Highly accurate calculation of radial spheroidal functions

A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters.     

INFLUENCE OF A LEVELNESS DEFECT IN A THRUST BEARING ON THE DYNAMIC BEHAVIOUR OF AN ELASTIC SHAFT

This paper examines the non-linear dynamic behaviour of a flexible shaft. The shaft is mounted on two journal bearings and the axial load is supported by a defective hydrodynamic thrust bearing at one end. The defect is a levelness defect of the rotor. The thrust bearing behaviour must be considered to be non-linear because of the effects of the defect. The shaft is modelled with typical beam finite elements including effects such as the gyroscopic effects. A modal technique is used to reduce the number of degrees of freedom. Results show that the thrust bearing defects introduce supplementary critical speeds. The linear approach is unable to show the supplementary critical speeds which are obtained only by using non-linear analysis.     

Effect of hydrogen on the photoelectronic properties of GaAs/InGaAs quantum-well heterostructures with an island palladium layer on the surface

The effect of hydrogen on the photoluminescence and planar conductivity of GaAs/InGaAs quantum-well heterostructures with an island Pd layer at the anodically oxidized surface was studied. Unlike continuous deposited Pd layers, island layers do not cause the formation of defects in the GaAs surface region and yet the Pd layer maintains high catalytic activity with respect to hydrogen. It is found that the thermal treatment of such a structure in a hydrogen atmosphere causes atomic-hydrogen passivation of the defects in quantum wells. Studies of the characteristics of planar photoresistors with an island Pd layer acting as hydrogen sensors show that their hydrogen detectivity is approximately two orders of magnitude higher than that of diode structures with continuous Pd layers.     

Hydromagnetic instability of streaming fluids in porous medium

The instability of the plane interface between two uniform, superposed, electrically conducting and counter-streaming fluids through a porous medium is considered in the presence of a horizontal magnetic field. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored. For perturbations in all other directions there exists instability for a certain wavenumber range. The instability of this system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference between the streaming velocities and the Alfvén velocity.This research forms a part of the research project awarded to the first author (R.C.S.) by the University Grants Commission.     

High-throughput screening of fuel cell electrocatalysts

The drawbacks of our earlier report of preparing fuel cell catalyst arrays by borohydride reduction of inkjet prepared arrays of metal salts are discussed along with the need for inclusion of state-of-the-art metrics in all array screening. An alternative method for screening of hydrogen/air cathode catalysts, direct methanol fuel cell (DMFC) anode catalysts, and catalyst loading studies is provided. State-of-the-art Johnson Matthey catalysts were used in control experiments to demonstrate the utility of the array fuel cell for high throughput screening of fuel cell catalysts in the 3-4 mg/cm² range. This report lays out hard learned rules for high throughput screening and demonstrates that the array fuel cell can be used for very precise screening of libraries of membrane electrode assembly (MEA) components without the pitfalls discussed in the introduction.     

Estimates for the Second Order Derivatives of Eigenvectors in Thin Anisotropic Plates with Variable Thickness

For the second order derivatives of eigenvectors in a thin anisotropic heterogeneous plate Ω_h, we derive estimates of their weighted L₂-norms with majorants whose dependence on the plate thickness h and on the eigenvalue number is expressed explicitly. These estimates maintain the asymptotic sharpness throughout the entire spectrum, whereas inside its low-frequency band the majorants remain bounded as h → +0. The latter is a rather unexpected fact, because for the first eigenfunction u¹ of a similar boundary-value problem for a scalar second order differential operator with variable coefficients, the norm ‖∇ _x ² u⁰; L₂(Ω_h)‖ is of order h⁻¹ and grows as h tends to zero. Bibliography: 35 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 161–180.     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

ON THE ROLES OF COMPLEMENTARY AND ADMISSIBLE BOUNDARY CONSTRAINTS IN FOURIER SOLUTIONS TO THE BOUNDARY VALUE PROBLEMS OF COMPLETELY COUPLED r TH ORDER PDES

A heretofore unavailable double Fourier series based approach, for obtaining non-separable solution to a system of completely coupled linear r th order partial differential equations with constant coefficients and subjected to general (completely coupled) boundary conditions, has been presented. The method has been successfully implemented to solve a class of hitherto unsolved boundary-value problems, pertaining to free and forced vibrations of arbitrarily laminated anisotropic doubly curved thin panels of rectangular planform, with arbitrarily prescribed (both symmetric and asymmetric with respect to the panel centerlines) admissible boundary conditions and subjected to general transverse loading.Existing solutions such as those due to Navier or Levy are based on the well-known method of separation of variables. Such solutions represent particular solutions whenever the method of separation of variables work, and when these particular solution functions fortuitously satisfy the boundary conditions. For derivation of the complementary solution, the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives. Such discontinuities form sets of measure zero.Various cases of lamination, geometry and dynamic response (forced and free vibrations) of a class of thin anisotropic laminated shells (curved panels) have been shown to follow from the above. Six sets of boundary conditions are used to illustrate the present method for the derivation of complementary solutions. Navier-type solutions whenever available form special cases of the present general solution.