University of WaterlooThe University of Waterloo institution-wide UWSpace community.http://hdl.handle.net/10012/12023-06-05T14:20:16Z2023-06-05T14:20:16ZDevelopment of a Moving Front Kinetic Monte Carlo Algorithm to Simulate Moving Interface SystemsChaffart, Donovanhttp://hdl.handle.net/10012/195202023-06-03T02:31:02Z2023-06-02T00:00:00ZDevelopment of a Moving Front Kinetic Monte Carlo Algorithm to Simulate Moving Interface Systems
Chaffart, Donovan
Moving interfaces play vital and crucial roles in a wide variety of different natural, technological, and industrial processes, including solids dissolution, capillary action, sessile droplet spreading, and superhydrophobicity. In each of these systems, the fundamental process behaviour is entirely dependent on the interface and on the underlying physics governing its movement. As a result, there is significant interest in studying and developing models to capture the behaviour of these moving interface systems over a wide variety of different applications. However, the simulation techniques used to model moving interfaces are limited in their application, as the molecular-level models are unable to simulate interface behaviour over large spatial and temporal scales, whereas the large-scale modeling techniques cannot account for the nanoscale processes that govern the interface behaviour or the molecular-scale fluctuations and deviations in the interface. Furthermore, methods developed to bridge the gap between the two scales are prone to error-induced force imbalances at the interface that can result in fictitious behaviour.
In order to overcome these challenges, this study developed a novel kinetic Monte Carlo (kMC)-based modelling technique referred to as Moving Front kMC (MFkMC) to adequately and efficiently capture the molecular-scale events and forces governing the moving interface behaviour over large length and timescales. This framework was designed to capture the movement of transiently-varying interfaces in a kinetic-like manner so that its movement can be described using Monte Carlo sampling. The MFkMC algorithm accomplishes this task by evaluating the behaviour of the interfacial molecules and assigning kinetic Monte Carlo-style rate equations that describe the transition probability that a molecule would advance into the neighbouring phase, displacing an interfacial molecule from the opposing phase and thus changing the interface. The proposed algorithm was subsequently used to capture the moving interface behaviour within crystal dissolution, capillary rise, and sessile droplet spreading on both smooth and superhydrophobic surfaces. The individual system models for each application were used to analyze the behaviour within each application and to tackle challenges within each field.
The MFkMC modelling method was initially used to capture crystal dissolution for applications in pharmaceutical drug delivery. The developed model was designed to predict the dissolution of a wide variety of crystalline minerals, regardless of their composition and crystal structure. The MFkMC approach was compared against a standard kMC model of the same system to validate the MFkMC approach and highlight its advantages and limitations. The proposed framework was used to explore ways of enhancing crystal dissolution processes by assessing the variability from environmental uncertainties and by performing robust optimization to improve the dissolution performance. The approach was used to simulate calcium carbonate dissolution within the human gastrointestinal system. Polynomial chaos expansions (PCEs) were used to propagate the parametric uncertainty through the kMC model. Robust optimization was subsequently performed to determine the crystal design parameters that achieve target dissolution specifications using low-order PCE coefficient models (LPCMs). The results showcased the applicability of the kMC crystal dissolution model and the need to account for dissolution uncertainty within key biological applications.
The MFkMC approach was additionally used to capture capillary rise in cavities of different shapes. The proposed model was adapted to capture the movement of a fluid-fluid interface, such as the moving interface present in capillary action studies, using kMC type approaches based on the forces acting locally upon the interface. The proposed force balance-based MFkMC (FB-MFkMC) expressions were subsequently coupled with capillary action force balance equations to capture capillary rise within any axisymmetric cavity. The developed model was validated against known analytical models that capture capillary rise dynamics in perfect cylinders. Furthermore, the resulting multiscale model was used to analyze capillary rise within axisymmetric cavities of irregular shape and in cylinders subject to surface roughness. These studies highlighted that the FB-MFkMC algorithm can capture the macroscale behaviour of a system subject to molecular-level irregularities such as surface roughness. Furthermore, they highlighted that phenomena such as roughness can significantly affect moving interface behaviour and highlight the need to accommodate for these phenomena.
MFkMC was furthermore extended to capture sessile droplet spreading on a smooth surface. The developed approach adapted the capillary action FB-MFkMC model to capture the spreading behaviour of a droplet based on the force balance acting upon the droplet interface, which was developed using analytical inertial and capillary expressions from the literature. This study furthermore derived a new semi-empirical expression to depict the viscous damping force acting on the droplet. The developed viscous force term depends on a fitted parameter c, whose value was observed to vary solely depending on the droplet liquid as captured predominantly by the droplet Ohnesorge number. The proposed approach was subsequently validated using data obtained both from conducted experiments and from the literature to support the robustness of the framework. The predictive capabilities of the developed model were further inspected to provide insights on the sessile droplet system behaviour.
The developed FB-MFkMC model was additionally modified to capture sessile droplet spreading on pillared superhydrophobic surfaces (SHSs). These adjustments included developing the Periodic Unit (PU) method of capturing periodic SHS pillar arrays and accommodating for the changes necessary to capture the droplet spreading behaviour across the gaps between the pillars (i.e., Cassie mode wetting). The proposed SHS-based FB-MFkMC (SHS-MFkMC) model was furthermore adapted to accommodate for spontaneous Cassie-to-Wenzel (C2W) droplet transitions on the solid surface. The capabilities of the full SHS-MFkMC model to capture both radial sessile droplet spread and spontaneous C2W transitions were compared to experimental results from within the literature. Furthermore, a sensitivity analysis was conducted to assess the effects of the various system parameters on the model performance and compare them with the expected system results.
2023-06-02T00:00:00ZAlgorithms in Intersection Theory in the PlaneSt-Pierre, Catherinehttp://hdl.handle.net/10012/195192023-06-03T02:30:59Z2023-06-02T00:00:00ZAlgorithms in Intersection Theory in the Plane
St-Pierre, Catherine
This thesis presents an algorithm to find the local structure of intersections of plane curves. More precisely, we address the question of describing the scheme of the quotient ring of a bivariate zero-dimensional ideal $I\subseteq \mathbb K[x,y]$, \textit{i.e.} finding the points (maximal ideals of $\mathbb K[x,y]/I$) and describing the regular functions on those points. A natural way to address this problem is via Gr\"obner bases as they reduce the problem of finding the points to a problem of factorisation, and the sheaf of rings of regular functions can be studied with those bases through the division algorithm and localisation.
Let $I\subseteq \mathbb K[x,y]$ be an ideal generated by $\mathcal F$, a subset of $\mathbb A[x,y]$ with $\mathbb A\hookrightarrow\mathbb K$ and $\mathbb K$ a field. We present an algorithm that features a quadratic convergence to find a Gr\"obner basis of $I$ or its primary component at the origin.
We introduce an $\mathfrak m$-adic Newton iteration to lift the lexicographic Gr\"obner basis of any finite intersection of zero-dimensional primary components of $I$ if $\mathfrak m\subseteq \mathbb A$ is a \textit{good} maximal ideal. It relies on a structural result about the syzygies in such a basis due to Conca \textit{\&} Valla (2008), from which arises an explicit map between ideals in a stratum (or Gr\"obner cell) and points in the associated moduli space. We also qualify what makes a maximal ideal $\mathfrak m$ suitable for our filtration.
When the field $\mathbb K$ is \textit{large enough}, endowed with an Archimedean or ultrametric valuation, and admits a fraction reconstruction algorithm, we use this result to give a complete $\mathfrak m$-adic algorithm to recover $\mathcal G$, the Gr\"obner basis of $I$. We observe that previous results of Lazard that use Hermite normal forms to compute Gr\"obner bases for ideals with two generators can be generalised to a set of $n$ generators. We use this result to obtain a bound on the height of the coefficients of $\mathcal G$ and to control the probability of choosing a \textit{good} maximal ideal $\mathfrak m\subseteq\mathbb A$ to build the $\mathfrak m$-adic expansion of $\mathcal G$.
Inspired by Pardue (1994), we also give a constructive proof to
characterise a Zariski open set of $\mathrm{GL}_2(\mathbb K)$ (with action on $\mathbb K[x,y]$) that changes coordinates in such a way as to ensure the initial term ideal of a zero-dimensional $I$ becomes Borel-fixed when $|\mathbb K|$ is sufficiently large. This sharpens our analysis
to obtain, when $\mathbb A=\mathbb Z$ or $\mathbb A=k[t]$, a complexity less than cubic in terms of the dimension of $\mathbb Q[x,y]/\langle \mathcal G\rangle$ and softly linear in the height of the coefficients of $\mathcal G$.
We adapt the resulting method and present the analysis to find the $\langle x,y\rangle$-primary component of $I$. We also discuss the transition towards other primary components via linear mappings, called \emph{untangling} and \emph{tangling}, introduced by van der Hoeven and Lecerf (2017). The two maps form one isomorphism to find points with an isomorphic local structure and, at the origin, bind them. We give a slightly faster tangling algorithm and discuss new applications of these techniques. We show how to extend these ideas to bivariate settings and give a bound on the arithmetic complexity for certain algebras.
2023-06-02T00:00:00ZIdentifying Determinants of Performance for Females Completing a Paramedic Physical Employment TestMalone, Alexanderhttp://hdl.handle.net/10012/195182023-06-03T02:30:55Z2023-06-02T00:00:00ZIdentifying Determinants of Performance for Females Completing a Paramedic Physical Employment Test
Malone, Alexander
Background: Sex disparities exist in employment and injury rates in the paramedic sector. Low success rates among females attempting physical employment standards could explain the elevated injury risk among female paramedics. Identifying factors that underpin successful work-related performance can inform pre-hire and return-to-work based physical training programs to address these disparities.
Purpose: The purpose of this thesis was to identify the determinants of successful physical performance for females engaged in paramedic tasks.
Research Question 1: Participant demographics, college type, employment status and heart rate were obtained from female participants who completed the Ottawa Paramedic Physical Abilities Test (OPPAT), a physical employment standard for paramedics. These data were used in a logistic regression model to determine which factors could predict the likelihood of successfully completing the OPPAT. Females who were actively employed, who were educated in a public paramedic college, who had higher body mass, or those who had lower BMI were more likely to successfully complete the OPPAT.
Research Question 2: Lift duration and the time between peak knee and hip joint angular velocity during the Scoop and Barbell lift were compared between females who passed and failed the Ottawa Paramedic Physical Abilities Test. Four ANCOVAs were used for these comparisons where college type (public or private) and employment status (employed or unemployed) were used as categorical factors and body mass and BMI were used as covariates. No significant differences were found between passing and failing females.
Discussion: Modulating demographic factors that increase the likelihood of success could lead to improved performance outcomes, but other determinants should be explored to improve the predictive ability of the current model. Future research should continue to leverage emerging technology, such as markerless motion capture and unsupervised machine learning, to identify determinants of success for females in paramedic tasks.
2023-06-02T00:00:00ZOn Nonlinear Time-Invariant Behavioural Models of Power Transistors Used in the Computer-Aided Design of Power AmplifiersAmini, Amir-Rezahttp://hdl.handle.net/10012/195172023-06-02T02:30:57Z2023-06-01T00:00:00ZOn Nonlinear Time-Invariant Behavioural Models of Power Transistors Used in the Computer-Aided Design of Power Amplifiers
Amini, Amir-Reza
The Radio Frequency (RF) Power Amplifier (PA) is the main consumer of power in a wireless transmitter. Energy efficient PA design aided with circuit simulation tools requires accurate nonlinear models of the power transistors that lie at the heart of the PAs. This thesis proposes a novel methodology for extracting and implementing power transistor behavioral models from load-pull measurements. These models provide a valuable design aid to power amplifier designers looking to simulate the nonlinear behaviour of their RF circuit designs based on nonlinear characterizations of the power transistors.
Two types of power transistor behavioural models are proposed in this work. The first type is called the time-domain poly-harmonic distortion model (TD-PHD) and it targets the nonlinear multi-harmonic response of power transistors at a fixed fundamental frequency. This type of model allows the PA designer to simulate how the harmonic impedances of their designed RF matching networks effects the large signal behaviour of the PA. The TD-PHD model is shown to be able to replicate the time-domain waveforms of a power transistor under multi-harmonic source and load-pull characterization.
The second model is a generalization of the first model to target a set of non-uniformly spaced fundamental frequencies and is called the time-domain multi-tone distortion model (TD-MTD). Time-domain multi-tone distortion models that are extracted from load-pull measurements spanning multiple carrier frequencies are shown to recreate the load-pull performance contours of interest to PA designers. As a demonstration of TD-MTD models, two distinct behavioural models for the main and peaking transistors of a two-way Doherty PA design are extracted from load-pull measurements and the resulting PA design is then simulated and shown to accurately reflect the measured performance of the fabricated PA as a validation of the usefulness of this modelling methodology for high power amplifier design.
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