Numerical Analysis and Computation Commons^™

Approximation Of The Scattering Amplitude Using Nonsymmetric Saddle Point Matrices, Amber Sumner Robertson

Master's Theses

In this thesis we look at iterative methods for solving the primal (Ax = b) and dual (A^T y = g) systems of linear equations to approximate the scattering amplitude defined by g^Tx =y^Tb. We use a conjugate gradient-like iteration for a unsymmetric saddle point matrix that is contructed so as to have a real positive spectrum. We find that this method is more consistent than known methods for computing the scattering amplitude such as GLSQR or QMR. Then, we use techniques from "matrices, moments, and quadrature" to compute the scattering amplitude …

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 …

Impacts Of Climate Change On The Evolution Of The Electrical Grid, Melissa Ree Allen

Doctoral Dissertations

Maintaining interdependent infrastructures exposed to a changing climate requires understanding 1) the local impact on power assets; 2) how the infrastructure will evolve as the demand for infrastructure changes location and volume and; 3) what vulnerabilities are introduced by these changing infrastructure topologies. This dissertation attempts to develop a methodology that will a) downscale the climate direct effect on the infrastructure; b) allow population to redistribute in response to increasing extreme events that will increase under climate impacts; and c) project new distributions of electricity demand in the mid-21^st century.

The research was structured in three parts. The first …

Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic

Masters Theses

Schramm-Loewner Evolution (SLE) has both mathematical and physical roots that extend as far back as the early 20th century. We present the progression of these humble roots from the Ideal Gas Law, all the way to the renormalization group and conformal field theory, to better understand the impact SLE has had on modern statistical mechanics. We then explore the potential application of the percolation exploration process to crack propagation processes, illustrating the interplay between mathematics and physics.

Numerical Methods And Algorithms For High Frequency Wave Scattering Problems In Homogeneous And Random Media, Cody Samuel Lorton

Doctoral Dissertations

This dissertation consists of four integral parts with a unified objective of developing efficient numerical methods for high frequency time-harmonic wave equations defined on both homogeneous and random media. The first part investigates the generalized weak coercivity of the acoustic Helmholtz, elastic Helmholtz, and time-harmonic Maxwell wave operators. We prove that such a weak coercivity holds for these wave operators on a class of more general domains called generalized star-shape domains. As a by-product, solution estimates for the corresponding Helmholtz-type problems are obtained.

The second part of the dissertation develops an absolutely stable (i.e. stable in all mesh regimes) interior …

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. …

General Sampling Schemes For The Bergman Spaces, Newton Foster

Graduate Theses and Dissertations

A characterization of sampling sequences for the Bergman spaces was originally provided by Seip and later expanded upon by Schuster. We consider a generalized notion of sampling using the infimum norm of the quotient space. Adapting some old techniques, we provide a characterization of general sampling sequences in terms of the lower uniform density.

Generating Combinatorial Objects- A New Perspective, Alexander Chizoma Nwala

Computer Science Theses & Dissertations

Combinatorics is the science of "possibilities." This definition, while not formal is a fair statement because all too often, in order to gain insight into the solution of many counting problems, we explore the possibilities. In some cases we seek to know how many options, while in other cases we seek to enumerate or list the options. Irrespective of the scenario, combinatorics plays a vital role today. In many instances such as exploring the options for choosing a new password for a combination lock, we employ combinatorics. In considering the possible license plate permutations for a state, or to see …

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. …

Energy-Driven Pattern Formation In Planar Dipole-Dipole Systems, Jaron P. Kent-Dobias

HMC Senior Theses

A variety of two-dimensional fluid systems, known as dipole-mediated systems, exhibit a dipole-dipole interaction between their fluid constituents. The com- petition of this repulsive dipolar force with the cohesive fluid forces cause these systems to form intricate and patterned structures in their boundaries. In this thesis, we show that the microscopic details of any such system are irrelevant in the macroscopic limit and contribute only to a constant offset in the system’s energy. A numeric model is developed, and some important stable domain morphologies are characterized. Previously unresolved bifurcating branches are explored. Finally, by applying a random energy background to …

A Posteriori Error Estimates For Surface Finite Element Methods, Fernando F. Camacho

Theses and Dissertations--Mathematics

Problems involving the solution of partial differential equations over surfaces appear in many engineering and scientific applications. Some of those applications include crystal growth, fluid mechanics and computer graphics. Many times analytic solutions to such problems are not available. Numerical algorithms, such as Finite Element Methods, are used in practice to find approximate solutions in those cases.

In this work we present L2 and pointwise a posteriori error estimates for Adaptive Surface Finite Elements solving the Laplace-Beltrami equation −△_Γ u = f . The two sources of errors for Surface Finite Elements are a Galerkin error, and a …

Building A Predictive Model For Baseball Games, Jordan Robertson Tait

All Graduate Theses, Dissertations, and Other Capstone Projects

In this paper, we will discuss a method of building a predictive model for Major League Baseball Games. We detail the reasoning for pursuing the proposed predictive model in terms of social popularity and the complexity of analyzing individual variables. We apply a coarse-grain outlook inspired by Simon Dedeos' work on Human Social Systems, in particular the open source website Wikipedia [2] by attempting to quantify the influence of winning and losing streaks instead of analyzing individual performance variables. We will discuss initial findings of data collected from the LA Dodgers and Colorado Rockies and apply further statistical analysis to …

Selection Of Step Size For Total Variation Minimization In Ct, Anna N. Yeboah

Electronic Theses and Dissertations

Medical image reconstruction by total variation minimization is a newly developed area in computed tomography (CT). In compressed sensing literature, it hasbeen shown that signals with sparse representations in an orthonormal basis may be reconstructed via l1-minimization. Furthermore, if an image can be approximately modeled to be piecewise constant, then its gradient is sparse. The application of l1-minimization to a sparse gradient, known as total variation minimization, may then be used to recover the image. In this paper, the steepest descent method is employed to update the approximation of the image. We propose a way to estimate an optimal step …

Relative Equilibria Of Isosceles Triatomic Molecules In Classical Approximation, Damaris Miriam Mckinley

Theses and Dissertations (Comprehensive)

In this thesis we study relative equilibria of di-atomic and isosceles tri-atomic molecules in classical approximations with repulsive-attractive interaction. For di-atomic systems we retrieve well-known results. The main contribution consists of the study of the existence and stability of relative equilibria in a three-atom system formed by two identical atoms of mass $m$ and a third of mass $m_3$, constrained in an isosceles configuration at all times.

Given the shape of the binary potential only, we discuss the existence of equilibria and relative equilibria. We represent the results in the form of energy-momentum diagrams. We find that fixing the masses …