Applied Mathematics
This is the collection for the University of Waterloo's Department of Applied Mathematics .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
Recent deposits

Particle Clustering and Subclustering as a Proxy for Mixing in Geophysical Flows
(University of Waterloo, 20190816)The Eulerian point of view is the traditional theoretical and numerical tool to describe fluid mechanics. Some modern computational fluid dynamics codes allow for the efficient simulation of particles, in turn facilitating ... 
Prandtl number dependence of stratified turbulence
(University of Waterloo, 20190815)Stratified turbulence is affected by buoyancy forces that suppress vertical motion, resulting in a horizontallylayered structure with quasitwodimensional vortices. The Prandtl number Pr quantifies the relative strengths ... 
Model for the RETC thalamic circuit with application to childhood absence epilepsy
(University of Waterloo, 20190812)Childhood absence epilepsy (CAE) is an idiopathic neurological disorder aﬀecting roughly 28 children per 100,000 children worldwide. It is characterized by absence seizures, or short lapses in consciousness, and the ... 
Relativistic Theory of the Interaction of TwoDimensional Materials with Moving Charged Particles
(University of Waterloo, 20190808)Prompted by the recent surge of interest in integrating atomically thin layers of conducting materials into nanophotonic and nanoplasmonic devices; we propose, in this thesis, a theoretical framework to analyze the ... 
Correlation and Communication via a Quantum Field
(University of Waterloo, 20190715)We study the ability of qubit detectors to i) extract correlations from, and ii) transmit quantum information through, a quantum field. We start by perturbatively studying the harvesting of correlations from thermal and ... 
Invariant manifold theory for impulsive functional differential equations with applications
(University of Waterloo, 20190703)The primary contribution of this thesis is a development of invariant manifold theory for impulsive functional differential equations. We begin with an indepth analysis of linear systems, immersed in a nonautonomous ... 
Kalman Filter Based Sensor Placement For Burgers Equation
(University of Waterloo, 20190603)The algorithm used for determining sensor placement in this thesis will be based on the Kalman filter. This filter is very famous and its application are numerous  some examples include aircraft navigation, finance and ... 
Numerical Simulations of Internal Solitary and SolitaryLike Waves: Wave Interactions and Instabilities
(University of Waterloo, 20190531)Internal solitary and solitarylike waves (ISWs) are commonly observed in stably stratified fluids such as the Earth's atmosphere and oceans. As these waves interact with other physical processes and/or move through a ... 
Estimation for Linear and Semilinear Infinitedimensional Systems
(University of Waterloo, 20190521)Estimating the state of a system that is not fully known or that is exposed to noise has been an intensely studied problem in recent mathematical history. Such systems are often modelled by either ordinary differential ... 
Three Results in Quantum Physics
(University of Waterloo, 20190509)This thesis is split into three disjoint sections. The ﬁrst deals with two practical issues regarding the use of unitary 2designs. A simpliﬁed description of how to generate elements of the smallest known unitary 2design ... 
Microswimmer Propulsion by Two Steadily Rotating Helical Flagella
(MDPI, 20190101)Many theoretical studies of bacterial locomotion adopt a simple model for the organism consisting of a spheroidal cell body and a single corkscrewshaped flagellum that rotates to propel the body forward. Motivated by ... 
Harnessing surfacebound enzymatic reactions to organize microcapsules in solution
(American Association for the Advancement of Science (AAAS), 201603)By developing new computational models, we examine how enzymatic reactions on an underlying surface can be harnessed to direct the motion and organization of reagentladen microcapsules in a fluidfilled microchannel. In ... 
The effects of flagellar hook compliance on motility of monotrichous bacteria: A modeling study
(AIP Publishing, 201206)A crucial structure in the motility of flagellated bacteria is the hook, which connects the flagellum filament to the motor in the cell body. Early mathematical models of swimming bacteria assume that the helically shaped ... 
Harnessing catalytic pumps for directional delivery of microparticles in microchambers
(Springer Nature, 20170217)The directed transport of microparticles in microfluidic devices is vital for efficient bioassays and fabrication of complex microstructures. There remains, however, a need for methods to propel and steer microscopic cargo ... 
Convective flow reversal in selfpowered enzyme micropumps
(Proceedings of the National Academy of Sciences, 20160222)Surfacebound enzymes can act as pumps that drive largescale fluid flows in the presence of their substrates or promoters. Thus, enzymatic catalysis can be harnessed for "on demand" pumping in nanoand microfluidic devices ... 
Synthetic quorum sensing in model microcapsule colonies
(Proceedings of the National Academy of Sciences, 20170724)Biological quorum sensing refers to the ability of cells to gauge their population density and collectively initiate a new behavior once a critical density is reached. Designing synthetic materials systems that exhibit ... 
An Integral Projection Model for Giant Hogweed
(University of Waterloo, 20190204)In this thesis I investigate the impact that the choice of model may have on predictions of giant hogweed population dynamics. It has been shown in two case studies that population growth rates predicted by matrix population ... 
What is a field, what is a particle?...what about algebras?
(University of Waterloo, 20190125)Much of the structure of quantum field theory (QFT) is predicated on the principle of locality. Adherence to locality is achieved in Algebraic QFT (AQFT) by the association of algebras of observables with regions of ... 
Sensitivity of Idealized Squall Line Simulation to Resolution and Subgrid Turbulence Mixing
(University of Waterloo, 20190123)In this project, the sensitivity of idealized squall line simulations to horizontal grid spacing and turbulent mixing parameterization will be discussed. Inconsistent results from numerical simulations of convective ... 
Wave Refraction Effects in High Intensity Focused Ultrasound
(University of Waterloo, 20190122)HighIntensity Focused Ultrasound (HIFU) is a promising field of research being developed as an alternative to surgery and radiation therapy for the treatment of tumours. Within this field, many current methods of ...