Browsing Applied Mathematics by Title
Now showing items 410-429 of 494
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Simulating lake dynamics: the effects of bathymetry and bottom drag
(University of Waterloo, 2011-10-31)This work seeks, through numerical simulations as well as analysis, to derive from relatively simple models an intuitive understanding of the dynamics and behaviour of flow in lakes near the bottom boundary. The main body ... -
Simulating Wintertime Lake Dynamics Using the MITgcm Ice Model
(University of Waterloo, 2020-09-23)Lake Erie is an important source of drinking water, a location for recreational activities and a haven for unique ecosystems (e.g. Point Pelee). Recent research has suggested that some wintertime processes are significantly ... -
Simulation of the Navier-Stokes Equations in Three Dimensions with a Spectral Collocation Method
(University of Waterloo, 2011-05-13)This work develops a nonlinear, three-dimensional spectral collocation method for the simulation of the incompressible Navier-Stokes equations for geophysical and environmental flows. These flows are often driven by the ... -
Simulation of Vortex Interactions With a Solid Wall Using Adaptive Mesh Refinement
(University of Waterloo, 2016-05-12)One feature that is common to many fluid flows is that phenomena of interest often occur at disparate length scales, whether it be vortices interacting with a boundary layer, or shear instabilities on an internal gravity ... -
Simulations of Radiatively Driven Convection and Spatially Heterogeneous Solar Radiation Intensity in Ice-Covered Lakes
(University of Waterloo, 2023-12-22)At the end of winter as sunlight and increasing air temperatures melt the snow layer above the ice, allowing significant radiation from the sun to enter the water column. In the cold water regime (T < 4 °C, where 4 °C is ... -
Smooth centre manifolds for impulsive delay differential equations
(Elsevier, 2018-04-16)The existence and smoothness of centre manifolds and a reduction principle are proven for impulsive delay differential equations. Several intermediate results of theoretical interest are developed, including a variation ... -
Socio-Ecological Dynamics Of Caribbean Coral Reef Ecosystems And Conservation Opinion Propagation
(Nature Publishing Group, 2018-02-07)The Caribbean coral reef ecosystem has experienced a long history of deterioration due to various stressors. For instance, over-fishing of parrotfish - an important grazer of macroalgae that can prevent destructive overgrowth ... -
Solving Hyperbolic PDEs using Accelerator Architectures
(University of Waterloo, 2009-07-27)Accelerator architectures are used to accelerate the simulation of nonlinear hyperbolic PDEs. Three different architectures, a multicore CPU using threading, IBM’s Cell Processor, and Nvidia’s Tesla GPUs are investigated. ... -
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 ... -
Some Theory and Applications of Probability in Quantum Mechanics
(University of Waterloo, 2012-07-19)This thesis investigates three distinct facets of the theory of quantum information. The first two, quantum state estimation and quantum process estimation, are closely related and deal with the question of how to estimate ... -
Space-time Hybridizable Discontinuous Galerkin Method for the Advection-Diffusion Problem
(University of Waterloo, 2024-05-22)In this thesis, we analyze a space-time hybridizable discontinuous Galerkin (HDG) method for the time-dependent advection-dominated advection-diffusion problem. It is well-known that solutions to these problems may admit ... -
Space-time hybridizable discontinuous Galerkin methods for free-surface wave problems
(University of Waterloo, 2020-08-28)Free-surface problems arise in many real-world applications such as in the design of ships and offshore structures, modeling of tsunamis, and dam breaking. Mathematically, free-surface wave problems are described by a set ... -
Sparse Identification of Epidemiological Models from Empirical Data
(University of Waterloo, 2018-09-20)Current modelling practices in mathematical epidemiology are predicated on mechanisms stemming from theoretical assumptions, such as mass action incidence. Deterministic disease models can describe many patterns observed ... -
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 ... -
Spatial and Temporal Discounting in a Social-Climate Model
(University of Waterloo, 2024-01-25)This thesis analyzes how individuals' devaluation of distant impacts of climate change affects mitigation behaviours and projected climate conditions. To approach this question, spatial and temporal discounting is applied ... -
Spatial correlation as an early warning signal of regime shifts in a multiplex disease-behaviour network
(Elsevier, 2018-07-07)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 ... -
A spatially explicit modelling approach for predicting and managing the effects of coral reef stressors
(University of Waterloo, 2022-09-09)Coral reefs represent simultaneously one of the most beloved and one of the most endangered ecosystems in the world. Millions of people visit coral reefs every year for tourism purposes, and millions of people living in ... -
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 ... -
Spatially-Implicit Modelling Of Disease-Behaviour Interactions In The Context Of Non-Pharmaceutical Interventions
(American Institute of Mathematical Sciences, 2018-04-01)Pair approximation models have been used to study the spread of infectious diseases in spatially distributed host populations, and to explore disease control strategies such as vaccination and case isolation. Here we ... -
Spectral analysis of internal waves generated by tide-topography interaction
(University of Waterloo, 2007-08-21)Internal waves in the deep ocean play a deciding role in processes such as climate change and nutrient cycles. Winds and tidal currents over topography feed energy into internal waves at large scales; through nonlinear ...