Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

Design of Raman-based nonlinear loop mirror for all-optical 2R regeneration of differential phase-shift-keying transmission

We present a concept for all-optical regeneration of signals modulated in phase-sensitive modulation formats, which is based on a new design of Raman amplified nonlinear optical loop mirror (RA-NOLM). We demonstrate simultaneous amplitude-shape regeneration and phase-noise reduction in high-speed differential phase-shift-keying transmission systems by use of the RA-NOLM combined with spectral filtering.

Design of Raman-based nonlinear loop mirror for all-optical 2R regeneration of differential phase-shift-keying transmission

We present a concept for all-optical regeneration of signals modulated in phase-sensitive modulation formats, which is based on a new design of Raman amplified nonlinear optical loop mirror (RA-NOLM). We demonstrate simultaneous amplitude-shape regeneration and phase-noise reduction in high-speed differential phase-shift-keying transmission systems by use of the RA-NOLM combined with spectral filtering. © 2006 IEEE.

Differential perception of innovation with particular reference to the organisational context

Differential perception of innovation is a research area which has been advocated as a suitable topic for study in recent years. It developed from the problems encountered within earlier perception of innovation studies which sought to establish what characteristics of an innovation affected the ease of its adoption. While some success was achieved In relating perception of innovation to adoption behaviour, variability encountered Within groups expected - to fercelve innovation similarly suggested that the needs and experiences of the potential adopter were significantly affecting the research findings. Such analysis being supported by both sociological and psychological perceptual research. The present study sought to identify the presence of differential perception of innovation and explore the nature of the process. It was decided to base the research in an organisational context and to concentrate upon manufacturing innovation. It has been recognised that such adoption of technological innovation is commonly the product of a collective decision-making process, involving individuals from a variety of occupational backgrounds, both in terms of occupational speciality and level within the hierarchy. Such roles appeared likely to significantly influence perception of technological innovation, as gathered through an appropriate measure and were readily identifiable. Data vas collected by means of a face-to-face card presentation technique, a questionnaire and through case study material. Differential perception of innovation effects were apparent In the results, many similarities and differences of perception being related to the needs and experiences of the individuals studied. Phenomenological analysis, which recognises the total nature of experience in infiuencing behaviour, offered the best means of explaining the findings. It was also clear that the bureaucratic model of role definition was not applicable to the area studied, it seeming likely that such definitions are weaker under conditions of uncertainty, such as encountered in innovative decision-making.

Characterization of time-resolved laser differential phase using 3D complementary cumulative distribution functions

An experimental method for characterizing the time-resolved phase noise of a fast switching tunable laser is discussed. The method experimentally determines a complementary cumulative distribution function of the laser's differential phase as a function of time after a switching event. A time resolved bit error rate of differential quadrature phase shift keying formatted data, calculated using the phase noise measurements, was fitted to an experimental time-resolved bit error rate measurement using a field programmable gate array, finding a good agreement between the time-resolved bit error rates.

Reduction of the phase jitter in differential phase-shift-keying soliton transmission systems by in-line Butterworth filters

We examine reduction of phase jitter by use of in-line Butterworth filters in soliton systems in the context of differential phase-shift-keying coding. We also demonstrate numerically that the use of a Butterworth filter in a return-to-zero differential phase-shift-keying system can reduce continuum background radiation.

Uncovering the root cause of ethnic difference in ability testing:differential test functioning, test familiarity and trait optimism as explanations of ethnic group differences

The present research represents a coherent approach to understanding the root causes of ethnic group differences in ability test performance. Two studies were conducted, each of which was designed to address a key knowledge gap in the ethnic bias literature. In Study 1, both the LR Method of Differential Item Functioning (DIF) detection and Mixture Latent Variable Modelling were used to investigate the degree to which Differential Test Functioning (DTF) could explain ethnic group test performance differences in a large, previously unpublished dataset. Though mean test score differences were observed between a number of ethnic groups, neither technique was able to identify ethnic DTF. This calls into question the practical application of DTF to understanding these group differences. Study 2 investigated whether a number of non-cognitive factors might explain ethnic group test performance differences on a variety of ability tests. Two factors – test familiarity and trait optimism – were able to explain a large proportion of ethnic group test score differences. Furthermore, test familiarity was found to mediate the relationship between socio-economic factors – particularly participant educational level and familial social status – and test performance, suggesting that test familiarity develops over time through the mechanism of exposure to ability testing in other contexts. These findings represent a substantial contribution to the field’s understanding of two key issues surrounding ethnic test performance differences. The author calls for a new line of research into these performance facilitating and debilitating factors, before recommendations are offered for practitioners to ensure fairer deployment of ability testing in high-stakes selection processes.

On-line learning of unrealizable tasks

The dynamics of on-line learning is investigated for structurally unrealizable tasks in the context of two-layer neural networks with an arbitrary number of hidden neurons. Within a statistical mechanics framework, a closed set of differential equations describing the learning dynamics can be derived, for the general case of unrealizable isotropic tasks. In the asymptotic regime one can solve the dynamics analytically in the limit of large number of hidden neurons, providing an analytical expression for the residual generalization error, the optimal and critical asymptotic training parameters, and the corresponding prefactor of the generalization error decay.

Market-level information and the diffusion of competing technologies:an exploratory analysis of the LAN industry

Market-level information diffused by print media may contribute to the legitimation of an emerging technology and thus influence the diffusion of competing technological standards. After analyzing more than 10,000 trade media abstracts from the Local Area Networks (LAN) industry published between 1981 and 2000, we found the presence of differential effects on the adoption of competing standards by two market-level information types: technology and product availability. The significance of these effects depends on the technology's order of entry and suggests that high-tech product managers should make strategic use of market-level information by appropriately focusing the content of their communications. © 2007 Elsevier B.V. All rights reserved.

A study of the dynamic behaviour of a pulsed column solvent extraction plant

A study has been made of the dynamic behaviour of a nuclear fuel reprocessing plant utilising pulsed solvent extraction columns. A flowsheet is presented and the choice of an extraction device is discussed. The plant is described by a series of modules each module representing an item of equipment. Each module consists of a series of differential equations describing the dynamic behaviour of the equipment. The model is written in PMSP, a language developed for dynamic simulation models. The differential equations are solved to predict plant behaviour with time. The dynamic response of the plant to a range of disturbances has been assessed. The interactions between pulsed columns have been demonstrated and illustrated. The importance of auxillary items of equipment to plant performance is demonstrated. Control of the reprocessing plant is considered and the effect of control parameters on performance assessed.

Dynamic simulation of chemical plant

This thesis describes the design and implementation of a new dynamic simulator called DASP. It is a computer program package written in standard Fortran 77 for the dynamic analysis and simulation of chemical plants. Its main uses include the investigation of a plant's response to disturbances, the determination of the optimal ranges and sensitivities of controller settings and the simulation of the startup and shutdown of chemical plants. The design and structure of the program and a number of features incorporated into it combine to make DASP an effective tool for dynamic simulation. It is an equation-oriented dynamic simulator but the model equations describing the user's problem are generated from in-built model equation library. A combination of the structuring of the model subroutines, the concept of a unit module, and the use of the connection matrix of the problem given by the user have been exploited to achieve this objective. The Executive program has a structure similar to that of a CSSL-type simulator. DASP solves a system of differential equations coupled to nonlinear algebraic equations using an advanced mixed equation solver. The strategy used in formulating the model equations makes it possible to obtain the steady state solution of the problem using the same model equations. DASP can handle state and time events in an efficient way and this includes the modification of the flowsheet. DASP is highly portable and this has been demonstrated by running it on a number of computers with only trivial modifications. The program runs on a microcomputer with 640 kByte of memory. It is a semi-interactive program, with the bulk of all input data given in pre-prepared data files with communication with the user is via an interactive terminal. Using the features in-built in the package, the user can view or modify the values of any input data, variables and parameters in the model, and modify the structure of the flowsheet of the problem during a simulation session. The program has been demonstrated and verified using a number of example problems.

Characterisation and modification of hydrogel polymers

The work described in this thesis can be broadly divided into two sections. The first being the characterisation of hydrogel polymers in both their hydrated and dehydrated states and the second some aspects of the structural modification of polymers. The characterisation of hydrogel polymers in their dehydrated state (xerogels) involves such techniques as elemental analysis, pyrolysis gas liquid chromatography, infra-red spectroscopy, density determination and surface characterisation by contact angle measurements. The characterisation of some commercially available hydrogel materials was undertaken using such techniques and the results obtained were compared to laboratory synthesised systems in an attempt to assess the value of the combination of techniques employed. In the characterisation of hydrated polymers the amoumt and nature of water present is the single most important factor. The most convenient method of characterising this water involves the use of differential scanning calorimetry (DSC), coupled with total equilibrium water content measurements. DSC distinguishes between non-freezing and freezing water but in addition provides some information on the continuum of states in the freezing water fraction. Two aspects of the structural modification of hydrogel polymers were studied. The first involved the incorporation of acrylamide and substituted acryamide monomers into a copolymer system and an examination of the effect of this on the amino acid interaction of the polymers. The second was the attempted synthesis of cell surface analogues by the attachment of sugar type molecules to the polymer using a variety of reaction methods.

An experimental study of the effects of noise upon short term memory

The overall aim of this study was to examine experimentally the effects of noise upon short-term memory tasks in the hope of shedding further light upon the apparently inconsistent results of previous research in the area. Seven experiments are presented. The first chapter of the thesis comprised a comprehensive review of the literature on noise and human performance while in the second chapter some theoretical questions concerning the effects of noise were considered in more detail follovred by a more detailed examination of the effects of noise upon memory. Chapter 3 described an experiment which examined the effects of noise on attention allocation in short-term memory as a function of list length. The results provided only weak evidence of increased selectivity in noise. In further chapters no~effects Here investigated in conjunction vrith various parameters of short-term memory tasks e.g. the retention interval, presentation rate. The results suggested that noise effects were significantly affected by the length of the retention interval but not by the rate of presentation. Later chapters examined the possibility of differential noise effects on the mode of recall (recall v. recognition) and the type of presentation (sequential v. simultaneous) as well as an investigation of the effect of varying the point of introduction of the noise and the importance of individual differences in noise research. The results of this study were consistent with the hypothesis that noise at presentation facilitates phonemic coding. However, noise during recall appeared to affect the retrieval strategy adopted by the subject.

Settlement of fill with particular reference to opencast coal mining sites

A study of information available on the settlement characteristics of backfill in restored opencast coal mining sites and other similar earthworks projects has been undertaken. In addition, the methods of opencast mining, compaction controls, monitoring and test methods have been reviewed. To consider and develop the methods of predicting the settlement of fill, three sites in the West Midlands have been examined; at each, the backfill had been placed in a controlled manner. In addition, use has been made of a finite element computer program to compare a simple two-dimensional linear elastic analysis with field observations of surface settlements in the vicinity of buried highwalls. On controlled backfill sites, settlement predictions have been accurately made, based on a linear relationship between settlement (expressed as a percentage of fill height) against logarithm of time. This `creep' settlement was found to be effectively complete within 18 months of restoration. A decrease of this percentage settlement was observed with increasing fill thickness; this is believed to be related to the speed with which the backfill is placed. A rising water table within the backfill is indicated to cause additional gradual settlement. A prediction method, based on settlement monitoring, has been developed and used to determine the pattern of settlement across highwalls and buried highwalls. The zone of appreciable differential settlement was found to be mainly limited to the highwall area, the magnitude was dictated by the highwall inclination. With a backfill cover of about 15 metres over a buried highwall the magnitude of differential settlement was negligible. Use has been made of the proposed settlement prediction method and monitoring to control the re-development of restored opencase sites. The specifications, tests and monitoring techniques developed in recent years have been used to aid this. Such techniques have been valuable in restoring land previously derelict due to past underground mining.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.