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.

A mean field theory of coded CDMA systems

We present a mean field theory of code-division multiple access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.

Clinical evaluation of the Softec HD aberration-free aspheric intraocular lens

Purpose: To compare distance and near visual performance with a zero-aberration aspheric intraocular lens (IOL) (Softec HD, Lenstec, Inc. FL, USA) with that of an otherwise identical, but spherical IOL (Softec 1). Setting: Department of Ophthalmology, Solihull Hospital, West Midlands, United Kingdom. Methods: This prospective study comprised 37 patients with a Softec 1 spherical IOL implanted in one eye, who underwent phacoemulsification and received the Softec HD aspheric IOL in the fellow eye. One month post-operatively, unaided distance and near vision, residual refraction, best spectacle corrected distance and near visual acuity, reading speed, pseudoaccommodation and photopic contrast sensitivity were recorded. Wavefront analysis enabled comparison of higher order aberrations between the IOLs. Results: Prior to surgery, the Softec 1 and Softec HD eyes were not significantly different. Post-operatively, unaided vision, best spectacle corrected visual acuity and residual refraction were not significantly different between the eyes, nor were there significant differences observed between the measured wavefront aberrations. Once implanted, the range of focus was significantly better in the Softec HD IOL eye than the Softec 1 IOL eye and, although reading speed was equivalent to the Softec 1 eye, the print size at which this could be achieved was significantly smaller. Conclusions: Depth of field was significantly improved with the aspheric IOL compared with the spherical IOL, without any compromise in distance visual performance between the two IOLs.

Sequence distributions in free-radical polymers

This thesis is concerned with demonstrating how the visual representation of the sequence distribution of individual monomer units, of a polymer, that would be observed upon polymerisation, may be utilised in designing and synthesizing polymers with relatively low cell adhesion characteristics, The initial part of this thesis is concerned with demonstrating the use of a computer simulation technique, in illustrating the sequence distribution that would be observed upon the polymerisation of a set of monomers. The power of the computer simulation technique has been demonstrated through the simulation of the sequence distributions of some generic contact lens materials. These generic contact lens materials were chosen simply because in the field of biomaterials their compositions are amongst the most systematically regulated and they present a wide range of compositions. The validity of the computer simulation technique has been assessed through the synthesis and analysis of linear free-radical polymers at different conversions. Two main parameters were examined, that of composition and the number-average sequence lengths of individual monomer units, at various conversions. The polymers were synthesized through the solution polymerisation process. The monomer composition was determined by elemental analysis and 13C nuclear magnetic analysis (NMR). Number-average sequence lengths were determined exclusively through 13C NMR. Although the computer simulation technique provides a visual representation of the monomer sequence distribution up to 100% conversion, these assessments were made on linear polymers at a reasonably high conversion (above 50%) but below 100% conversion of ease for analysis. The analyses proved that the computer simulation technique was reasonably accurate in predicting the sequence distribution of monomer units, upon polymerisation, in the polymer.An approach has been presented which allows one to manipulate the use of monomers, with their reactivity ratios, thereby enabling us to design polymers with controlled sequence distributions.Hydrogel membranes, with relatively controlled sequence distributions and polymerised to 100% conversion, were synthesized to represent prospective biomaterials. Cell adhesion studies were used as a biological probe to investigate the susceptibility of the surface of these membranes to cell adhesion. This was necessary in order to assess the surface biocompatibility or biotolerance of these prospective biomaterials.

Surfactant-free purification of membrane proteins with intact native membrane environment

In order to study the structure and function of a protein, it is generally required that the protein in question is purified away from all others. For soluble proteins, this process is greatly aided by the lack of any restriction on the free and independent diffusion of individual protein particles in three dimensions. This is not the case for membrane proteins, as the membrane itself forms a continuum that joins the proteins within the membrane with one another. It is therefore essential that the membrane is disrupted in order to allow separation and hence purification of membrane proteins. In the present review, we examine recent advances in the methods employed to separate membrane proteins before purification. These approaches move away from solubilization methods based on the use of small surfactants, which have been shown to suffer from significant practical problems. Instead, the present review focuses on methods that stem from the field of nanotechnology and use a range of reagents that fragment the membrane into nanometre-scale particles containing the protein complete with the local membrane environment. In particular, we examine a method employing the amphipathic polymer poly(styrene-co-maleic acid), which is able to reversibly encapsulate the membrane protein in a 10 nm disc-like structure ideally suited to purification and further biochemical study.

PMD tolerance of 288 Gbit/s Coherent WDM and transmission over unrepeatered 124 km of field-installed single mode optical fiber

Low-cost, high-capacity optical transmission systems are required for metropolitan area networks. Direct-detected multi-carrier systems are attractive candidates, but polarization mode dispersion (PMD) is one of the major impairments that limits their performance. In this paper, we report the first experimental analysis of the PMD tolerance of a 288Gbit/s NRZ-OOK Coherent Wavelength Division Multiplexing system. The results show that this impairment is determined primarily by the subcarrier baud rate. We confirm the robustness of the system to PMD by demonstrating error-free performance over an unrepeatered 124km field-installed single-mode fiber with a negligible penalty of 0.3dB compared to the back-to-back measurements. (C) 2010 Optical Society of America

Field experiments with a grooming switch for OTDM meshed networking

Field experiments of 42.7/128.1 Gb/s wavelength-division multiplexed, optical time-division multiplexed (WDM-OTDM) transmultiplexing and all-optical dual-wavelength regeneration at the OTDM rate are presented in this paper. By using the asynchronous retiming scheme, we achieve error-free bufferless data grooming with time-slot interchange capability for OTDM meshed networking. We demonstrate excellent performance from the system, discuss scalability, applicability, and the potential reach of the asynchronous retiming scheme for transparent OTDM-domain interconnection.

A compact free space quantum key distribution system capable of daylight operation

A free space quantum key distribution system has been demonstrated. Consideration has been given to factors such as field of view and spectral width, to cut down the deleterious effect from background light levels. Suitable optical sources such as lasers and RCLEDs have been investigated as well as optimal wavelength choices, always with a view to building a compact and robust system. The implementation of background reduction measures resulted in a system capable of operating in daylight conditions. An autonomous system was left running and generating shared key material continuously for over 7 days. © 2009 Published by Elsevier B.V..

5,745 km DWDM transcontinental field trial using 10 Gbit/s dispersion managed solitons and dynamic gain equalization

Error free unregenerated transmission is demonstrated looped-back over 5,745 km (62 spans) of installed SSMF along the Adelaide-Perth leg of the IP1 Australia network, which is now the world's longest commercially deployed unregenerated 10 Gbit/s DWDM terrestrial transmission system. © 2000 Optical Society of America.

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

Template-free and eco-friendly synthesis of hierarchical Ag3PO4 microcrystals with sharp corners and edges for enhanced photocatalytic activity under visible light

Herein, we demonstrate a template-free and eco-friendly strategy to synthesize hierarchical Ag3PO4 microcrystals with sharp corners and edges via silver–ammine complex at room temperature. The as-synthesized hierarchical Ag3PO4 microcrystals were characterized by X-ray diffraction, field-emission scanning electron microscope (FESEM), UV–vis diffuse reflectance spectroscopy (UV–vis DRS), BET surface area analyzer, and photoluminescence analysis (PL). Our results clearly indicated that the as-synthesized Ag3PO4 microcrystals possess a hierarchical structure with sharp corners and edges. More attractively, the adsorption ability and visible light photocatalytic activity of the as-synthesized hierarchical Ag3PO4 is much higher than that of conventional Ag3PO4.