The research in this thesis was undertaken because information on the relationship between scan parameters and image quality for the MARS spectral CT was lacking. However, the MARS spectral CT is expected to extend into clinical use in the future, so it is absolutely crucial that we know how the quality of the images that it produces is effected by different can parameters. This will allow us to make further improvements to the machine, and ultimately help clinicians to visualise important information in patients which are not revealed by other imaging modalities. This thesis provides information on how the image quality is affected by different scan parameters on the MARS spectral CT using a Medipix3 silicon quad detector. In particular, it explores how different numbers of projections, exposure time products (mAs), and peak tube voltages (kVp) with different threshold energies (kV) effect the image noise, image resolution and image uniformity, respectively. This provides a set of guidelines for future work using the MARS scanner to obtain images of optimal quality. This thesis also determines that the new image reconstruction software mART developed by Niels de Ruiter, is a suitable replacement for the reconstruction software OctopusCT that is currently being used by the MARS team. Using mART reduces the scan times and dose delivered by the MARS spectral CT.

The extra energy information provided by spectral x-ray imaging using novel photon counting x-ray detectors may allow for improved decomposition of materials compared to conventional and dual-energy imaging. The information content of spectral x-ray images, however, depends on how the photons are grouped together. This thesis deals with the theoretical aspect of optimising material discrimination in spectral x-ray imaging. A novel theoretical model was developed to map the confidence region of material thicknesses to determine the uncertainties in thickness quantification. Given the thickness uncertainties, photon counts per pixel can be optimised for material quantification in the most dose efficient manner. Minimisation of the uncertainties enables the optimisation of energy bins for material discrimination. Using Monte Carlo simulations based on the BEAMnrc package, material decomposition of up to 3 materials was performed on projection images, which led to the validation of the theoretical model. With the inclusion of scattered radiation, the theoretical optima of bin border energies were accurate to within 2 keV. For the simulated photon counts, excellent agreement was achieved between the theoretical and the BEAMnrc models regarding the signal-to-noise ratio in a decomposed image, particularly for the decomposition of two materials. Finally, this thesis examined the implementation of the Medipix detector. The equalisation of pixel sensitivity variations and the processing of photon counting projection images were studied. Measurements using the Medipix detector demonstrated promising results in the charge summing and the spectroscopic modes of acquisition, even though the spectroscopic performance of the detector was relatively limited due to electronic issues known to degrade the equalisation process. To conclude, the theoretical model is sufficient in providing guidelines for scanning parameters in spectral x-ray imaging and may be applied on spectral projection measurements using e.g. the redesigned MedipixRX detector with improved spectroscopic performance, when it becomes available.

Combined Electric-acoustic stimulation (EAS) is becoming an increasingly viable treatment option for individuals with sloping severe to profound high frequency hearing loss and residual low frequency hearing. Sound stimulation via EAS is delivered to the high frequency region electrically using cochlear implantation, and to the low frequency region acoustically with or without amplification from hearing aids. This combined mode of stimulation often results in improved speech recognition in background noise compared to either mode of stimulation in isolation. It is important to note that many EAS listeners have some degree of hearing loss in the low frequency region, and may experience associated effects such as reduced frequency selectivity and elevated audiometric thresholds. This study simulated EAS listening in 20 normal hearing listeners by combining vocoded high frequency sound with low frequency sound. Low frequency sound was further manipulated by applying varying degrees of spectral smearing and attenuation to the low frequency region in an EAS simulation, to simulate changes in frequency selectivity and sensitivity that usually accompany sensorineural hearing loss. The aim of this study was to investigate the effects of spectral smearing and attenuation of low frequency information on the identification of vocoded speech in noise. Participants were required to complete a sentence recognition task in the presence of competing talkers for six simulated listening conditions with varying degrees of processing in the low frequency region. Results indicated that the advantage for speech in noise of simulated combined EAS over simulated electric stimulation alone was 3.9 dB when low frequency sound was unprocessed, 2.9 dB when low frequency sound had spectral smearing of x3 applied, and 2.4 dB when low frequency sound had spectral smearing of x6 applied. When 30 dB attenuation was applied as well as x3 spectral smearing, no significant benefit was observed. When 60 dB attenuation was applied as well as x3 spectral smearing, a significant negative relationship was found, with a 3 dB disadvantage found for simulated EAS compared to simulated electric stimulation alone. Overall, the results of this study indicate that there is indeed a significant improvement in speech recognition in a background of competing speakers with simulated EAS compared to simulated electric stimulation only. However, when reduced hearing thresholds were simulated for the residual low frequency hearing, we found that this benefit was either absent or reversed. These results therefore support the use of amplification for individuals with reduced hearing thresholds in the low frequencies in order to utilize the benefit they are able to achieve with combined EAS.

Chemical abundances as measured from stellar spectral lines are often subject to uncertainties due to lack of accurate data for inelastic collisions, which is needed for non-local thermodynamic equilibrium (non-LTE) modelling. For cool stars, understanding of collision processes with electrons and hydrogen atoms is required to achieve high precision measurements. In this thesis, I have investigated the role of these collisions on the non-LTE formation of Li and Mg spectral lines in late-type stars. In the case of Li, electron impact excitation processes were calculated using the R-matrix with pseudo states method and the results found to agree well with recent calculations using the convergent close-coupling technique. These modern data were employed in non-LTE calculations by updating an existing model atom, which already included modern data for hydrogen collision processes. Our results were compared with calculations using older semi-empirical approximation calculations and only small differences were found: about 0.01 dex (~ 2%) or less in the abundance corrections. We therefore conclude that the influence of uncertainties in the electron collision data on non-LTE calculations is negligible. Indeed, together with the collision data for the charge transfer process Li + H ↔ Li+ + H- now available, and barring the existence of an unknown important collisional process, the collisional data in general is not a source of significant uncertainty in non-LTE Li line formation calculations. In the case of Mg, electron impact excitation processes were again calculated with the Rmatrix with pseudo states method, and used together with recent hydrogen collision calculations to build and test a model atom, without free parameters, for non-LTE modelling. Both electron and hydrogen collision processes, including charge transfer and excitation, are found to be important thermalising agents in various cases. The modelled spectra agree well with observed spectra from benchmark stars in the optical and infrared. The modelling predicts non-LTE abundance corrections ∆A(Mg)NLTE–LTE in dwarfs, both solar metallicity and metal-poor, to be very small (of order 0.01 dex), even smaller than found in previous studies. In giants, corrections vary greatly between lines, but can be as large as 0.4 dex. Results of calculations in a large grid of 1D model atmospheres are presented, and the implications for studies of Mg discussed. The propagation of uncertainties in the inelastic collision data to those in stellar abundances is investigated, and found to lead to small uncertainties, once again typically less than 0.01 dex (2%), although for few stellar models in specific lines (e.g., metal-poor suns, in the 7691 Å line) uncertainties can be as large as 0.03 dex (7%).

<p>In this dissertation, the spectral element method is developed to simulate electromagnetic field in nano-structure consisting of dielectric, metal or semiconductor. The spectral element method is a special kind of high order finite element method, which has spectral accuracy. When the order of the basis function increases, the accuracy increases exponentially. The goal of this dissertation is to implement the spectral element method to calculate the electromagnetic properties of various semiconductor nano-structures, including photonic crystal, photonic crystal slab, finite size photonic crystal block, nano dielectric sphere. The linear electromagnetic characteristics, such as band structure and scattering properties, can be calculated by this method with high accuracy. In addition, I have explored the application of the spectral element method in nonlinear and quantum optics. The effort will focus on second harmonic generation and quantum dot nonlinear dynamics. </p><p>The electromagnetic field can be simulated in both frequency domain and time domain. Each method has different application for research and engineering. In this dissertation, the first half of the dissertation discusses the frequency domain solver, and the second half of the dissertation discusses the time domain solver.</p><p>For frequency domain simulation, the basic equation is the second order vector Helmholtz equation of the electric field. This method is implemented to calculate the band structure of photonic crystals consisting of dielectric material as well as metallic materials. Because the photonic crystal is periodic, only one unit cell need to be simulated in the computational domain, and a periodic boundary condition is applied. The spectral accuracy is inspected. Adding the radiation boundary condition at top and bottom of the computational region, the scattering properties of photonic crystal slab can be calculated. For multiple layers photonic crystal slab, the block-Thomas algorithm is used to increase the efficiency of the calculation. When the simulated photonic crystals are finite size, unlike an infinitely periodic system, the periodic boundary condition does not apply. In order to increase the efficiency of the simulation, the domain decomposition method is implemented. </p><p>The second harmonic generation, which is a kind of nonlinear optical effect, is simulated by the spectral element method. The vector Helmholtz equations of multiple frequencies are solved in parallel and the consistence solution with nonlinear effect is obtained by iterative solver. The sensitivity of the second harmonic generation to the thickness of each layer can be calculated by taking the analytical differential of the equation to the thickness of each element. </p><p>The quantum dot dynamics in semiconductor are described by the Maxwell-Bloch equations. The frequency domain Maxwell-Bloch equations are deduced. The spectral element method is used to solve these equations to inspect the steady state quantum dot dynamic behaviors under the continuous wave electromagnetic excitation.</p><p>For time domain simulation, the first order curl equations in Maxwell equations are the basic equations. A spectral element method based on brick element is implemented to simulate a nano-structure consisting of woodpile photonic crystal. The resonance of a micro-cavity consisting of a point defect in the woodpile photonic crystal block is simulated. In addition, the time domain Maxwell-Bloch equations are implemented in the solver. The spontaneous emission process of quantum dot in the micro-cavity is inspected. </p><p>Another effort is to implement the Maxwell-Bloch equations in a previously implemented domain decomposition spectral element/finite element time domain solver. The solver can handle unstructured mesh, which can simulate complicated structure. The time dependent dynamics of a quantum dot in the middle of a nano-sphere are investigated by this implementation. The population inversion under continuous and pulse excitation is investigated. </p><p>In conclusion, the spectral element method is implemented for frequency domain and time domain solvers. High efficient and accurate solutions for multiple layers nano-structures are obtained. The solvers can be applied to design nano-structures, such as photonic crystal slab resonators, and nano-scale semiconductor lasers.</p> / Dissertation

Spectral flow, in its simplest incarnation, counts the net number of eigenvalues which change sign as one traverses a path of self-adjoint Fredholm operators in the set of of bounded operators B(H) on a Hilbert space. A generalization of this idea changes the setting to a semifinite von Neumann algebra N and uses the trace τ to measure the amount of spectrum which changes from negative to positive along a path; the operators are still self-adjoint, but the Fredholm requirement is replaced by its von Neumann algebras counterpart, Breuer-Fredholm. Our work is ensconced in this semifinite von Neumann algebra setting. We prove a uniqueness result in the case when N is a factor. In the case when the operators under consideration are bounded perturbations of a fixed unbounded operator with τ-compact resolvents, we give a different proof of a p-summable integral formula which calculates spectral flow, and fill in some of the gaps in the proof that spectral flow can be viewed as an intersection number if N = B(H). / Graduate / 0280

Spectrum utilization efficiency is one of the primary concerns in the design of future wireless communication systems. Most performance metrics for wireless communication systems focus on either link level capacity or network throughput while ignore the spatial property of wireless transmissions. In this dissertation, we focus on the spatial spectral utilization efficiency of wireless transmissions. We first study the spatial spectral efficiency of single-cell and multi-cell wireless relay systems using area spectral efficiency (ASE) performance metric. We then generalize the performance metric, termed as generalized area spectral efficiency (GASE), to measure the spatial spectral utilization efficiency of arbitrary wireless transmissions. In particular, we first introduce the definition of GASE by illustrating its evaluation for conventional point-to-point transmission. Then we extend the analysis to four different transmission scenarios, namely dual-hop relay transmission, three-node cooperative relay transmission, two-user X channels, and underlay cognitive radio transmission. Finally, we apply the GASE performance metric to investigate the spatial spectral efficiency of wireless network with Poisson distributed nodes and quantify the spatial spectral opportunities that could be explored with secondary cognitive systems. Our research on the spatial spectral utilization efficiency provides a new perspective on the designing of wireless communication systems, especially on the transmission power optimization and space-spectrum resource exploitation. / Graduate / 0544 / leizhang@uvic.ca

Pyrolysis mass spectrometry (PyMS) is a rapid, automated analytical technique that is used for chemical and biological characterisation of organisms. It has been limited in its use outside the discipline of microbiology and has rarely been applied to the analysis of multi-cellular organisms. This study aimed to investigate the potential of using PyMS as a routine analytical tool to resolve problems in marine algal systematics. The technical constraints of PyMS were also examined. The effect of sample concentration proved to be an important consideration for the production of meaningful results. PyMS analysis of macroalgae from the order Fucales demonstrated that this technique was robust to the influence of environmental variability and challenged the assertion that it is limited to use as a phenotypic technique only. Characterisation of samples was also possible at the sub-species level. Experimentally induced variation among cultures of the diatom Skeletonema costatum, including silicate limitation, low salinity and reduced irradiance, was detectable by PyMS. PyMS is subject to technical limitations including day to day variability among spectral data and does not produce a permanent classification. This study showed that PyMS is a highly discriminatory, sensitive technique that is capable of resolving chemical and biological variability among marine algae.

Wall-bounded turbulent flows are prevalent in engineering and industrial applications. Walls greatly affect turbulent characteristics in many ways including production and propagation of turbulent stresses. While computational fluid dynamics can be used as an important design tool, its use is hindered due to the fine-mesh requirements in the near-wall region to capture all of the pertinent turbulent data. To resolve all relevant scales of motion, the number of grid points scales with Reynolds number as N ≈ Re9/4, making it nearly impossible to solve real engineering problems, most of which feature high Reynolds numbers. A method to help alleviate the resolution requirements is the use of wall models. This method allows for a coarser mesh to be used in which the near-wall region is modeled and the first grid point is placed in the log-law region. The shear stress at the wall is correlated with the velocity at a point outside the near-wall region, drastically reducing the number of elements required and reducing the computational time and cost of the simulation. The goal of this study was to test the speed increase and element reduction capabilities of combining a wall function solution with the massively-parallel, spectral element solver, Nek5000, and verify the method using a turbulent channel simulation. The first grid point is placed at y+ = 100, in the log-law region, for Reτ = 950 and the sub-grid scales are modeled using a dynamic Smagorinski model. The results are then compared to a DNS performed by Jimenez and Hoyas for model verification.

Spectral geometry is a mathematical discipline that studies the relationship between the geometry of Riemannian manifolds and the spectra of natural differential operators defined on them. The spectra of Laplacians are the ones most studied in this context. A sub-field of this discipline, called inverse spectral geometry, studies how much geometric information one can recover from such spectra. The motivation behind our study of inverse spectral geometry is a physical one. It has recently been proposed that inverse spectral geometry could be the missing mathematical link between quantum field theory and general relativity needed to unify those theories into a single theory of quantum gravity. Unfortunately, this proposed link is not well understood. Most of the efforts in inverse spectral geometry were historically concentrated on the generation of counterexamples to the most general formulation of inverse spectral geometry and the few positive results that exist are quite limited. In order to remedy to that, it has been proposed to linearize the problem, and study an infinitesimal version of inverse spectral geometry. In this thesis, I begin by reviewing the theory of pseudodifferential operators and using it to prove the spectral theorem for elliptic operators. I then define the commonly used Laplacians and survey positive and negative results in inverse spectral geometry. Afterwards, I briefly discuss a coordinate free reformulation of Riemannian geometry via the notion of spectral triple. Finally, I introduce a formulation of inverse spectral geometry adapted for numerical implementations and apply it to the inverse spectral geometry of a particular class of star-shaped domains in ℝ².