Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 21 for “"MATHEMATICS::Applied mathematics"”.
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Efficient variable mesh techniques to solve interior layer problems
Singularly perturbed problems have been studied extensively over the past few years from different perspectives. The recent research has focussed on the problems whose solutions possess interior layers. These interior layers appear in the interior of the domain, location of which is difficult to …
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Generalised nonlinear stability of stratified shear flows: adjoint-based optimisation, Koopman modes, and reduced models
In this thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application of adjoint based optimisation to find nonlinear optimal perturbations and …
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Spectral methods and computational trade-offs in high-dimensional statistical inference
Spectral methods have become increasingly popular in designing fast algorithms for modern highdimensional datasets. This thesis looks at several problems in which spectral methods play a central role. In some cases, we also show that such procedures have essentially the best performance among all …
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Information, insider trading and takeover announcements
This thesis focuses on the effect of takeover announcements in financial markets. We want to use a math model to analyze the inside traders' behavior when there is a potential takeover in the market. The thesis starts with a math model to capture the stock price dynamics, and then it states the …
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A Proposed Numerical Method for the 3D Wave Equation with Constant Speed
This thesis implements a new numerical scheme to solve the (classical) constant speed wave equation in the three dimensional space, currently existing methods (even if more restrictive) rely on time iterations and observe the accumulation of error at each time step iteration, the new method is …
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Chaos and Dynamical Systems
Throughout the ages, mathematics has been evolving and creating new branches. In the middle to late twentieth century, a new branch formed: chaos. Chaos is the study of dynamical systems that vary greatly with respect to initial conditions. The slightest change in an initial condition, a seemingly …
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The power spectrum and bispectrum of inflation and cosmic defects
Much of the recent progress in cosmology has come from studying the power spectrum of the cosmic microwave background (CMB). The latest results from the Planck satellite confirmed that the inflationary paradigm with the $\Lambda$CDM six-parameter model provides a very good description of the …
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Macroscopic Coupling Conditions with Partial Blocking for Highway Ramps
We consider the Lighthill-Whitman-Richards traffic model on a network consisting of a highway with an off ramp, connected by a junction. We compare the known coupling conditions for the evolution of traffic at the junction and suggest a novel improvement to the existing conditions. That is, we …
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Circuits, Perfect Matchings and Paths in Graphs
We primarily consider the problem of finding a family of circuits to cover a bidgeless graph (mainly on cubic graph) with respect to a given weight function defined on the edge set. The first chapter of this thesis is going to cover all basic concepts and notations will be used and a survey of this …
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On decompositions and Connes's embedding problem of finite von Neumann algebras
<p>A longstanding open question of Connes asks whether every finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras. As of yet, algebras verified to satisfy Connes's embedding property belong to just a few special classes (e.g. amenable algebras and free group …
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A Dynamical Study of the Poisson-Nernst-Planck System for Three Ions
Ionic channels and semiconductor devices use atomic scale structures to control macroscopic flows from one reservoir to another. The one-dimensional steady-state Poisson-Nernst-Planck (PNP) system is a useful representation of these devices, but experience shows that describing the reservoirs as …
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The analysis and implementation of exponential almost Runge-Kutta methods for semilinear problems
We look at two families of Exponential Integrators, the multi-step Exponential Time Differencing Methods and the multi-stage Exponential Runge-Kutta Methods. A broader framework of Exponential General Linear Methods builds on these two families. We extend the classical Almost Runge-Kutta Method …
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First-order gradient regularisation methods for image restoration: reconstruction of tomographic images with thin structures and denoising piecewise affine images
The focus of this thesis is variational image restoration techniques that involve novel non-smooth first-order gradient regularisers: Total Variation (TV) regularisation in image and data space for reconstruction of thin structures from PET data and regularisers given by an infimal-convolution of …
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Mathematical models and numerical methods for the movement and life cycle of invasive pests across multiple scales
Invasive pests pose a significant threat to agriculture and native ecosystems. An important tool for managing these invasive pests is mathematical modeling, which enables forecasting of movements and the establishment potential of invasive species in an area, and can provide warnings to …
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Fast Solution Methods For Fractional Diffusion Equations and Their Applications
<p>Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not be modeled accurately by the second order diffusion equations. Because of the non-local property of fractional differential operators, the numerical methods have full coefficient matrices which require …
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Acoustic Scattering in Sheared Flow
Airframe noise, the noise of an aircraft in flight not due to the engine or other mechanical devices, is often a major contribution to the sound heard from an aircraft during landing approach. Over the past few decades certification requirements have gradually tightened, reaching the point where …
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Stability analysis of a bilayer contained within a cylindrical tube
Airways in the lung are coated with a liquid bilayer consisting of a serous layer adjacent to a more viscous mucus layer which is contiguous with the air core. An instability due to surface tension at the interfaces may lead to the formation of a liquid plug that blocks the passage of air. This is …
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Mathematical Modeling and Computational Studies for Cell Signaling
<p>The mitogen-activated protein kinase (MAPK) cascades that are evolutionally conserved from yeast to mammals play a pivotal role in many aspects of cellular functions. The mating decision in yeast is a switch-like or bistability response that allows cells to filter out weak pheromone signals or …
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