Applied Mathematics
This is the collection for the University of Waterloo's Department of Applied Mathematics.
Recent Submissions

Evolutionary Dynamics of Cancer: Spatial and Heterogeneous Effects
(University of Waterloo, 20170123)Despite significant advances in the study of cancer and associated combination therapeutic treatments, cancer still remains one of the most common and complex oftenterminal diseases. Acquisition of highthroughput ... 
LithiumIon battery SOC estimation
(University of Waterloo, 20170123)Lithiumion batteries are frequently used in Hybrid electric vehicles (HEVs), which are taking the place of gasengine vehicles. An important but not measurable quantity in HEVs is the amount of charge remaining in the ... 
Existence and uniqueness of attracting slow manifolds: An application of the Ważewski principle
(University of Waterloo, 20170123)In this work we present some of the geometric constructs that aid the application of the Ważewski Theorem. To illustrate the procedure the MichaelisMenten mechanism will be considered. We show that M, a slow manifold, ... 
Direct Numerical Simulation of Salt Fingering Gravity Currents and DoubleDiffusive RayleighTaylor Instabilities
(University of Waterloo, 20170118)Doublediffusion refers to a class of instabilities that develops when the density of a fluid depends on two components with different diffusivities. For example, when warm, salty water is layered over cool, fresh water, ... 
Structured Reverse Mode Automatic Differentiation in Nested Monte Carlo Simulations
(University of Waterloo, 20170117)In many practical large scale computational problems, the calculation of partial derivatives of the object function f with respect to input parameters are entailed and the dimension of inputs n is much larger the one of ... 
Probing Quantum Fields: Measurements and Quantum Energy Teleportation
(University of Waterloo, 20170110)Quantum Energy Teleportation provides a testbed for modern ideas involving the interplay between quantum correlations and energy in the quantum thermodynamical regime. In this work, we provide a new class of Quantum Energy ... 
Iterated Function Systems with PlaceDependent Probabilities and the Inverse Problem of Measure Approximation Using Moments
(University of Waterloo, 20161025)The study of iterated function systems has close ties with the subject of fractalbased analysis. One important application is the approximation of a target object by the fixed point of a contractive iterated function ... 
Mathematical Aspects of ScalarTensor Field Theories
(University of Waterloo, 20160927)This thesis is based on a study of Lagrange scalar densities which are, in general, concomitants of the metric tensor gij (and its first and second derivatives) together with a scalar field ∅ (and its first derivative). ... 
Infectious Disease Modeling with Interpersonal Contact Patterns as a Heterogeneous Network
(University of Waterloo, 20160926)In this thesis, we study deterministic compartmental epidemic models. The conventional massmixing assumption is replaced with infectious disease contraction occurring within a heterogeneous network. Modeling infectious ... 
Early Warning Signals of Vaccine Scares.
(University of Waterloo, 20160926)There exists strong evidence that vaccines are extremely effective in the prevention of pediatric infectious disease, yet despite this evidence, vaccine refusal is still popular amongst some parents. Existing mathematical ... 
Noncompact groups, tensor operators and applications to quantum gravity
(University of Waterloo, 20160923)This work focuses on noncompact groups and their applications to quantum gravity, mainly through the use of tensor operators. Noncompact groups appear naturally if the spacetime is of Lorentzian signature, but can also ... 
Decoupling of Information Propagation from Energy Propagation
(University of Waterloo, 20160831)Information and energy are concepts central to our understanding of nature. Their relevance, in physics, ranges from fundamental physics, e.g., in black hole physics, all the way to future quantum computing technology. ... 
A Taylor polynomial expansion line search for largescale optimization
(University of Waterloo, 20160829)In trying to cope with the Big Data deluge, the landscape of distributed computing has changed. Large commodity hardware clusters, typically operating in some form of MapReduce framework, are becoming prevalent for ... 
Stability of Nonlinear Functional Differential Equations by the Contraction Mapping Principle
(University of Waterloo, 20160829)Fixed point theory has a long history of being used in nonlinear differential equations, in order to prove existence, uniqueness, or other qualitative properties of solutions. However, using the contraction mapping ... 
Halocline mixing due to heavy rainfall in the cenote's of the Yucatan Peninsula
(University of Waterloo, 20160823)The hydrodynamics of the Yucatan peninsula are extremely important due to the strain on water resources caused by increasing development along the eastern coast. The geology of the peninsula is unique geologically in that ... 
Floating Bodies with Surface Tension
(University of Waterloo, 20160818)Capillary phenomena have been studied by mathematicians and physicists for hundreds of years. In this thesis, both twodimensional(2D) and threedimensional(3D) bodies floating on an unbounded reservoir are studied based ... 
Indirect Quantum Control: An ImplementationIndependent Scheme
(University of Waterloo, 20160817)The ability to control quantum systems rapidly as compared to their coherence times is a central requirement for most proposed quantum technologies, such as quantum computing and quantum metrology. Improving the ratio of ... 
Modeling Photoluminescence Decay Dynamics in Nanocrystals
(University of Waterloo, 20160817)Photoluminescence resulting from donoracceptor recombination in gallium oxide nanocrystals was studied at short and long time scales for different nanocrystal sizes. A model for the intensity decay was formulated with two ... 
Mathematical Modelling of Social Factors in Decision Making Processes at the Individual and Population Levels
(University of Waterloo, 20160811)In this thesis we apply mathematical modelling techniques to investigate the implications of social influence on decision making processes in two related contexts. The first problem concerns the mathematical modelling ... 
A Model for Shear Response in Swimming Plankton
(University of Waterloo, 20160811)The responses of zooplankton to the hydrodynamic variables of their environment, such as shear, are not well understood. We examine stochastic swimming models of the run and tumble type for plankton moving in a velocity ...