Applications of canonical relations in generic differential geometry

Conflict sets are loci of intersecting wavefronts emanating from $l$ different surfaces. We show that generically conflict sets are Legendrian: locally they admit the structure of wavefronts. Simple stable singularities for this problem in $\R^n$ occur when $0 \leq n-l \leq 4$. Other related sets, such as kite curves and centre sets are also defined and discussed. Throughout canonical relations are used as an essential tool to carry out several of these geometrical constructions.Comment: 20 pages, 12 figure

On dangerous self-tangencies in families of conflict sets

In this note we observe an interesting link between an intersection of two Legendrian manifolds in $ST^\ast\R^2$ - or dangerous self-tangencies, on the one hand and hyperbolic Morse transition of immersed curves on a torus on the other hand. The connection between these two arises naturally in the study of one-parameter families of conflict sets

The dynamic behaviour of rail vehicles operating at high speeds for manriding in British coal mines

The behaviour of trains used at high speeds for transporting men along mine railways is examined using a number of mathematical models. These models predict the responses of different rail vehicles to typical irregularities in the track, and are used to examine the guidance, the ride, and the likelihood of derailment of the main classes of manriding trains used in British coal mines. The outcome of the modelling compares favourably with the results of tests carried out on actual vehicles. The investigation has shown that the safe speed at which trains may operate is ultimately restricted by the condition of the track, but changes in the design of the vehicles can lead to an improved performance. The use of conventional wheelsets, for example, can reduce flange wear significantly and so allows higher speeds to be reached. Guidelines for the design of vehicles intended for high speed use are included in this thesis