Browsing Applied Mathematics by Type "Master Thesis"
Now showing items 120 of 215

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 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 ... 
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 ... 
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 ... 
Bayesian Analysis of Intratumoural Oxygen Data
(University of Waterloo, 20090828)There is now ample evidence to support the notion that a lack of oxygen (hypoxia) within the tumour adversely affects the outcome of radiotherapy and whether a patient is able to remain disease free. Thus, there is increasing ... 
Bidirectional TopK Sparsification for Distributed Learning
(University of Waterloo, 20220527)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 ... 
Bifurcation analysis of a system of MorrisLecar neurons with time delayed gap junctional coupling
(University of Waterloo, 20080827)We consider a system of two identical MorrisLecar neurons coupled via electrical coupling. We focus our study on the effects that the coupling strength, γ , and the coupling time delay, τ , cause on the dynamics of the ... 
Black Hole to White Hole Quantum Tunnelling
(University of Waterloo, 20190826)In this thesis, we explore the proposal that near the end of its lifetime, a Schwarzschild black hole will undergo a quantum transition into a 'white hole': an object which is precisely the timereversal of the black hole. ... 
Bohmian Trajectories of the TwoElectron Helium Atom
(University of Waterloo, 20080117)We introduce the de BroglieBohm causal interpreation of quantum mechanics and compare it to the standard interpretation of quantum mechanics, the Copenhagen interpretation. We examine the possibility of experimentally ... 
BoundaryBound Reactions: Pattern Formation with and without Hydrodynamics
(University of Waterloo, 20220823)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 ... 
Brownian Dynamics Simulation of Dusty Plasma: Comparison with Generalized Hydrodynamics
(University of Waterloo, 20100414)Brownian dynamics (BD) simulation method has been widely used for studying problems in dispersed systems, such as polymer solutions, colloidal suspensions and more recently, complex (dusty) plasmas. The main problem addressed ... 
Calcium Transport and Regulation in Male and Female Rat Kidney
(University of Waterloo, 20230516)Calcium is an essential mineral that plays a critical role in many biological processes, such as muscle contraction, nerve function, and bone health. However, maintaining the right balance of calcium in the body is crucial ... 
Combination of Chemotherapy and Antiangiogenic Therapies: A Mathematical Modelling Approach
(University of Waterloo, 20090908)A brief introduction to cancer biology and treatment is presented with a focus on current clinical advances in the delivery of chemotherapy and antiangiogenic therapies. Mathematical oncology is then surveyed with summaries ... 
A Comparative and Exploratory Study of Homogeneous and Inhomogeneous Stratified Turbulence
(University of Waterloo, 20210825)The study of turbulence in the oceans and atmosphere is farflung and everreaching in the academic world with research being done theoretically, experimentally and numerically. With great strides in the increasing power ... 
Comparison of Approximation Schemes in Stochastic Simulation Methods for Stiff Chemical Systems
(University of Waterloo, 20090730)Interest in stochastic simulations of chemical systems is growing. One of the aspects of simulation of chemical systems that has been the prime focus over the past few years is accelerated simulation methods applicable ... 
A comparison of the Kalman filter and recurrent neural networks for state estimation of dynamical systems
(University of Waterloo, 20230830)The study of dynamical systems is of great interest in many fields, with a wide range of applications. In some cases, these dynamical systems may be affected by noise and the availability of measurements may be limited. ...