Aspects of the transpiration model for aerofoil design

Transpiration is a technique in which extra non-physical normal flows are created on an aerofoil surface in order to form a new streamline pattern such that the surface streamlines no longer follow the aerofoil surface under inviscid flow. The transpiration model is an important technique adopted in aerofoil design either to avoid mesh regeneration when aerofoil profile co-ordinates are adjusted or to find shape corrections in inverse design methods. A first-order approximation (with respect to the normal streamline displacement) to the transpiration model is commonly adopted; it is shown that this can be a poor approximation especially in regions of high curvature. In this paper more accurate approximations are developed to address this problem and improve the accuracy.     

Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations

Summary. We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier-Stokes equations. With a combination of analytic and empirical results, we study the effects of fundamental parameters on convergence. We demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. The structure of these distributions is independent of the discretization mesh size, but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller. These characteristics are directly correlated with the convergence properties of iterative solvers. Received August 5, 2000 / Published online June 20, 2001     

Advances in the chemical synthesis of brassinosteroids

This review generalizes the latest advances in the chemical synthesis of the plant growth regulators brassinosteroids in 1990–1994.Institute of Bioorganic Chemistry, Belarus Academy of Sciences, 220141, Minsk, ul. Zhodinskaya, 5/2. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 507–544, July–August, 1997.     

Characterization of high-order harmonic radiation on femtosecond and attosecond time scales

We characterize the temporal structure of high-order harmonic radiation on both the femtosecond and attosecond time scales. The harmonic emission is characterized by mixed-color two-photon ionization with an infrared femtosecond laser using a Mach–Zehnder interferometer where both pump and probe arms travel completely separate paths. In a first experiment, we measure the duration and chirp of individual harmonics. In a second experiment, we resolve, for the first time with this type of setup, the attosecond beating of several harmonics generated under conditions similar to the first experiment. We suggest that the results of both measurements can be combined to determine the full attosecond time structure of the harmonic emission. PACS 32.80.Rm; 42.65.Ky     

Elevation of the glass transition temperature in flexible‐chain semicrystalline polymers

In the idealized two‐phase model of a semicrystalline polymer, the amorphous intercrystalline layers are considered to have the same properties as the fully‐amorphous polymer. In reality, these thin intercrystalline layers can be substantially influenced by the presence of the crystals, as individual polymer molecules traverse both crystalline and amorphous phases. In polymers with rigid backbone units, such as poly(etheretherketone), PEEK, previous work has shown this coupling to be particularly severe; the glass transition temperature (T_g) can be elevated by tens of degrees celsius, with the magnitude of the elevation correlating directly with the thinness of the amorphous layer. However, this connection has not been explored for flexible‐chain polymers, such as those formed from vinyl‐type monomers. Here, we examine T_g in both isotactic polystyrene (iPS) and syndiotactic polystyrene (sPS), crystallized under conditions that produce a range of amorphous layer thicknesses. T_g is indeed shown to be elevated relative to fully‐amorphous iPS and sPS, by an amount that correlates with the thinness of the amorphous layer; the magnitude of the effect is severalfold less than that in PEEK, consistent with the minimum lengths of polymer chain required to make a fold in the different cases. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1198–1204, 2007     

Static dust sphere in Einstein-Cartan theory

Physically meaningful solutions of the field equations for static spherical dust distributions in the Einstein-Cartan theory have been obtained. There is one in which the spin is zero at the center and another with zero spin at the boundary of the sphere.     

Modal properties of circular and noncircular optical waveguides

We give a review and a comparison of recent methods of analyzing circular and noncircular optical waveguides. Comparison among competing methodologies is made as follows: Galerkin's method is used with Laguerre-Gauss basis functions in circular geometry to examine the modal solution in a step index fiber, and comparison with the exact solution is made. A W-fiber, which has no exact solution, is then examined. Rectangular geometry is considered, and discussion centers on the use of Galerkin's method using trigonometric basis functions and Hermite-Gauss basis functions. Re difficulty arising from the use of basis functions that do not decay exponentially for large argument (trigonometric functions) is illustrated. Finally, a square step index waveguide is used to illustrate a comparison between a variational method that uses the Gaussian approximation as the starting point, and Galerkin's method using Hermite-Gauss basis functions. We conclude that the variational method does well in predicting the propagation constant β but does not do well in predicting the modal field.     

Temperature dependence of magnetization in nanocrystalline FeCoZr alloy

The temperature dependence of magnetization of a nanocrystalline Fe₆₀Co₃₀Zr₁₀ alloy annealed at various temperatures to varying crystal sizes was investigated down to 5 K in the field range up to 5 T. The fitting procedure gave T^3/2 as the leading term irrespective of the crystal size. We suggest that the increase of the coefficient by this term for smaller crystals may be connected to an increased relative volume of their surface.