UWSpace

UWSpace is the University of Waterloo’s institutional repository for the free, secure, and long-term home of research produced by faculty, students, and staff.

Depositing Theses/Dissertations or Research to UWSpace

Are you a Graduate Student depositing your thesis to UWSpace? See our Thesis Deposit Help and UWSpace Thesis FAQ pages to learn more.

Are you a Faculty or Staff member depositing research to UWSpace? See our Waterloo Research Deposit Help and Self-Archiving pages to learn more.

Photo by Waterloo staff

Communities in UWSpace

Select a community to browse its collections.

Recent Submissions

  • Thumbnail Image
    Item type: Item ,
    Continued Fractions
    (University of Waterloo, 2026-04) Boghossian, Khajak
    A capstone project submitted in partial fulfillment of the requirements for the degree of Master of Mathematics for Teachers. Continued Fractions are beautiful and powerful expressions with many important applications in number theory. It’s difficult to pinpoint their exact origins, but mathematicians have discovered references to these fractions in many ancient texts. Euclid discovered an algorithm for finding the greatest common divisor (gcd) of two numbers, which involved converting rational numbers into continued fractions. Other historical works include those of ¯Aryabhata, an Indian mathematician who attempted to find a general solution of a linear indeterminate equation using these fractions around 550 A.D. Leonard Euler (1707-1783), Johan Heinrich Lambert (1728-1777) and Joseph Louis Lagrange (1736-1813) are also credited with contributing to this topic and developing the theory. Finally, it was John Wallis who coined the term “continued fraction” in 1655 in the book Arithmetica Infinitorum. The following is a short course on continued fractions. In working through these lessons, it is my hope that the reader will be inspired to conduct further research on this fascinating topic.
  • Thumbnail Image
    Item type: Item ,
    "Looks cool, I'll try this later!": Understanding the faces and uses of online tutorials
    (University of Waterloo, 2012-01-05) Lafreniere, Ben; Bunt, Andrea; Lount, Matthew; Terry, Michael
    Despite their prevalence, little is known about how users make use of web tutorials or feature-rich applications, and why authors take the time to create them. In this paper, we analyze comments posted to web tutorials to understand the purposes that tutorials serve for users, and examine the tutorials themselves to understand their structure and authors' motivations to create them. Our results indicate that users come to tutorials for help performing techniques with applications, and to achieve complex end results beyond their current expertise. As for tutorial authors, we found that most tutorials had clear extrinsic reasons for existing, including earning ad or referral revenue, promoting premium products or services, or acting as portfolios for their authors. Based on these results, we suggest a number of improvements to current tutorial interfaces.
  • Thumbnail Image
    Item type: Item ,
    Overview of Projective Quantum Monte Carlo Methods for Stoquastic Hamiltonians
    (University of Waterloo and the Perimeter Institute for Theoretical Physics, 2024-06) Wah, Lavoisier
    Projective quantum Monte Carlo algorithms are among the most powerful computational techniques to simulate the ground state properties of quantum many-body systems. In the present thesis, we provide an implementation of the algorithms both in the simple case where no knowledge of the wave function is needed and in the case of importance sampling where we advocate the use of a guiding wave function to guide the simulation. We show that in the latter, the algorithm converges faster with less relative error. In the particular case of the 1D transverse field Ising model, we find the algorithm to be unstable due to the biases introduced by the system size, time step, and auto-correlation. We find in the case of non-symmetrized and symmetrized Trotter approximation of the Green’s function a linear and quadratic dependence of the relative error on the time step, respectively, which is nothing more than the consequence of the bias due to the time step. First, we address the issue of auto-correlation in our data set with the so-called block averaging, which yields uncorrelated data sets. Later, we implement projective quantum Monte Carlo in the continuous time limit, which enables us to eradicate completely the error due to the time step. Finally, we propose a protocol using recurrent neural networks that enables us to formally generalize the idea of generating, through an unsupervised self-learning process, a good approximated guiding wave function.
  • Thumbnail Image
    Item type: Item ,
    Nanite vs. Traditional LOD: Real-Time Performance and User Experience in VR for Participatory Urban Planning
    (University of Waterloo, 2026-09-10) Li, Fu
    Virtual reality (VR) now becomes an emerging tool in urban planning to help people visualize designs, especially in participatory planning. However, showing high-polygons 3D models in VR can slow down computers, particularly in real-time rendering scenarios. Traditional level of details (LODs) techniques addresses this issue through manual mesh simplification and distance-based model switching, but these approaches are labor-intensive and may result in visual artifacts. Nanite, Unreal Engine 5’s virtualized geometry system, promises to overcome these limitations by dynamically streaming and rendering the only visible pixels in real time. Although Epic Games officially promotes Nanite as a superior alternative to conventional LOD workflows, several inconsistent evaluation results have been reported in the community. Several reports have already shown that Nanite incurred substantial GPU overhead and did not outperform traditional overdraw LODs in gaming and filming area, while its applicability in urban planning workflows remains underexplored. Accordingly, this study evaluates the real-time performance of Nanite in comparison to traditional LOD-based workflows, with a focus on computational efficiency and user experience. The University of Waterloo’s new M4 building and its surrounding campus serve as the case study. A 3D model of the building was developed using Autodesk Revit, processed in ArcGIS Pro, and imported into Unreal Engine to develop a VR environment. Two VR versions were created: one using a traditional LOD workflow and the other using Nanite-enabled assets, both derived from the same base model to ensure a fair comparison. User experience data and computational performance metrics were collected from 28 participants who experienced both two VR models. The results show that Nanite significantly reduces polygon counts compared to traditional LOD, confirming its advantage for dense architectural models. However, Nanite also introduces higher GPU overhead and less stable frame rate under VR conditions, challenging its direct applicability in participatory planning. User experience data indicated that participants preferred the traditional LOD approach with 64% favouring it over Nanite. This research addresses a gap in the literature by assessing Nanite’s suitability for participatory planning applications through both system performance evaluation and user experience analysis within architectural VR environments.
  • Thumbnail Image
    Item type: Item ,
    Design and Evaluation of the Effectiveness of a Scaled Single-Compartment Experimental System
    (University of Waterloo, 2026-09-10) Dabrowski, Jan
    Introducing a combustible material like mass timber will increase the fuel loading of the compartment, where this added fuel can lead to ‘non-standard’ fire behavior that changes with ventilation conditions. The National Building Code of Canada guidelines lack design provisions that address this ‘non-standard’ fire behavior, and there are no elaboration provided on how the thermal boundary conditions and the fire induced environment changes with the introduction of exposed mass timber for different ventilation conditions. To validate the impact of changing the design parameters such as introducing exposed mass timber or altering the ventilation conditions, then it is crucial to describe the thermal boundary conditions and the fire induced environment. However, to describe the thermal boundary conditions and the fire induced environment of a compartment fire, single-compartment fire tests with variety and high resolution data are necessary. As a part of the ‘Compartment Fire Dynamics in Timber Structures Under Differing Ventilation Scenarios’ research project, the focus is to collect and review existing experiments and data on the behavior of fires in compartments within mass timber buildings under realistic fire exposure. In addition, the work undertook to design and characterize an instrumented scaled single-compartment experimental system in which design parameters, such as the ventilation conditions, location and percentages of exposed mass timber could systematically be varied is outlined. Compartment fire tests with different loads and fuels are tested within the experimental system to establish a suitable realistic fire exposure for the scaled compartment. The tests aimed to utilize established realistic fire exposure for further testing and to investigate the effectiveness of the experimental system to capture differences in the thermal boundary conditions and the fire induced environment between a reference case and one with 5% exposed CLT. For the instrumented scaled single-compartment experimental system, the design fire determined as suitable to achieve the thermal boundary conditions required for ignition and charring of the exposed CLT was a 36 stick wood crib fire with an average fuel loading of 130 MJ/m². The comparative plots between the other fuel loads and types reveal that the wood crib could achieve gas temperatures and heat fluxes above the threshold values (500ᵒC and 20 kW/m²) most consistently for the longest duration of time. A broad summary of the compartment fire results present the high resolution of thermocouples and DFT heat flux gauges inside the compartment and the instrumentation in the compartment opening of the test compartment are determined to be effective. The effectiveness of the high resolution of thermocouples instrumented inside the test compartment was demonstrated by the creation of detailed gas temperature results, which captured the contribution of the added 5% exposed CLT to the compartment fire environment in comparison to the reference case. Capturing the increased gas temperatures both globally and locally to the walls in proximity to the burning CLT. Sufficient data was obtained to estimate the HRR in the compartment opening, model the time evolution of the NP height throughout the fire, and model the mass inflow and outflow across the compartment opening. Details of small changes in the NP height, mass outflow, and mass inflow due to the introduction of 5% exposed CLT were captured. Estimations of opening HRR revealed that the majority of combustion occurred inside the test compartment even with the introduction of 5% exposed CLT, but further testing is needed to confirm if this would hold for different ventilation conditions. In addition, these comparisons have revealed that the mixing in the compartment opening and fluctuations in the NP height could influence estimations of opening HRR. Future testing is needed with changes in the percentages of exposed mass timber and ventilation conditions to determine if the fluctuations in NP height or mixing in the compartment opening worsens such that estimation of the opening HRR is no longer feasible. The sensitivity of the thermocouples inside the compartment was demonstrated by its ability to capture that the ignition of the CLT occurred within a range of gas temperatures between 423ᵒC to 481ᵒC, and that the CLT flameout occurred within a range of gas temperatures between 573ᵒC to 588ᵒC. The effectiveness of the high density of heat flux gauges was highlighted by its ability to capture that the exposed CLT increases the severity of heat flux exposure in different locations through a fire test. The high resolution of O₂, CO₂, and CO effectively captured local and global differences with the introduction of 5% exposed CLT. These differences included the overall greater consumption of oxygen globally, the creation of locally oxygen-limited state that affects both the hot layer and the wood crib, increased global production of CO₂, and decreased local production of CO. The furniture calorimeter captured that even with 5% exposed CLT it could significantly increase the fire size and severity. The high variety of instrumentation captured that the introduction of 5% exposed CLT decreased the combustion efficiency of the wood crib fuel. Furthermore, the combination of in-depth thermocouples and the ability to perform cross-sectional cuts of the reduced scale CLT specimen provided insight into the impact compartment fire exposure has on charring and the thermal propagation of heat. Overall, the instrumented scaled single-compartment experimental system is effective in capturing differences in thermal boundary conditions and fire induced environment generated in fires with and without a small percentage of exposed CLT. However, recommendations are presented on how to increase the robustness of data collected by test compartment and to improve the effectiveness of test compartment in capturing differences in the fire induced environments. Recommendations were also advanced for future work with different design parameters that will provide further insight into the test compartments effectiveness and address current knowledge gaps.