Vacuum spacetimes of embedding class two

Doubt is cast on the much quoted results of Yakupov that the torsion vector in embedding class two vacuum space-times is necessarily a gradient vector and that class 2 vacua of Petrov type III do not exist. The rst result is equivalent to the fact that the two second fundamental forms associated with the embedding necessarily commute and has been assumed in most later investigations of class 2 vacuum space-times. Yakupov stated the result without proof, but hinted that it followed purely algebraically from his identity: Rijkl Ckl = 0 where Cij is the commutator of the two second fundamental forms of the embedding.From Yakupov's identity, it is shown that the only class two vacua with non-zero commutator Cij must necessarily be of Petrov type III or N. Several examples are presented of non-commuting second fundamental forms that satisfy Yakupovs identity and the vacuum condition following from the Gauss equation; both Petrov type N and type III examples occur. Thus it appears unlikely that his results could follow purely algebraically. The results obtained so far do not constitute denite counter-examples to Yakupov's results as the non-commuting examples could turn out to be incompatible with the Codazzi and Ricci embedding equations. This question is currently being investigated.

Mode control in multimode optical fibre and its applications

This thesis describes an investigation into methods for controlling the mode distribution in multimode optical fibres. The major contributions presented in this thesis are summarised below. Emerging standards for Gigabit Ethernet transmission over multimode optical fibre have led to a resurgence of interest in the precise control, and specification, of modal launch conditions. In particular, commercial LED and OTDR test equipment does not, in general, comply with these standards. There is therefore a need for mode control devices, which can ensure compliance with the standards. A novel device consisting of a point-load mode-scrambler in tandem with a mode-filter is described in this thesis. The device, which has been patented, may be tuned to achieve a wide range of mode distributions and has been implemented in a ruggedised package for field use. Various other techniques for mode control have been described in this work, including the use of Long Period Gratings and air-gap mode-filters. Some of the methods have been applied to other applications, such as speckle suppression and in sensor technology. A novel, self-referencing, sensor comprising two modal groups in the Mode Power Distribution has been designed and tested. The feasibility of a two-channel Mode Group Diversity Multiplexed system has been demonstrated over 985m. A test apparatus for measuring mode distribution has been designed and constructed. The apparatus consists of a purpose-built video microscope, and comprehensive control and analysis software written in Visual Basic. The system may be fitted with a Silicon camera or an InGaAs camera, for measurement in the 850nm and 130nm transmission windows respectively. A limitation of the measurement method, when applied to well-filled fibres, has been identified and an improvement to the method has been proposed, based on modelled Laguerre Gauss field solutions.

A CFD study of biomass pyrolysis in a downer reactor equipped with a novel gas-solid separator - I:hydrodynamic performance

This study presents the first part of a CFD study on the performance of a downer reactor for biomass pyrolysis. The reactor was equipped with a novel gas-solid separation method, developed by the co-authors from the ICFAR (Canada). The separator, which was designed to allow for fast separation of clean pyrolysis gas, consisted of a cone deflector and a gas exit pipe installed inside the downer reactor. A multi-fluid model (Eulerian-Eulerian) with constitutive relations adopted from the kinetic theory of granular flow was used to simulate the multiphase flow. The effects of the various parameters including operation conditions, separator geometry and particle properties on the overall hydrodynamics and separation efficiency were investigated. The model prediction of the separator efficiency was compared with experimental measurements. The results revealed distinct hydrodynamic features around the cone separator, allowing for up to 100% separation efficiency. The developed model provided a platform for the second part of the study, where the biomass pyrolysis is simulated and the product quality as a function of operating conditions is analyzed. Crown Copyright © 2014 Published by Elsevier B.V. All rights reserved.