Numerical Analysis and Computation Commons^™

Observational Signatures From Self-Gravitating Protostellar Disks, Alexander L. Desouza

Electronic Thesis and Dissertation Repository

Protostellar disks are the ubiquitous corollary outcome of the angular momentum conserving, gravitational collapse of molecular cloud cores into stars. Disks are an essential component of the star formation process, mediating the accretion of material onto the protostar, and for redistributing excess angular momentum during the collapse. We present a model to explain the observed correlation between mass accretion rates and stellar mass that has been inferred from observations of intermediate to upper mass T Tauri stars. We explain this correlation within the framework of gravitationally driven torques parameterized in terms of Toomre’s Q criterion. Our models reproduce both the …

Options Pricing And Hedging In A Regime-Switching Volatility Model, Melissa A. Mielkie

Electronic Thesis and Dissertation Repository

Both deterministic and stochastic volatility models have been used to price and hedge options. Observation of real market data suggests that volatility, while stochastic, is well modelled as alternating between two states. Under this two-state regime-switching framework, we derive coupled pricing partial differential equations (PDEs) with the inclusion of a state-dependent market price of volatility risk (MPVR) term.

Since there is no closed-form solution for this pricing problem, we apply and compare two approaches to solving the coupled PDEs, assuming constant Poisson intensities. First we solve the problem using numerical solution techniques, through the application of the Crank-Nicolson numerical scheme. …

Study Of Virus Dynamics By Mathematical Models, Xiulan Lai

Electronic Thesis and Dissertation Repository

This thesis studies virus dynamics within host by mathematical models, and topics discussed include viral release strategies, viral spreading mechanism, and interaction of virus with the immune system.

Firstly, we propose a delay differential equation model with distributed delay to investigate the evolutionary competition between budding and lytic viral release strategies. We find that when antibody is not established, the dynamics of competition depends on the respective basic reproduction numbers of the two viruses. If the basic reproductive ratio of budding virus is greater than that of lytic virus and one, budding virus can survive. When antibody is established for …

Image Fusion And Axial Labeling Of The Spine, Brandon Miles

Electronic Thesis and Dissertation Repository

In order to improve radiological diagnosis of back pain and spine disease, two new algorithms have been developed to aid the 75% of Canadians who will suffer from back pain in a given year. With the associated medical imaging required for many of these patients, there is a potential for improvement in both patient care and healthcare economics by increasing the accuracy and efficiency of spine diagnosis. A real-time spine image fusion system and an automatic vertebra/disc labeling system have been developed to address this. Both magnetic resonance (MR) images and computed tomography (CT) images are often acquired for patients. …