A variety of lepton number violating processes related to Majorana neutrino masses

A Majorana type of the neutrino mass matrix induces a class of lepton number violating processes. Cross sections of these reactions are given in terms of the neutrino mass matrix element, and a semi-realistic event rate is estimated. These processes provide mass and mixing parameters not directly accessible by the neutrino oscillation experiments. If these processes are discovered with a larger rate than given here, it would imply a new physics of the lepton number violation not directly related to the Majorana neutrino mass, such as R-parity violating operators in SUSY models.Comment: 15 pages, 1 figur

Negative Specific Heat in a Quasi-2D Generalized Vorticity Model

Negative specific heat is a dramatic phenomenon where processes decrease in temperature when adding energy. It has been observed in gravo-thermal collapse of globular clusters. We now report finding this phenomenon in bundles of nearly parallel, periodic, single-sign generalized vortex filaments in the electron magnetohydrodynamic (EMH) model for the unbounded plane under strong magnetic confinement. We derive the specific heat using a steepest descent method and a mean field property. Our derivations show that as temperature increases, the overall size of the system increases exponentially and the energy drops. The implication of negative specific heat is a runaway reaction, resulting in a collapsing inner core surrounded by an expanding halo of filaments.Comment: 12 pages, 3 figures; updated with revision

A system-approach to the elastohydrodynamic lubrication point-contact problem

The classical EHL (elastohydrodynamic lubrication) point contact problem is solved using a new system-approach, similar to that introduced by Houpert and Hamrock for the line-contact problem. Introducing a body-fitted coordinate system, the troublesome free-boundary is transformed to a fixed domain. The Newton-Raphson method can then be used to determine the pressure distribution and the cavitation boundary subject to the Reynolds boundary condition. This method provides an efficient and rigorous way of solving the EHL point contact problem with the aid of a supercomputer and a promising method to deal with the transient EHL point contact problem. A typical pressure distribution and film thickness profile are presented and the minimum film thicknesses are compared with the solution of Hamrock and Dowson. The details of the cavitation boundaries for various operating parameters are discussed

On generalised Paley graphs and their automorphism groups

The generalised Paley graphs are, as their name suggests, a generalisation of the Paley graphs, first defined by Paley in 1933 (see \cite{Paley}). They arise as the relation graphs of symmetric cyclotomic association schemes. However, their automorphism groups may be much larger than the groups of the corresponding schemes. We determine the parameters for which the graphs are connected, or equivalently, the schemes are primitive. Also we prove that generalised Paley graphs are sometimes isomorphic to Hamming graphs and consequently have large automorphism groups, and we determine precisely the parameters for this to occur. We prove that in the connected, non-Hamming case, the automorphism group of a generalised Paley graph is a primitive group of affine type, and we find sufficient conditions under which the group is equal to the one-dimensional affine group of the associated cyclotomic association scheme. The results have been applied in \cite{LLP} to distinguish between cyclotomic schemes and similar twisted versions of these schemes, in the context of homogeneous factorisations of complete graphs.Comment: 15 pages. This is extensively revised from the first version, and is accepted for publication by Michigan Math. Journa

Silicon resistor to measure temperature during rapid thermal annealing

A resistor composed of a piece of Si wafer and two thin silver wires attached to it, can reliably sense the temperature during rapid thermal annealing (RTA). As constant electric current passes through the Si piece, the resistivity change of Si with temperature produces a voltage signal that can be readily calibrated and converted to an actual temperature of the samples. An accuracy better than ±10 °C is achieved between 300° and 600 °C

On the numerical solution of the dynamically loaded hydrodynamic lubrication of the point contact problem

The transient analysis of hydrodynamic lubrication of a point-contact is presented. A body-fitted coordinate system is introduced to transform the physical domain to a rectangular computational domain, enabling the use of the Newton-Raphson method for determining pressures and locating the cavitation boundary, where the Reynolds boundary condition is specified. In order to obtain the transient solution, an explicit Euler method is used to effect a time march. The transient dynamic load is a sinusoidal function of time with frequency, fractional loading, and mean load as parameters. Results include the variation of the minimum film thickness and phase-lag with time as functions of excitation frequency. The results are compared with the analytic solution to the transient step bearing problem with the same dynamic loading function. The similarities of the results suggest an approximate model of the point contact minimum film thickness solution