-methyl furanochromone. As an alternative route oxidation of the allyl phenol in two stages using performing acid followed by periodic acid has been successfully employed in the synthesis of karanjin.     

Asymmetric first-order Bragg interactions in an active dielectric waveguide

The asymmetric first-order Bragg interactions in an active planar dielectric waveguide are investigated for the case of even TE modes. Either the index or the gain is assumed to have a sinusoidal variation in the propagation direction. By a singular perturbation procedure using multiple space scales, the coupled-mode equations governing the nature of the Bragg interactions are systematically deduced and the characteristics of this instability are examined. For the gain-modulated waveguide having an average loss, there are two threshold values for the modulation index of the gain, one for absolute instability and the other for traveling wave amplification, and these threshold values are deduced. Representative numerical results are presented to illustrate the characteristics of the Bragg interactions.