The analytic torsion of the finite metric cone over a compact manifold

We give an explicit formula for the $L^2$ analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the different factors appearing in this formula. We prove that the analytic torsion of the cone is the finite part of the limit obtained collapsing one of the boundaries, of the ratio of the analytic torsion of the frustum to a regularising factor. We show that the regularising factor comes from the set of the non square integrable eigenfunctions of the Laplace Beltrami operator on the cone.Comment: To appear in Journal of the Mathematical Society of Japa

The effect of circumferential distortion on fan performance at two levels of blade loading

Single stage fans designed for two levels of pressure ratio or blade loading were subjected to screen-induced circumferential distortions of 90-degree extent. Both fan rotors were designed for a blade tip speed of 425 m/sec, blade solidity of 1.3 and a hub-to-tip radius ratio of 0.5. Circumferential measurements of total pressure, temperature, static pressure, and flow angle were obtained at the hub, mean and tip radii at five axial stations. Rotor loading level did not appear to have a significant influence on rotor response to distorted flow. Losses in overall pressure ratio due to distortion were most severe in the stator hub region of the more highly loaded stage. At the near stall operating condition tip and hub regions of (either) rotor demonstrated different response characteristics to the distorted flow. No effect of loading was apparent on interactions between rotor and upstream distorted flow fields

Supercharged topping rocket propellant feed system

A rocket propellant feed system utilizing a bleed turbopump to supercharge a topping turbopump is presented. The bleed turbopump is of a low pressure type to meet the cavitation requirements imposed by the propellant storage tanks. The topping turbopump is of a high pressure type and develops 60 to 70 percent of the pressure rise in the propellant

The Frobenius group T13 and the canonical see-saw mechanism applied to neutrino mixing

The compatibility of the Frobenius group T13 with the canonical see-saw mechanism of neutrino mixing is examined. The Standard Model is extended in a minimalist way, by introducing a family symmetry and three right-handed neutrinos. To fit experiments and place constraints on the possibilities, tribimaximal mixing is used as a guideline. The application of both a family symmetry group and the canonical see-saw mechanism naturally generates small neutrino masses. The various possibilities from combining these two models are listed. Enough constraints are produced to narrow down the parameters of the neutrino mass matrix to two. This is therefore a predictive model where neutrino mass eigenvalues and allowed regions for neutrinoless double beta decay are suggested.Comment: Accepted for publication in Physical Review D. 13 page

Spinning Solitons of a Modified Non-Linear Schroedinger equation

We study soliton solutions of a modified non-linear Schroedinger (MNLS) equation. Using an Ansatz for the time and azimuthal angle dependence previously considered in the studies of the spinning Q-balls, we construct multi-node solutions of MNLS as well as spinning generalisations.Comment: 8 Revtex pages, 5 ps figures; v2: minor change