Browsing Applied Mathematics by Title
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Aging affects circadian clock and metabolism and modulates timing of medication
(Elsevier, 202104)Aging is associated with impairments in the circadian rhythms, and with energy deregulation that affects multiple metabolic pathways. The goal of this study is to unravel the complex interactions among aging, metabolism, ... 
Algebraic Multigrid for Markov Chains and Tensor Decomposition
(University of Waterloo, 20130123)The majority of this thesis is concerned with the development of efficient and robust numerical methods based on adaptive algebraic multigrid to compute the stationary distribution of Markov chains. It is shown that classical ... 
Algorithms and Models for Tensors and Networks with Applications in Data Science
(University of Waterloo, 20160119)Big data plays an increasingly central role in many areas of research including optimization and network modeling. We consider problems applicable to large datasets within these two branches of research. We begin by ... 
AlmostSure Stability of a Noisy Autoparametric Vibration Absorber
(University of Waterloo, 20221213)This thesis investigates the almostsure stability of the single mode solution of a two degreeoffreedom, noisy, nonlinear autoparametric system. While only the first mode is forced in such a system, the nonlinear coupling ... 
Analysis of a pressurerobust hybridized discontinuous Galerkin method for the stationary NavierStokes equations
(Springer, 20190830)We present wellposedness and an a priori error analysis of the hybridized discontinuous Galerkin method for the stationary form of the NavierStokes problem proposed in (J Sci Comput, 76(3):1484{ 1501, 2018). This scheme ... 
Analysis of Asymptotic Solutions for Cusp Problems in Capillarity
(University of Waterloo, 20070927)The capillary surface $u(x,y)$ near a cusp region satisfies the boundary value problem: \begin{eqnarray} \nabla \cdot \frac{\nabla u}{\sqrt{1+\left\nabla u \right^2}}&=&\kappa u \qquad \textrm{in }\left\{(x,y): ... 
Analysis of LightMatter Systems
(University of Waterloo, 20220118)In this thesis we introduce the simplest model of a two–level system coupled to a single mode of an optical cavity, called the JaynesCummings model. This model is then extended to an ensemble of identical twolevel systems ... 
Analysis of Plasmons Sustained on the Surface of Graphene
(University of Waterloo, 20140811)This thesis is broken into two parts, both dealing with the role of twodimensional graphene in electronic and optical applications. The first section develops a phenomenological relationship for the polarizability of the ... 
An Analysis of Stockwell Transforms, with Applications to Image Processing
(University of Waterloo, 20140430)Timefrequency analysis is a powerful tool for signal analysis and processing. The Fourier transform and wavelet transforms are used extensively as is the ShortTime Fourier Transform (or Gabor transform). In 1996 the ... 
Angles, Majorization, Wielandt Inequality and Applications
(University of Waterloo, 20130529)In this thesis we revisit two classical definitions of angle in an inner product space: realpart angle and Hermitian angle. Special attention is paid to Krein’s inequality and its analogue. Some applications are given, ... 
An Anisotropic SubgridScale Parameterization for LargeEddy Simulations of Stratified Turbulence
(AMS, 20201001)Subgridscale (SGS) parameterizations in atmosphere and ocean models are often defined independently in the horizontal and vertical directions because the grid spacing is not the same in these directions (anisotropic ... 
Annular Capillary Surfaces: Properties and Approximation Techniques
(University of Waterloo, 20070917)The capillary surface formed within a symmetric annular tube is analyzed. Assuming identical contact angles along each boundary, we consider surfaces u(x,y) that satisfy the capillary problem on an annular region. Several ... 
An Antibiotic Protocol To Minimize Emergence Of DrugResistant Tuberculosis
(Elsevier, 20140415)A withinhost model of the spread of tuberculosis is proposed here where the emergence of drug resistance and bacterial dormancy are simultaneously combined. We consider both sensitive and resistant strains of tuberculosis ... 
Application of Mixture Theory to solid tumors and normal pressure hydrocephalus
(University of Waterloo, 20140115)In this thesis, the theory of poroelasticity, namely the Mixture Theory version  a homogenized, macroscopic scale approach used to describe fluid flow through a porous medium  is employed in three separate cases ... 
Application of repetitive control to the lateral motion in a rolltoroll web system
(University of Waterloo, 20120410)In a rolltoroll web system lateral motion of a web caused by disturbances, which are often periodic, results in poor product quality. To reduce the effect of such disturbances, two control strategies are applied. First, ... 
Application of the LANSalpha Model to Gravity Currents
(University of Waterloo, 20191021)This thesis aims to investigate how HERCULES performs when running a lockexchange gravity current case. The LANSalpha model with stratification is also tested as a subgrid model in HERCULES using the same gravity current ... 
Applications of Deep Learning to Differential Equation Models in Oncology
(University of Waterloo, 20230725)The integration of quantitative tools in biology and medicine has led to many groundbreaking advances in recent history, with many more promising discoveries on the horizon. Conventional mathematical models, particularly ... 
Backscatter in stratified turbulence
(Elsevier, 201611)In this paper, kinetic and potential energy transfers around a spectral test fil ter scale in direct numerical simulations of decaying stratified turbulence are studied in both physical and spectral domains. It is shown ... 
Bandlimited functions, curved manifolds, and selfadjoint extensions of symmetric operators
(University of Waterloo, 20080520)Sampling theory is an active field of research that spans a variety of disciplines from communication engineering to pure mathematics. Sampling theory provides the crucial connection between continuous and discrete ...