BRST Resolution for the Principally Graded Wakimoto Module of $$\widehat{\mathfrak{s}\mathfrak{l}}_2 $$

BRST resolution is studied for the principally graded Wakimoto module of recently found in math.QA/0005203. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group.     

Anharmonic properties of rocksalt structure solids

An effort has been made for obtaining the anharmonic properties of rocksalt structure solids starting from primary physical parameters viz. nearest-neighbor distance and hardness parameter assuming long- and short-range potentials at elevated temperatures. The elastic energy density for a deformed crystal can be expanded as power series of strains for obtaining coefficients of quadratic, cubic and quartic terms which are known as the second-, third- and fourth-order elastic constants, respectively. When the values of the higher-order elastic constants are known for a crystal, many of the anharmonic properties of the crystal can be treated within the limit of the continuum approximation in a quantitative manner. In this study, higher-order elastic constants are computed up to their melting temperature for rocksalt structure solids, which are alkali cyanides, sodium and potassium halides. The first order pressure derivatives of second- and third-order elastic constants, the second-order pressure derivatives of second-order elastic constants and partial contractions are also evaluated at different temperatures for these substances. The results thus obtained are compared with experimental data and found in well agreement with present values.     

Synthesis and crystal structure of [Re2Cl2(CO)6(S e)]

The dinuclear complex [Re₂Cl₂(CO)₆S e] has been prepared and characterized in the solid state by X-ray crystallography. Proton NMR spectroscopy has shown the structure to be stereochemically rigid in solution.     

Flow past a cylinder: shear layer instability and drag crisis

Flow past a circular cylinder for Re=100 to 10⁷ is studied numerically by solving the unsteady incompressible two‐dimensional Navier–Stokes equations via a stabilized finite element formulation. It is well known that beyond Re ～ 200 the flow develops significant three‐dimensional features. Therefore, two‐dimensional computations are expected to fall well short of predicting the flow accurately at high Re. It is fairly well accepted that the shear layer instability is primarily a two‐dimensional phenomenon. The frequency of the shear layer vortices, from the present computations, agree quite well with the Re^0.67 variation observed by other researchers from experimental measurements. The main objective of this paper is to investigate a possible relationship between the drag crisis (sudden loss of drag at Re ～ 2 × 10⁵) and the instability of the separated shear layer. As Re is increased the transition point of shear layer, beyond which it is unstable, moves upstream. At the critical Reynolds number the transition point is located very close to the point of flow separation. As a result, the shear layer eddies cause mixing of the flow in the boundary layer. This energizes the boundary layer and leads to its reattachment. The delay in flow separation is associated with narrowing of wake, increase in Reynolds shear stress near the shoulder of the cylinder and a significant reduction in the drag and base suction coefficients. The spatial and temporal power spectra for the kinetic energy of the Re=10⁶ flow are computed. As in two‐dimensional isotropic turbulence, E(k) varies as k^?5/3 for wavenumbers higher than energy injection scale and as k^?3 for lower wavenumbers. The present computations suggest that the shear layer vortices play a major role in the transition of boundary layer from laminar to turbulent state. Copyright © 2004 John Wiley & Sons, Ltd.     

Sedimentation analysis of organic–inorganic hybrid colloids

Hybrid organic–inorganic latex particles are synthesized to combine the beneficial properties of the constituents which thus lead to synergistic improvement in the properties. The properties of hybrid particles are dependent on the successful hybridization process, thus controlling or tuning of such processes by effective characterization is immensely important. Analytical ultracentrifugation provides these characterization possibilities owing to its high statistical capability and ability to characterize multiple parameters. The use of different detection methodologies can help in generating valuable information on the overall size and density distributions of the particles. Apart from that, it is also possible to quantify the presence of any free polymer and inorganic particles in the hybrid latex which would affect the properties of hybrid latexes. By following the densities of the pure and hybrid particles, it is also possible to quantify the amounts of the constituent phases in the hybrid particles. The density gradients generated in preparative ultracentrifugation also provide additional possibilities for the characterization of the hybrid particles which have densities higher than the measurable range in the analytical ultracentrifuge. Evolution of hybrid particles can also be studied as a function of time. It also provides advantage of separation of the various fractions for further characterization.     

Document control: status of calibration/test certificate

The ISO/IEC 17025 standard requires that all documents that form part of the management system of the organization must be controlled. However, as customary, the certificates issued from testing or calibration laboratories do no bear any unique identity mark/number similar to other documents to announce control over the document. This leaves enough room for doubt to many in treating this document at par with other management system documentation. Some auditors had raised this question during accreditation visits.     

A High-Order Immersed Boundary Method for Acoustic Wave Scattering and Low-Mach Number Flow-Induced Sound in Complex Geometries

A new sharp-interface immersed boundary method based approach for the computation of low-Mach number flow-induced sound around complex geometries is described. The underlying approach is based on a hydrodynamic/acoustic splitting technique where the incompressible flow is first computed using a second-order accurate immersed boundary solver. This is followed by the computation of sound using the linearized perturbed compressible equations (LPCE). The primary contribution of the current work is the development of a versatile, high-order accurate immersed boundary method for solving the LPCE in complex domains. This new method applies the boundary condition on the immersed boundary to a high-order by combining the ghost-cell approach with a weighted least-squares error method based on a high-order approximating polynomial. The method is validated for canonical acoustic wave scattering and flow-induced noise problems. Applications of this technique to relatively complex cases of practical interest are also presented.