Browsing Applied Mathematics by Title
Now showing items 305-324 of 491
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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 ... -
Nonlinear screening of external charge by doped graphene
(University of Waterloo, 2010-04-28)In the rst part of this thesis we discuss some details of properties of graphene and we explain the tight-binding approach to nd the energy spectrum in graphene. In the second part of the thesis, we solve a nonlinear ... -
Nonlinear Wave Propagation in Brass Instruments
(University of Waterloo, 2013-01-25)The study of wave production and propagation is a common phenomenon seen within a variety of math and physics problems. This thesis in particular will investigate the production and propagation of sound waves through musical ... -
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 ... -
Normal Mode Spectra of Idealized Baroclinic Waves
(AMS, 2020-02-01)Normal modes are used to investigate the contributions of geostrophic vortices and inertia–gravity waves to the energy spectrum of an idealized baroclinic wave simulation. The geostrophic and ageostrophic modal spectra ... -
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 ... -
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 ... -
A Novel Class of Intensity-based Metrics for Image Functions which Accommodate a Generalized Weber's Model of Perception
(University of Waterloo, 2020-04-29)Even though the usual L2 image fidelity measurements, such as MSE and PSNR, characterize the mean error for each pixel of the images, these traditional measurements are not designed to predict human visual perception of ... -
A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis
(University of Waterloo, 2018-08-09)In the area of signal analysis and processing, the Fourier transform and wavelet transform are widely applied. Empirical Mode Decomposition(EMD) was proposed as an alternative frequency analysis tool. Although shown to ... -
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 ... -
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 ... -
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 ... -
Numerical analysis of space-time hybridized discontinuous Galerkin methods for incompressible flows
(University of Waterloo, 2022-08-09)Many industrial problems require the solution of the incompressible Navier-Stokes equations on moving and deforming domains. Notable examples include the simulation of rotating wind turbines in strong air flow, wave impact ... -
Numerical Methods for Hamilton-Jacobi-Bellman Equations with Applications
(University of Waterloo, 2019-08-26)Hamilton-Jacobi-Bellman (HJB) equations are nonlinear controlled partial differential equations (PDEs). In this thesis, we propose various numerical methods for HJB equations arising from three specific applications. First, ... -
Numerical Modelling of Wind Storms in the Lower Great Lakes
(University of Waterloo, 2019-01-07)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 ... -
Numerical Simulation of Nonlinear and Dispersive Wave Equations using Adaptive Mesh Refinement (AMR)
(University of Waterloo, 2020-06-24)Numerical solution of time dependent Partial Differential Equations plays an important role in different fluid flow modelling problems. Sometimes a little portion of the computational domain needs high grid resolution in ... -
Numerical Simulation of Surface Waves using Meshfree Methods
(University of Waterloo, 2009-04-27)Smoothed Particle Hydrodynamics (SPH) is a Lagrangian-based numerical method used for simulating problems in fluid and solid mechanics. In this thesis, a basic introduction to particle and Smoothed Particle (SP) approximations ... -
Numerical simulations of convection and gravity currents near the temperature of maximum density
(University of Waterloo, 2022-08-09)Recently, the dynamics of flows in cold freshwater (temperatures around the temperature of maximum density, 3.98 oC) has garnered much interest in the environmental fluid dynamics community. From a dynamical perspective, ... -
Numerical Simulations of Internal Solitary and Solitary-Like Waves: Wave Interactions and Instabilities
(University of Waterloo, 2019-05-31)Internal solitary and solitary-like 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 ... -
Numerical Simulations of Shoaling Internal Solitary Waves of Elevation
(University of Waterloo, 2015-04-13)We present high-resolution, two- and three-dimensional direct numerical simulations of laboratory-scale, fully nonlinear internal solitary waves of elevation shoaling onto and over a small-amplitude shelf. The three-dimensional, ...