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
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Analysis of a pressure-robust hybridized discontinuous Galerkin method for the stationary Navier-Stokes equations
(Springer, 2019-08-30)We present well-posedness and an a priori error analysis of the hybridized discontinuous Galerkin method for the stationary form of the Navier-Stokes problem proposed in (J Sci Comput, 76(3):1484{ 1501, 2018). This scheme ... -
Mathematical Modeling of Kidney Function During Pregnancy
(University of Waterloo, 2022-05-16)During pregnancy major adaptations must occur in the maternal body to be able to support the rapidly developing fetus and placenta. Adaptations occur in almost all tissues and organs. These changes are dynamic, complex, ... -
Some Mathematical Perspectives of Graph Neural Networks
(University of Waterloo, 2022-05-12)Many real-world entities can be modelled as graphs, such as molecular structures, social networks, or images. Despite coming with such a great expressive power, the complex structure of graphs poses significant challenges ... -
A Sparse Random Feature Model for Signal Decomposition
(University of Waterloo, 2022-05-11)Signal decomposition and multiscale signal analysis provide useful tools for time-frequency analysis. In this thesis, an overview of the signal decomposition problem is given and popular methods are discussed. A novel ... -
Characteristics of quasistationary near-wall turbulence subjected to strong stable stratification in open-channel flows
(American Physical Society, 2020-06-05)Characteristics of near-wall turbulence at quasistationarity under strong wall cooling are studied using direct numerical simulation of open-channel flow. It is shown that if turbulence reaches quasistationarity, then the ... -
Three-dimensional Simulations of an Internal Solitary Wave Shoaling Over a Shallow Slope
(University of Waterloo, 2022-05-03)The transport of sediment is vital for ecological and climatological processes. Sediment can either move up the shelf, or mix into the upper water column as nepheloid layers. Internal solitary waves (ISWs) shoaling along ... -
Numerical analysis of divergence-free discontinuous Galerkin methods for incompressible flow problems
(University of Waterloo, 2022-04-29)In the first major contribution of this thesis, we present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact ... -
Tensors: Entanglement, Geometry, and Combinatorics
(University of Waterloo, 2022-04-26)In this thesis, we use algebraic-geometric and combinatorial techniques to study tensor decompositions, with applications in quantum information theory, algebraic complexity theory, and algebraic statistics. A tensor is a ... -
A Phase Model with Large Time Delayed Coupling
(Elsevier, 2020-10)We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting ... -
Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks
(AIMS Press, 2020-11)We study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which ... -
Normalized Connectomes Show Increased Synchronizability with Age through Their Second Largest Eigenvalue
(Society for Industrial and Applied Mathematics, 2021-01)The synchronization of different brain regions is widely observed under both normal and pathological conditions, such as epilepsy. However, the relationship between the dynamics of these brain regions, the connectivity ... -
The Impact of Small Time Delays on the Onset of Oscillations and Synchrony in Brain Networks
(Frontiers Publishing, 2021-07)The human brain constitutes one of the most advanced networks produced by nature, consisting of billions of neurons communicating with each other. However, this communication is not in real-time, with different communication ... -
Dynamics of a Diffusive Nutrient-Phytoplankton-Zooplankton Model with Spatio-temporal Delay
(SIAM, 2021-01)We study a diffusive nutrient-phytoplankton-zooplankton (NPZ) model with spatio-temporal delay. The closed nature of the system allows the formulation of a conservation law of biomass that governs the ecosystem. We advance ... -
Stability of Connected Autonomous Vehicle Networks with Commensurate Time Delays
(IEEE, 2021-05)In this paper, we study the stability of Connected Autonomous Vehicle Networks (CAVN) with commensurate time delays under the assumption that communication time delays increase as the distance between the vehicles increases. ... -
The Effect of Input Signals Time-Delay on Stabilizing Traffic with Autonomous Vehicles
(IEEE, 2021-05)This paper extends the results in [1] considering time delays in Standard Car Following models (CFMs). In [1], connected vehicles are characterized with CFMs models and controlled using linear string analysis to stabilize ... -
Spatially localized cluster solutions in inhibitory neural networks
(Elsevier, 2021-06)Neurons in the inhibitory network of the striatum display cell assembly firing patterns which recent results suggest may consist of spatially compact neural clusters. Previous computational modeling of striatal neural ... -
Hysteresis bifurcation and application to delayed FitzHugh-Nagumo neural systems
(Elsevier, 2021-08)Hysteresis dynamics has been described in a vast number of biological experimental studies. Many such studies are phenomenological and a mathematical appreciation has not attracted enough attention. In the paper, we explore ... -
M-current induced Bogdanov–Takens bifurcation and switching of neuron excitability class
(Springer, 2021-02-15)In this work, we consider a general conductance-based neuron model with the inclusion of the acetycholine sensitive, M-current. We study bifurcations in the parameter space consisting of the applied current Iapp, the maximal ... -
Mathematical Models of Mitochondria in the Kidney and Liver
(University of Waterloo, 2022-03-24)Mitochondria are key players in several kinds of tissue injury, and are even the site of mechanism of certain diseases. In this work we introduce new models of mitochondrial ATP generation in multiple tissues, including ... -
Scale-dependent anisotropy in forced stratified turbulence
(American Physical Society, 2019-04)In stratified turbulence, buoyancy forces inhibit vertical motion and lead to anisotropy over a wide range of length scales, which is characterized by layerwise pancake vortices, thin regions of strong shear, and patches ...
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