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

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 ... 
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 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 ... 
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 ... 
Shape & cutoff in superconducting qubits, work fluctuations in correlation creation, & critical commentary
(University of Waterloo, 20190122)Part I We apply the UnruhDeWitt model for a qubit interacting with a quantum field to a superconducting qubit. We use the flexibility of this model, as compared to the spinboson model used widely in the literature, ... 
Qualitative Properties of Hybrid Singular Systems
(University of Waterloo, 20190115)A singular system model is mathematically formulated as a set of coupled differential and algebraic equations. Singular systems, also referred to as descriptor or differential algebraic systems, have extensive applications ... 
Dimensionality Reduction of the Chemical Master Equation
(University of Waterloo, 20190111)The dynamics of biochemical systems show significant variability when the reactant populations are small. Standard approaches via deterministic modeling exclude such variability. A well established stochastic model, the ... 
Numerical Modelling of Wind Storms in the Lower Great Lakes
(University of Waterloo, 20190107)Convective storms are incredible meteorological events; the impact of just one storm can be extreme and widespread. On July 21 1998, a convective storm formed west of Lake Michigan, moving quickly across the lower Great ... 
Development and Application of Models and Diagnostics for Geophysical Fluid Flows
(University of Waterloo, 20190107)This thesis presents the development and application of numerical tools for simulating and diagnosing quasigeostrophic fluid systems. In this thesis we present a new numerical model called SPIQG that is pseudospectral ... 
Studies of tumor heterogeneity, tumor microenvironment, and radiotherapy: A mathematical and computational approach
(University of Waterloo, 20190104)Radiotherapy uses high doses of energy to eradicate cancer cells and thus destroy the bulk of tumors. Radiobiologists try to precisely deliver radiation to a targeted area in order to maximize the cancer cell kill rate ... 
Spatial correlation as an early warning signal of regime shifts in a multiplex diseasebehaviour network
(Elsevier, 20180707)Early warning signals of sudden regime shifts are a widely studied phenomenon for their ability to quantify a system’s proximity to a tipping point to a new and contrasting dynamical regime. However, this effect has been ... 
On the optimal CFL number of SSP methods for hyperbolic problems
(Elsevier, 20190101)We show that the theory for strong stability preserving (SSP) time stepping methods employed with the method of linestype discretizations of hyperbolic conservation laws may result in overly stringent time step restrictions. ... 
On fixed points of self maps of the free ball
(Elsevier, 20180701)In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ... 
Convergence of socioecological dynamics in disparate ecological systems under strong coupling to human social systems
(20180406)It is widely recognized that coupled socioecological dynamics can be qualitatively different from the dynamics of social or ecological systems in isolation from one another. The influence of the type of ecological dynamics ...