The location of roots of equations with particular reference to the generalized eigenvalue problem

A survey is presented of algorithms which are in current use for the solution of a single algebraic or transcendental equation in one unknown, together with an appraisal of their practical performance. The first part of the thesis consists of an account of the theoretical basis of a number of iterative methods and an examination of the problems to be overcome in order to achieve a successful computer implementation. In the selection of specific programs for testing, the emphasis has been placed on methods which are suitable for use, in conjunction with determinant evaluation, for the solution of standard eigenvalue problems and generalized problems of the form A(λ)x = O, where the elements of A are linear or non-linear functions of λ. The principal requirements for such purposes are that: 1. the algorithm should not be restricted to polynomial equations 2. derivative evaluation should not be required. Examples of eigenvalue problems arising from engineering applications illustrate the potential difficulties of determining roots. Particular attention is given to the problem of calculating a number of roots in cases where a priori estimates for each root are not available. The discussion is extended to give a brief account of possible approaches to the problem of locating complex roots. Interpolation methods are found to be particularly versatile and can be recommended for their accuracy and efficiency. It is also suggested that such algorithms may often be employed as search strategies in the absence of good initial estimates of the roots. Mention is also made of those features of practical implementation which were found to be particularly useful, together with a list of some outstanding difficulties, associated principally with the automatic computation of several roots of an equation

Stray current induced corrosion of steel fibre reinforced concrete

Stray current induced corrosion is a major technical challenge for modern electric railway systems. The leakage of stray current to surrounding reinforced concrete structures can lead to steel reinforcement corrosion and the subsequent disintegration of concrete. Steel fibre reinforced concrete has been increasingly used as the railway tunnel lining material but it is not clear if discrete steel fibres can still pick up and transfer stray current in the same way as conventional steel reinforcement and lead to similar corrosion reactions. The corrosion behaviour of steel fibres was investigated through voltammetry tests and electrochemical impedance spectroscopy. The presence of high concentration chloride ions was found to increase the pitting corrosion tendency of steel fibres in simulated concrete pore solutions and mortar specimens. The chloride threshold level for corrosion of steel fibres in concrete is approximately 4% NaCl (by mass of cement) which is significantly higher than that of conventional steel reinforcement

Recent developments on the STAR detector system at RHIC

The STAR detector system is designed to provide tracking, momentum analysis and particle identification for many of the mid-rapidity charged particles produced in collisions at the RHIC collider. A silicon vertex detector (SVT) provides three layers of tracking near the interaction point. This is followed by the main time projection chamber (TPC), which continues tracking out to 200 cm radial distance from the interaction region. The detector design also includes an electromagnetic calorimeter, various trigger detectors, and radial TPCs in the forward region. The entire system is enclosed in a 0.5 T solenoid magnet. A progress report is given for the various components of the STAR detector system. The authors report on the recent developments in the detector proto-typing and construction, with an emphasis on the main TPC, recent TPC cosmic ray testing and shipping to Brookhaven National Laboratory