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Algebraic Solitons in the Massive Thirring Model
No full textThis thesis presents exact solutions describing dynamics of N identical algebraic
solitons in the massive Thirring model. Each algebraic soliton corresponds to a
simple embedded eigenvalue in the Kaup–Newell spectral problem and attains the
maximal mass among solitary waves traveling with the same speed. In the case
of N = 2 solitons, we use expressions for two exponential solitons and find a new
solution in the singular limit for the algebraic double-soliton which corresponds
to a double embedded eigenvalue. To systematically derive the rational solutions
for N identical algebraic solitons for any N ≥ 1, we employ the double-Wronskian
method, a determinant-based approach that generates solitons to Hirota’s bilinear
equations. While traditional stability techniques fail for algebraic solitons due to
their embedded spectral nature, the exact solutions obtained here suggest persistence of algebraic solitons under time evolution.ThesisMaster of Science (MSc
GPU-ACCELERATED TURBULENCE SIMULATOR FOR SPACE-BASED OPTICAL COMMUNICATIONS
No full textIn modern space-based networks, growing bandwidth demands and increasing mission complexity drive the need for accurate, high-resolution simulations that capture
small-scale turbulence features and rapid satellite movement. By leveraging GPU
parallelization, this simulator manages large data volumes and frequent time steps,
enabling the modeling of wavefront distortions essential for robust system design,
adaptive optics, and performance optimization. This thesis presents a novel, highspeed simulator for optical propagation through dynamic atmospheric turbulence affecting satellite downlinks. The method begins by calculating the effective refractive
index structure parameter (C
2
n
) which captures the turbulence strength, along the
observation path between the satellite and ground receiver. This derived C
2
n
informs
the atmospheric slicer, which distributes phase screens throughout the propagation
path. The simulation focuses on the first 20 km of atmosphere, where the majority
of turbulence affecting free-space optical links occurs. The angular spectrum propagation formula is implemented to achieve Fresnel propagation between planes where
phase screens represent integrated turbulence slices at specific altitudes. Temporal
evolution is achieved via the frozen flow hypothesis and an adjustable wind model
with altitude-dependent wind speeds. Numerical simulation of optical propagation through turbulence with high spatial sampling poses significant computational challenges, especially for rapidly moving Low Earth Orbit (LEO) satellites and simulations with numerous phase screen layers. This work addresses this challenge with an
innovative GPU architecture that parallelizes intensive computations and large loops
across GPU cores. This advancement enables the use of large phase screens, many
layers, and rapid propagation loops, efficiently simulating fast-translating LEO satellites. This comprehensive approach significantly enhances the speed of atmospheric
turbulence simulations for satellite communications, offering a powerful tool for system design, performance prediction, and optimization of adaptive optics strategies
in free-space optical communication systems. The GPU-accelerated implementation
achieves speedup factors of 310× to 600× over conventional CPU-based simulators.ThesisMaster of Applied Science (MASc)Optical satellite communications (SatCom) provides high data throughput and low
latency, particularly for low Earth orbit (LEO) satellite applications over distances
ranging from 500 to 1,500 km, making them essential for emerging space-based networks. However, due to wind and temperature shifts, atmospheric turbulence severely
impacts the quality of downlink channels, necessitating robust simulation tools to inform system design and ensure reliable performance under dynamic conditions.
Numerical simulation of optical propagation through turbulence with high spatial
sampling poses significant computational challenges, especially for rapidly moving
LEO satellites and simulations with a number of phase screen layers. This highresolution sampling is essential for accurately predicting how atmospheric turbulence
will affect signal quality, which directly impacts the reliability and performance of
these critical communications links. This work addresses this challenge with a Graphic
Processing Unit (GPU) architecture that parallelizes intensive computations and large
loops across GPU cores. This advancement enables the use of large phase screens,
many layers, and rapid propagation loops, efficiently simulating fast-translating LEO
satellites. This approach significantly enhances the speed of atmospheric turbulence
simulations for satellite communications, offering a powerful tool for system design,
performance prediction, and optimization of adaptive optics strategies in free-space
optical communication systems.
The simulator employs a multi-layered approach to optical propagation, accounting for varying wind speeds and satellite elevation angles to create a comprehensive
path simulation of wavefront degradation. The speed and accuracy of the simulator
also make it ideal for machine learning applications, generating large datasets of realistic turbulent wavefronts matching atmospheric theory. Validation results demonstrate
excellent agreement between theoretical predictions and simulated outputs across various atmospheric conditions and satellite positions. Performance benchmarks show
that GPU-accelerated implementation achieves up to 600 times faster execution time
within the same conditions compared to a publicly available optical turbulence simulator intended for astronomy, while maintaining equivalent accuracy. This simulator
introduces a GPU-accelerated, multi-layer architecture that captures both fast orbital
motion and fine-scale atmospheric distortion
SENIORITY-ZERO CANONICAL TRANSFORMATION THEORY
No full textThe standard method for solving the electronic Schrodinger equation for chemical
systems is to add dynamic (CI, CC, MBPT) correlation to a single reference wave
function, usually Hartree-Fock. When static correlation is important, i.e., when there
are multiple important electron configurations—one instead uses explicitly multireference
methods like CASSCF or DMRG, and then adds corrections for dynamic correlation.
Such approaches are typically very expensive, with cost growing exponentially
with the orbital subspace that contains the dominant electron configurations. There
are very few methods in the literature that treat both static (multireference) and
dynamic correlation together, and they usually suffer from poor scalability and/or
technical/numerical problems like intruder states.
In this thesis, we propose a method based on the ideas of canonical transformation
(CT) theory to add dynamic correlation on top of multireference wave functions.
Specifically, we are interested in seniority-zero (SZ) wave functions. This type of
wave function is used to describe the static part of the correlation, and due to the
facility to compute its reduced density matrices, it becomes the perfect reference for
a method based on CT theory. Because our static correlation model is determined
simultaneously with its dynamic correlation correction, our method treats static and
dynamic correlation on equal footing.Specifically, we apply a unitary transformation to a Hamiltonian of a physical system,
seeking the specific transformation that makes the final Hamiltonian seniority-zero.
This strategy is motivated by the realization that it is relatively easy to solve
seniority-zero Schrodinger equations, a task that would be especially easy on a quantum
computer. To evaluate the action of the unitary transformation we use the
Baker–Campbell–Hausdorff (BCH) formula, with two different truncation schemes.
In the first scheme, we truncate each commutator in the expansion to a maximum of
two-body terms using the operator decomposition technique introduced in CT theory;
we call this method seniority-zero LCT (SZ-LCT). In the second, we delay the truncation
to every double commutator, expecting thereby to recover more information
about the system’s correlation; we call this method seniority-zero QCT (SZ-QCT).
We tested SZ-LCT in H4, H6, BeH2; and SZ-QCT in H4, H6. For H4, both truncation
schemes yielded energy errors ∼ 1mEh. Although SZ-QCT is an improvement
over linear truncation, our results indicate that when the seniority-zero reference already
provides a good approximation to the true wave function, the added complexity
of the transformation does not enhance accuracy. For H6 and BeH2, the SZ-LCT
method produced average energy errors ∼ 10−2Eh, with the largest deviations occurring
near the equilibrium bond length. In contrast, testing SZ-QCT on H6 revealed
an improvement over linear truncation; while the average energy error remains of the
same order, with SZ-QCT the errors are stable along the entire dissociation curve.ThesisMaster of Science (MSc)We propose a method to solve the electronic Schrodinger equation for strongly correlated
systems by transforming the Hamiltonian that describes the physical system
into a new Hamiltonian that is easier to solve. Specifically, we choose the final
Hamiltonian to be seniority-zero (SZ) because such Hamiltonians are (relatively) easy
to treat computationally, yet suitable for treating strong correlation within electron
pairs. To evaluate the transformation we use the Baker–Campbell–Hausdorff (BCH)
formula, truncating the commutators of the expansion to a maximum of two-body
operators by using the operator decomposition method of canonical transformation
(CT) theory to (approximately) rewrite many-body terms in terms of 1- and 2-body
operators. We consider two possible truncation schemes: (a) decomposing single commutators
in the BCH expansion (SZ-LCT) and (b) delaying truncation until after the
double-commutator is evaluated (SZ-QCT). We tested SZ-LCT on H4, H6, BeH2 and
SZ-QCT on H4 and H6. The accuracy of the method depends on two factors: (1)
how well the seniority-zero reference approximates the true wave function and (2)
the size of the generator of the transformation. For cases where the seniority-zero
reference is a good approximation to the true wave function, SZ-LCT gave better
results; where the seniority-zero wave function was not a good approximation, the
delayed truncation in SZ-QCT improves the accuracy and stability of the method
Quantum Walks and Application to Quantum Money
No full textThis thesis explores the foundations of quantum computation, focusing on quantum walks
and their application to quantum money. Quantum walks, particularly continuous-time
quantum walks based on group actions, serve as a powerful computational tool with applications
in search algorithms and cryptographic protocols. We examine their mathematical
structure and their advantages over classical random walks, emphasizing their efficiency in
state evolution and probability distribution spreading. As a part of this work, we examine
efficient implementations of transforms such as the Quantum Fourier Transform (QFT) and
the Quantum Hartley Transform (QHT), analyzing their role in encoding quantum states
for secure cryptographic applications. In particular, we discuss a novel instantiation of a
quantum money scheme based on QHT, leveraging its unique properties for improved security
and efficiency. To ensure the robustness of this quantum money scheme, we develop a
verification mechanism utilizing quantum walks. Unlike previous approaches, which rely on
standard quantum state measurements, our method employs continuous-time quantum walks
to authenticate quantum money, preventing counterfeiting while maintaining computational
feasibility. Additionally, we present a detailed discussion on the efficient implementation of
this scheme, including optimized circuit designs and error mitigation strategies.ThesisMaster of Applied Science (MASc
Effect of methylprednisolone on acute kidney injury in patients undergoing cardiac surgery with a cardiopulmonary bypass pump: a randomized controlled trial
No full textBACKGROUND: Perioperative corticosteroid use may reduce acute kidney injury. We sought to test whether methylprednisolone reduces the risk of acute kidney injury after cardiac surgery. METHODS: We conducted a prespecified substudy of a randomized controlled trial involving patients undergoing cardiac surgery with cardiopulmonary bypass (2007–2014); patients were recruited from 79 centres in 18 countries. Eligibility criteria included a moderate-to-high risk of perioperative death based on a preoperative score of 6 or greater on the European System for Cardiac Operative Risk Evaluation I. Patients (n = 7286) were randomly assigned (1:1) to receive intravenous methylprednisolone (250 mg at anesthetic induction and 250 mg at initiation of cardiopulmonary bypass) or placebo. Patients, caregivers, data collectors and outcome adjudicators were unaware of the assigned intervention. The primary outcome was postoperative acute kidney injury, defined as an increase in the serum creatinine concentration (from the preoperative value) of 0.3 mg/dL or greater (≥ 26.5 µmol/L) or 50% or greater in the 14-day period after surgery, or use of dialysis within 30 days after surgery. RESULTS: Acute kidney injury occurred in 1479/3647 patients (40.6%) in the methylprednisolone group and in 1426/3639 patients (39.2%) in the placebo group (adjusted relative risk 1.04, 95% confidence interval 0.96 to 1.11). Results were consistent across several definitions of acute kidney injury and in patients with preoperative chronic kidney disease. INTERPRETATION: Intraoperative corticosteroid use did not reduce the risk of acute kidney injury in patients with a moderate-to-high risk of perioperative death who had cardiac surgery with cardiopulmonary bypass. Our results do not support the prophylactic use of steroids during cardiopulmonary bypass surgery
Communicating Statecharts (CSC)
No full textConcurrency is increasingly gaining importance due to the rapid development of networked applications. However, concurrency comes with some complexities, including handling race conditions or deadlocks. Therefore, learning this concept and understanding its correct implementation is challenging, even for experienced programmers. This problem arises from the current practices of teaching concurrency because of the focus on confusing details instead of necessary concepts.
We propose a new concurrency paradigm called Communicating StateCharts (CSC) to simplify the teaching of concurrency to beginner programmers. CSC preserves five main principles, aiming to make concurrency easier to learn and use for novices: software visualization, Model-Driven Development (MDD), pure functions, separation of concerns, and raising abstraction levels. In this regard, CSC adapts features from existing concurrency models that aligned with our principles, namely process calculi, the actor model, and Harel’s statecharts. This synthesis led to CSC’s atomic statecharts, communicating through messages transmitted via channels.
To make CSC accessible for beginners, a visual MDD tool called CSCDraw is designed and developed. The main requirements that guided the design of CSCDraw include enforcing CSC principles, considering beginner-friendly features, ensuring faithful code generation, supporting conditional branches, and channel cardinality. We also present the design of a pilot study that investigates the most effective
way of teaching CSC to beginning programmers. This study serves as a prelude to
a more rigorous experiment to compare the effectiveness of CSC with the existing
paradigms.ThesisMaster of Computer Science (MCS
PRECAST CONCRETE BRIDGE SUBSTRUCTURES: FROM SERVICE PERFORMANCE TO SEISMIC RESILIENCE
No full textHighway bridges in Canada are rapidly aging and deteriorating due to various environmental factors, resulting in a significant backlog in repair and replacement. To support and advance accelerated bridge construction, this dissertation tackles the multifaceted challenges faced by precast bridge elements and systems (PBES) under both service and extreme load conditions. It focuses on two distinct PBES substructures: emulative piers, which replicate the behavior of cast-in-place structures, and non-emulative piers, which use controlled rocking to minimize damage. The goal is to develop resilient PBES substructures that not only withstand seismic forces but also adapt to evolving environmental and transportation demands.
The research begins with a seismic risk assessment of conventional cast-in-place highway bridges in a designated case study area, incorporating the compounded effects of chloride-induced corrosion and climate change. This analysis reveals varying degrees of progressive earthquake-induced damage across regions over time, emphasizing the critical need for PBES to address the growing risks and maintenance challenges associated with seismic and environmental deterioration.
With this critical need for PBES established, the thesis then focuses on the seismic design of PBES substructures. For emulative piers, finite element analyses validated against experimental data led to the development of a strut-and-tie model for precast column-to-pile shaft assemblies. This model, which predicts force transfer and strain distributions, was used in a parametric study that indicates that enhancing the transverse reinforcement ratio is particularly effective in preventing prying-action failure in pile shaft foundations. Subsequent experimental investigations demonstrated that employing ultra-high-performance concrete (UHPC) in pile shafts not only prevents prying-action damage but also reduces the required dimensions and reinforcement by 13.3% and 25%, respectively, without compromising overall seismic performance. For non-emulative piers, the thesis presents seismic design approaches for post-tensioned (PT) rocking piers. The study develops explicit analytical equations for viscous dampers and genetic programming-derived models for ED bars, and validates these design frameworks through nonlinear response history analyses, achieving displacement demand predictions within acceptable margins.
Addressing serviceability concerns under disruptive transportation technologies—specifically automated truck platooning—the thesis develops a reliability analysis framework to evaluate its impact on PBES substructures. By incorporating dynamic vehicle-bridge interaction and soil-structure uncertainties, the framework identifies critical thresholds for platoon operation parameters to prevent excessive axial loads and settlement.
The contributions of this thesis include quantifying the impacts of climate change and corrosion on elevated seismic damage risks, developing innovative seismic design approaches and tools, experimentally validating UHPC-enhanced designs, and performing reliability analyses to characterize the effects of truck platooning on service performance. These contributions to PBES can address the critical need for rapid bridge construction and replacement while ensuring infrastructure remains resilient in the face of intensified environmental stresses and evolving transportation technologies.DissertationDoctor of Philosophy (PhD)In Canada, aging highway bridges are increasingly vulnerable to compounded effects of corrosion and climate change. Conventional cast-in-place construction methods for repair or replacement are often both time-consuming and disruptive. In response, this thesis centers on precast bridge elements and systems (PBES), which can be fabricated off-site and rapidly assembled on-site to minimize traffic closures and accelerate construction.
By examining how chloride-induced corrosion—exacerbated by changing climate conditions—intensifies the seismic vulnerability of existing concrete bridges, this thesis underscores the urgent need for PBES-based construction for greater efficiency. It then explores design strategies to design PBES substructures for effective earthquake resistance and demonstrates that integrating ultra-high-performance concrete (UHPC) into connection regions can reduce member sizes and reinforcement without compromising seismic performance. Lastly, the additional challenge posed by truck platooning—where service load demands increase—prompts the development of a reliability-based framework to confirm that PBES substructures can safely accommodate these intensified conditions.
Overall, this research delivers new analytical models, design guidelines, and lifecycle performance insights for PBES substructures. The findings support accelerated bridge construction methods that maintain seismic resistance while accommodating evolving environmental and traffic demands, ultimately contributing to safer, longer-lasting highway infrastructure
Phase Field Modelling of TRISO SiC Layer Growth by Chemical Vapour Deposition
No full textThe layers of TRISO (TRistructural ISOtropic) particles are manufactured by Fluidized Bed Chemical
Vapour Deposition (FB-CVD). The microstructures of the Inner Pyrolitic Carbon (IPyC), Outer Pyrolitic
Carbon (OPyC), and SiC layers are affected by the manufacturing conditions of temperature, pressure,
and precursor gas concentration during the CVD process. The microstructure and grain morphology
of the SiC layer is important since it affects the strength of the adhesion between IPyC-SiC and OPyC-
SiC layers as well as the overall integrity of the fuel particle, and permeability of certain elements.
Understanding the relationship between the fluidized bed parameters and microstructure facilitates
scaling and optimizing particle production and particle performance.
Phase field modelling is a proven robust tool for predicting mesoscale phenomena such as mi-
crostructure evolution. A thermodynamically informed phase field model was developed to simulate
the deposition of the SiC layer during the CVD process. This work presents results of modelling the
nucleation, growth, microstructure evolution, and the columnar to equiaxed grain transition; as well
as advances in multiphase, polygranular, and stoichiometric phase implementation, density varia-
tion between phases, and the use of the computationally efficient Geometric Multigrid (GM) solver
in the Firedrake finite element code. The implementation of the GM solver resulted in a significant
gain in computational efficiency and enabled the simulation of experimentally-relevant length-scales
in 3 dimensions. The results were compared to layer growth data with good quantitative agreement
and Electron Backscatter Diffraction (EBSD) images of the SiC layer in surrogate TRISO fuel with good
qualitative agreement.ThesisMaster of Applied Science (MASc)TRISO is a form of nuclear fuel that will be used in some advanced nuclear reactors. The TRISO fuel
manufacturing process includes growing a layered structure using a technique called Fluidized Bed
Chemical Vapour Deposition. Temperature, pressure, and concentration of gases used during the de-
position process affect the structure and performance of the layers and consequently the entire fuel
particle. The structure of the Silicon Carbide (SiC) layer is especially important because of its role in
the overall structural integrity of the particle and is the heart of the safety case made by vendors to the
regulators. To support the capability of predicting the microstructure of the SiC layer and to inform
and optimize experiments, this thesis developed a computational model of SiC deposition by CVD us-
ing a thermodynamically-informed phase field model. The results demonstrate qualitative agreement
with experimental images and quantitative agreement with experimental results of deposition rates
Petrographic analysis of fault rock structures from Notre Dame Bay, Newfoundland, Canada
No full textSupervised by Dr. Alexander PeaceThis study investigates fault rocks in the Leading Tickles area of Notre Dame Bay Magmatic Province (NDBMP), Newfoundland, Canada. The NDBMP consists of alkaline mafic intrusions, and the Leading Tickles region is characterized by radial lamprophyre dykes, Leading Tickles Stock and Budgell’s Harbour Stock, which fold and fault the surrounding Ordovician host rocks. This region is within an eastern peri-Gondwanan exploits subzone which was affected by the Appalachian orogenic events including the Taconic, Salinic and Acadian orogenies. The primary objectives of this study were to examine fault rock deformation processes, investigate interactions between the fault rocks and lamprophyre dyke fragments, and examine fault rock kinematics and reactivation.
This thesis presents a petrographic analysis of two fault rock samples collected from Cull Island, near the town of Leading Tickles in NDBMP. The first sample is identified as a non-foliated Protocataclasite, displaying features of both brittle and ductile deformation, consistent with formation in the brittle to ductile transition zone and late-stage fluid infiltration. The second sample is classified as a non-foliated mosaic fault breccia, indicative of brittle deformation at shallower crustal levels in a fault zone with late-stage carbonate infiltration. The absence of lamprophyre dyke fragments within the samples suggests faulting processes predate the dyke intrusion. In addition, the observed fault rocks are likely related to the Luke’s Arm Fault Zone (LAFZ), which crosses the study area, and may reflect broader fault reactivation along Newfoundland’s margin during the Mesozoic
