Applied Mathematics: Recent submissions
Now showing items 41-60 of 491
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A Critical Examination of Two Specific Approaches Used to Characterize Medical Images: i) Projection-based Descriptors for Image Retrieval and ii) Estimating Fractal Dimensions of Discrete Sets
(University of Waterloo, 2022-08-31)In this thesis we provide a critical examination of two methods which are used to characterize medical images. Accordingly, this thesis is split into two main parts. First, we take a look at the problem of designing ... -
Boundary-Bound Reactions: Pattern Formation with and without Hydrodynamics
(University of Waterloo, 2022-08-23)Pattern formation through chemical morphogenesis has received a significant amount of attention since Alan Turing's original analysis in a Chemical Basis for Morphogenesis. In that article, Turing showed the surprising ... -
High-Resolution Analysis of Snow Albedo Interactions in the Arctic
(University of Waterloo, 2022-08-23)The Snow Albedo Feedback (SAF) is an important contributor to Arctic warming, however models disagree significantly on the strength of this effect. Previous work has investigated the influence of vegetation on surface ... -
q-deformed LQG in three dimensional space-time
(University of Waterloo, 2022-08-23)Loop quantum gravity (LQG) is a canonical, background-independent and non-perturbative approach to quantum gravity. This thesis is devoted to studying three-dimensional (3D) quantum gravity with a non-vanishing cosmological ... -
Limiting techniques for the discontinuous Galerkin method on unstructured meshes
(University of Waterloo, 2022-08-18)Many complex phenomena like shock-shock interactions, shock-vortex interactions, stratified flows, etc., are governed by nonlinear hyperbolic conservation laws. Higher order numerical schemes like the discontinuous Galerkin ... -
Numerical analysis of space-time hybridized discontinuous Galerkin methods for incompressible flows
(University of Waterloo, 2022-08-09)Many industrial problems require the solution of the incompressible Navier-Stokes equations on moving and deforming domains. Notable examples include the simulation of rotating wind turbines in strong air flow, wave impact ... -
Numerical simulations of convection and gravity currents near the temperature of maximum density
(University of Waterloo, 2022-08-09)Recently, the dynamics of flows in cold freshwater (temperatures around the temperature of maximum density, 3.98 oC) has garnered much interest in the environmental fluid dynamics community. From a dynamical perspective, ... -
Jets, Vortices and Turbulence in Quasi-Geostrophic Magnetohydrodynamics
(University of Waterloo, 2022-07-28)In this thesis, we model the dynamics of the solar tachocline and the Earth's molten core using a shallow, rapidly rotating, and electrically conducting fluid on an f-plane. We explore the effects of a strong uniform ... -
Machine Learning Techniques and Stochastic Modeling in Mathematical Oncology
(University of Waterloo, 2022-07-18)The cancer stem cell hypothesis claims that tumor growth and progression are driven by a (typically) small niche of the total cancer cell population called cancer stem cells (CSCs). These CSCs can go through symmetric ... -
Three-dimensional simulations of sound propagation in a trumpet with accurate mouthpiece shank geometry
(arXiv, 2016-11-01)The length and bore geometry of musical instruments directly influences the quality of sound that can be produced. In brass instruments, nonlinear effects from finite-amplitude wave propagation can lead to wave distortion ... -
Galerkin Finite Element Based Modeling of One Dimensional Packed Bed Reactor for Underground Coal Gasification (UCG) Process
(IEEE, 2020-12-11)Mathematical models of a complex physicochemical underground coal gasification process involve multidimensional non-linear partial differential equations (PDEs). Therefore, researchers always seek a suitable numerical ... -
On the TVD property of second order methods for 2D scalar conservation laws
(arXiv, 2021-10-05)The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation laws. However, it proved to be challenging ... -
Bidirectional TopK Sparsification for Distributed Learning
(University of Waterloo, 2022-05-27)Training large neural networks requires a large amount of time. To speed up the process, distributed training is often used. One of the largest bottlenecks in distributed training is communicating gradients across different ... -
Analysis of a pressure-robust hybridized discontinuous Galerkin method for the stationary Navier-Stokes equations
(Springer, 2019-08-30)We present well-posedness and an a priori error analysis of the hybridized discontinuous Galerkin method for the stationary form of the Navier-Stokes problem proposed in (J Sci Comput, 76(3):1484{ 1501, 2018). This scheme ... -
Mathematical Modeling of Kidney Function During Pregnancy
(University of Waterloo, 2022-05-16)During pregnancy major adaptations must occur in the maternal body to be able to support the rapidly developing fetus and placenta. Adaptations occur in almost all tissues and organs. These changes are dynamic, complex, ... -
Some Mathematical Perspectives of Graph Neural Networks
(University of Waterloo, 2022-05-12)Many real-world entities can be modelled as graphs, such as molecular structures, social networks, or images. Despite coming with such a great expressive power, the complex structure of graphs poses significant challenges ... -
A Sparse Random Feature Model for Signal Decomposition
(University of Waterloo, 2022-05-11)Signal decomposition and multiscale signal analysis provide useful tools for time-frequency analysis. In this thesis, an overview of the signal decomposition problem is given and popular methods are discussed. A novel ... -
Characteristics of quasistationary near-wall turbulence subjected to strong stable stratification in open-channel flows
(American Physical Society, 2020-06-05)Characteristics of near-wall turbulence at quasistationarity under strong wall cooling are studied using direct numerical simulation of open-channel flow. It is shown that if turbulence reaches quasistationarity, then the ... -
Three-dimensional Simulations of an Internal Solitary Wave Shoaling Over a Shallow Slope
(University of Waterloo, 2022-05-03)The transport of sediment is vital for ecological and climatological processes. Sediment can either move up the shelf, or mix into the upper water column as nepheloid layers. Internal solitary waves (ISWs) shoaling along ... -
Numerical analysis of divergence-free discontinuous Galerkin methods for incompressible flow problems
(University of Waterloo, 2022-04-29)In the first major contribution of this thesis, we present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact ...