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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Nonlinear Preconditioning Methods for Optimization and Parallel-In-Time Methods for 1D Scalar Hyperbolic Partial Differential Equations
(University of Waterloo, 2017-10-18)This thesis consists of two main parts, part one addressing problems from nonlinear optimization and part two based on solving systems of time dependent differential equations, with both parts describing strategies for ... -
Non-linear Interactions between Internal Wave Beams: Beyond the Traditional Approximation.
(University of Waterloo, 2017-09-22)The problem of nonlinear interactions of internal waves is solved using small-amplitude expansions beyond the traditional approximation; that is the horizontal component of the Earth’s rotation vector is included in our ... -
Mean field analysis gives accurate predictions of the behaviour of large networks of sparsely coupled and heterogeneous neurons
(BioMed Central, 2014-07-21)Large networks of integrate-and-fire (IF) model neurons are often used to simulate and study the behaviour of biologically realistic networks. However, to fully study the large network behaviour requires an exploration of ... -
Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons
(Frontiers Media, 2017-12-27)We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential ... -
One-Dimensional Population Density Approaches To Recurrently Coupled Networks Of Neurons With Noise
(Society for Industrial and Applied Mathematics, 2015)Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential, and quartic integrate-and-fire, among others. Unfortunately, ... -
Nonsmooth Bifurcations of Mean Field Systems of Two-Dimensional Integrate and Fire Neurons
(Society for Industrial and Applied Mathematics, 2016)Mean field systems have recently been derived that adequately predict the behaviors of large networks of coupled integrate-and-fire neurons [W. Nicola and S.A. Campbell, J. Comput. Neurosci., 35 (2013), pp. 87-108]. The ... -
An Npz Model With State-Dependent Delay Due To Size-Structure In Juvenile Zooplankton
(Society for Industrial and Applied Mathematics, 2016)The study of planktonic ecosystems is important as they make up the bottom trophic levels of aquatic food webs. We study a closed nutrient-phytoplankton-zooplankton (NPZ) model that includes size structure in the juvenile ... -
The Relation between Polygonal Gravity and 3D Loop Quantum Gravity
(University of Waterloo, 2017-09-13)In this thesis, we explore the relation between ’t Hooft polygonal gravity and loop quantum gravity (LQG) - two models of discrete gravity in 2+1 dimensions. While the relation between the two theories has been studied ... -
Clustering behaviour in networks with time delayed all-to-all coupling
(University of Waterloo, 2017-08-30)Networks of coupled oscillators arise in a variety of areas. Clustering is a type of oscillatory network behavior where elements of a network segregate into groups. Elements within a group oscillate synchronously, while ... -
On Perturbative Methods in Spectral Geometry
(University of Waterloo, 2017-08-28)The goal of spectral geometry is to establish how much information about the geometry of compact Riemannian manifolds is contained in the spectra of natural differential operators, especially Laplacians, defined on them. ... -
Impulsive Control of Dynamical Networks
(University of Waterloo, 2017-08-25)Dynamical networks (DNs) consist of a large set of interconnected nodes with each node being a fundamental unit with detailed contents. A great number of natural and man-made networks such as social networks, food networks, ... -
Control of the Landau–Lifshitz equation
(Elsevier, 2016-05)The Landau–Lifshitz equation describes the dynamics of magnetization inside a ferromagnet. This equation is nonlinear and has an infinite number of stable equilibria. It is desirable to control the system from one equilibrium ... -
Persistent oscillations in the Aplysia bag cell network
(University of Waterloo, 2017-08-24)Persistence is a phenomena by which a resting neuron enters a state of persistent behavior following a brief stimulus. Persistent neural systems can exhibit long-term responses that remain after the stimulus is removed, ... -
A Novel Mathematical Framework for the Analysis of Neural Networks
(University of Waterloo, 2017-08-22)Over the past decade, Deep Neural Networks (DNNs) have become very popular models for processing large amounts of data because of their successful application in a wide variety of fields. These models are layered, often ... -
Normal Mode Wave-Vortex Decompositions of Mesoscale Simulations
(University of Waterloo, 2017-08-18)The kinetic energy spectrum of the atmosphere has been well observed to exhibit a k^(-3) power law at synoptic scales with a transition to a shallower k^(-5/3) power law at the mesoscale. To better understand the mesoscale ... -
A modelling investigation into the impacts of the convective parameterization on the tropical circulation
(University of Waterloo, 2017-08-15)Many studies have shown that the tropical circulations (Walker and Hadley circulations) will weaken in a warmer world. This is sometimes attributed to changes in the tropical mean water cycling rate (driven by convective ... -
Sensor Choice for Minimum Error Variance Estimation
(Institute of Electrical and Electronics Engineers, 2017-06-12)A Kalman filter is optimal in that the variance of the error is minimized by the estimator. It is shown here, in an infinite-dimensional context, that the solution to an operator Riccati equation minimizes the steady-state ... -
Modeling and Stabilizability of Voltage-Actuated Piezoelectric Beams with Magnetic Effects
(Society for Industrial and Applied Mathematics, 2014-01-01)Models for piezoelectric beams and structures with piezoelectric patches generally ignore magnetic effects. This is because the magnetic energy has a relatively small effect on the overall dynamics. Piezoelectric beam ... -
The hydrodynamics of two-dimensional oscillating flows over ripples: the effect of asymmetries in ripple shape and currents
(University of Waterloo, 2017-04-28)The research presented in this thesis involved consideration of three increasingly asymmetric oscillatory flows over two ripple profiles, one of which is asymmetric and represents a small deviation from a symmetric ripple. ... -
Evolutionary Dynamics of Cancer: Spatial and Heterogeneous Effects
(University of Waterloo, 2017-01-23)Despite significant advances in the study of cancer and associated combination therapeutic treatments, cancer still remains one of the most common and complex often-terminal diseases. Acquisition of high-throughput ...
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