Physical Sciences and Mathematics Commons^™

Blow-Up Of Solutions To The Generalized Inviscid Proudman-Johnson Equation, Alejandro Sarria

University of New Orleans Theses and Dissertations

The generalized inviscid Proudman-Johnson equation serves as a model for n-dimensional incompressible Euler flow, gas dynamics, high-frequency waves in shallow waters, and orientation of waves in a massive director field of a nematic liquid crystal. Furthermore, the equation also serves as a tool for studying the role that the natural fluid processes of convection and stretching play in the formation of spontaneous singularities, or of their absence.

In this work, we study blow-up, and blow-up properties, in solutions to the generalized, inviscid Proudman-Johnson equation endowed with periodic or Dirichlet boundary conditions. More particularly,regularity of solutions in an Lp setting will …

Title Ix Compliance: A Comparison Of Division I Equality, Jacqueline Leake

Honors Theses

The passage of Title IX of the Education Amendments of 1972 has had a significant impact on college athletics. However, there is still a large disparity between opportunities offered for men and women. This study determined the true gender equality within Division I athletics. Inequalities were assessed in the areas of athletic participation, athletically related student aid, recruiting expenses, and total expenses. Data from these areas were gathered from the Equity in Athletics Disclosure Analysis Cutting Tool. Ratios and the difference between the ideal and current values were calculated for each category. Institutions were ranked in each category, as well …

The Reasonable Effectiveness Of Mathematics In The Natural Sciences, Nicolas Fillion

Electronic Thesis and Dissertation Repository

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements a strategy to show that the applicability of mathematics is very reasonable indeed.

I distinguish three forms of the …

Thermalization And Initial State-Recurrence In Discrete Kdv-Like Lattices, Garrett Taylor Nieddu

Theses, Dissertations and Culminating Projects

Three discretizations of the Korteweg de-Vries equation are studied; convergence rate, initial state-recurrence, and the energy distribution of the three schemes are all considered. For each discrete scheme over 300 lattices with varying grid sizes were investigated, and the solutions were compared with other lattices from the same scheme, as well as solutions from the other two. It is found that the two schemes that are least accurate display the best recurrence at intermediate grid sizes, away from convergence. This is a notable result because the best recurrence is expected to be found in the most accurate, and converged lattices. …

Sensitivity Analysis In Magnetic Resonance Elastography And A Local Wavelength Reconstruction Based On Wave Direction, Christopher Gillam

All Dissertations

or the detection of early stage cancer. MRE utilizes interior data for its inverse problems, which greatly reduces the ill-posedness from which most traditional inverse problems suffer.
In this thesis, we first establish a sensitivity analysis for viscoelastic scalar medium with complex wave number and compare it with the purely elastic case. Also we estimate the smallest detectable inclusion for breast and liver, which is about twice larger than using the purely elastic model. We also found the existence of optimal frequency (50 Hz) that maximizes the detectability when the Voigt model is used.
Second, we propose a local wavelength …

Polyhedral Approximations Of Quadratic Semi-Assignment Problems, Disjunctive Programs, And Base-2 Expansions Of Integer Variables, Frank Muldoon

All Dissertations

This research is concerned with developing improved representations for special families of mixed-discrete programming problems. Such problems can typically be modeled using different mathematical forms, and the representation employed can greatly influence the problem's ability to be solved. Generally speaking, it is desired to obtain mixed 0-1 linear forms whose continuous relaxations provide tight polyhedral outer-approximations to the convex hulls of feasible solutions. This dissertation makes contributions to three distinct problems, providing new forms that improve upon published works.
The first emphasis is on devising solution procedures for the classical quadratic semi-assignment problem(QSAP), which is an NP-hard 0-1 quadratic program. …

Convex Hull Characterization Of Special Polytopes In N-Ary Variables, Ruobing Shen

All Theses

This paper characterizes the convex hull of the set of n-ary vectors that are lexicographically less than or equal to a given such vector. A polynomial number of facets is shown to be sufficient to describe the convex hull. These facets generalize the family of cover inequalities for the binary case. They allow for advances relative to both the modeling of integer variables using base-n expansions, and the solving of n-ary knapsack problems with weakly super-decreasing coefficients.

Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman

Masters Theses

Extremization of a weak form for the continuum energy conservation principle differential equation naturally implements fluid convection and radiation as flux Robin boundary conditions associated with unsteady heat transfer. Combining a spatial semi-discretization via finite element trial space basis functions with time-accurate integration generates a totally node-based algebraic statement for computing. Closure for gray body radiation is a newly derived node-based radiosity formulation generating piecewise discontinuous solutions, while that for natural-forced-mixed convection heat transfer is extracted from the literature. Algorithm performance, mathematically predicted by asymptotic convergence theory, is subsequently validated with data obtained in 24 hour diurnal field experiments for …

Stability And Convergence For Nonlinear Partial Differential Equations, Oday Mohammed Waheeb

Boise State University Theses and Dissertations

If used cautiously, numerical methods can be powerful tools to produce solutions to partial differential equations with or without known analytic solutions. The resulting numerical solutions may, with luck, produce stable and accurate solutions to the problem in question, or may produce solutions with no resemblance to the problem in question at all. More such numerical computations give no hope of solving this troublesome feature and one needs to resort to investing time in a theoretical approach. This thesis is devoted not solely to computations, but also to a theoretical analysis of the numerical methods used to generate computationally the …

Incomplete Market Models Of Carbon Emissions Markets, Walid Mnif

Electronic Thesis and Dissertation Repository

New regulatory frameworks have been developed with the aim of decreasing global greenhouse gas emissions over both short and long time periods. Incentives must be established to encourage the transition to a clean energy economy. Emissions taxes represent a "price" incentive for this transition, but economists agree this approach is suboptimal. Instead, the "quantity" instrument provided by cap-and-trade markets are superior from an economic point of view. This thesis focuses on the cap-and-trade instrument. Carbon emissions markets have recently been implemented in different countries. We summarize the state of world cap-and-trade schemes. We also provide a literature review of existing …

Quantifying Performance Bias In Label Fusion, Alexander M. Venzin

Theses and Dissertations

Classification systems are employed to remotely assess whether an element of interest falls into a target class or non-target class. These systems have uses in fields as far ranging as biostatistics to search engine keyword analysis. The performance of the system is often summarized as a trade-off between the proportions of elements correctly labeled as target plotted against the number of elements incorrectly labeled as target. These are empirical estimates of the true positive and false positive rates. These rates are often plotted to create a receiver operating characteristic (ROC) curve that acts as a visual tool to assess classification …

Approximate Methods For Dynamic Portfolio Allocation Under Transaction Costs, Nabeel Butt

Electronic Thesis and Dissertation Repository

The thesis provides robust and efficient lattice based algorithms for solving dynamic portfolio allocation problems under transaction costs. The early part of the thesis concentrates upon developing a toolbox based on multinomial trees. The multinomial trees are shown to provide a reasonable approximation for most popular transaction cost models in the academic literature. The tool, once forged, is implemented in the powerful Mathematica based parallel computing environment. In the second part of the thesis we provide applications of our framework to real world problems. We show re-balancing portfolios is more valuable in an investment environment where the growth and volatility …

Molecular Dynamics Studies Of Water Flow In Carbon Nanotubes, Alexander D. Marshall

Electronic Thesis and Dissertation Repository

We present classical molecular dynamics (MD) simulations providing insight into the behaviour of water. We focus on confined water, the properties of which are often significantly different from the properties of bulk water.

First, we performed several simulations investigating the handling of long-range interactions in GROMACS [1], a MD simulation package. Selection of simulation protocols such as handling of long-range interactions is often overlooked, sometimes to the significant detriment of the final result [2, 3, 4]. Ensuring that the chosen simulation protocols are appropriate is a critical step in computer simulation.

Second, we performed MD simulations where water flowed between …

Preoperative Planning Of Robotics-Assisted Minimally Invasive Cardiac Surgery Under Uncertainty, Hamidreza Azimian

Electronic Thesis and Dissertation Repository

In this thesis, a computational framework for patient-specific preoperative planning of Robotics-Assisted Minimally Invasive Cardiac Surgery (RAMICS) is developed. It is expected that preoperative planning of RAMICS will improve the rate of success by considering robot kinematics, patient-specific thoracic anatomy, and procedure-specific intraoperative conditions. Given the significant anatomical features localized in the preoperative computed tomography images of a patient's thorax, port locations and robot orientations (with respect to the patient's body coordinate frame) are determined to optimize characteristics such as dexterity, reachability, tool approach angles and maneuverability. In this thesis, two approaches for preoperative planning of RAMICS are proposed that …

Pricing And Trading American Put Options Under Sub-Optimal Exercise Policies, William Wei Xing

Electronic Thesis and Dissertation Repository

No analytical expression has been found for the optimal exercise boundary of finite maturity American put options. This thesis evaluates the performance of approximating the optimal boundary with a class of analytically tractable sub-optimal exercise boundaries which admit known first passage time density functions. The performance is evaluated in two steps, first by computing and comparing the value of the put option under the sub-optimal exercise policy to existing numerical approximation methods such as the binomial price, then by examining the profit/loss of a trader that would result from hedging and trading strategies based on the sub-optimal exercise policy. We …

Hard And Soft Error Resilience For One-Sided Dense Linear Algebra Algorithms, Peng Du

Doctoral Dissertations

Dense matrix factorizations, such as LU, Cholesky and QR, are widely used by scientific applications that require solving systems of linear equations, eigenvalues and linear least squares problems. Such computations are normally carried out on supercomputers, whose ever-growing scale induces a fast decline of the Mean Time To Failure (MTTF). This dissertation develops fault tolerance algorithms for one-sided dense matrix factorizations, which handles Both hard and soft errors.

For hard errors, we propose methods based on diskless checkpointing and Algorithm Based Fault Tolerance (ABFT) to provide full matrix protection, including the left and right factor that are normally seen in …

Degree Constrained Triangulation, Roshan Gyawali

UNLV Theses, Dissertations, Professional Papers, and Capstones

Triangulation of simple polygons or sets of points in two dimensions is a widely investigated problem in computational geometry. Some researchers have considered variations of triangulation problems that include minimum weight triangulation, de-launay triangulation and triangulation refinement. In this thesis we consider a constrained version of the triangulation problem that asks for triangulating a given domain (polygon or point sites) so that the resulting triangulation has an increased number of even degree vertices. This problem is called Degree Constrained Triangulation (DCT). We propose four algorithms to solve DCT problems. We also present experimental results based on the implementation of the …

Sensitivity Anaylsis And Detectability For Magnetic Resonance Elastography, Catherine White

All Dissertations

This thesis is for a sensitivity analysis of magnetic resonance elastography, a hybrid imaging technique used in early-stage cancer screening. To quantitatively analyze the sensitivity, we introduce a notion of detectability, which is dened as a relative amplitude
drop in a small sti tumor region. This analysis is accomplished in both the full elastic and viscoelastic models and compared with that of the simpler scalar model which is frequently used in the actual application.
Some of the highlights are 1) a useful formula for detectability in terms of physical parameters, which will help the design of experiments; 2) the discrepancy …

Latin Hypercube Sampling And Partial Rank Correlation Coefficient Analysis Applied To An Optimal Control Problem, Boloye Gomero

Masters Theses

Latin Hypercube Sampling/Partial Rank Correlation Coefficient (LHS/PRCC) sensitivity analysis is an efficient tool often employed in uncertainty analysis to explore the entire parameter space of a model. Despite the usefulness of LHS/PRCC sensitivity analysis in studying the sensitivity of a model to the parameter values used in the model, no study has been done that fully integrates Latin Hypercube sampling with optimal control analysis.

In this thesis, we couple the optimal control numerical procedure to the LHS/PRCC procedure and perform a simultaneous examination of the effects of all the LHS parameter on the objective functional value. To test the effectiveness …

Physicic-Based Algorithms And Divergence Free Finite Elements For Coupled Flow Problems, Nicholas Wilson

All Dissertations

This thesis studies novel physics-based methods for
simulating incompressible fluid flow described by the Navier-Stokes equations (NSE) and
magnetohydrodynamics equations (MHD).
It is widely accepted in computational fluid dynamics (CFD) that numerical schemes which are more
physically accurate lead to more precise flow simulations especially over long time intervals.
A prevalent theme throughout will be the inclusion of as much
physical fidelity in numerical solutions as efficiently possible. In algorithm design, model
selection/development, and element choice, subtle changes can provide better physical accuracy,
which in turn provides better overall accuracy (in any measure). To this end we develop and study …

Sparsity Regularization In Diffuse Optical Tomography, John Cooper

All Dissertations

The purpose of this dissertation is to improve image reconstruction in Diffuse Optical Tomography (DOT), a high contrast imaging modality that uses a near infrared light source. Because the scattering and absorption of a tumor varies significantly from healthy tissue, a reconstructed spatial representation of these parameters serves as tomographic image of a medium. However, the high scatter and absorption of the optical source also causes the inverse problem to be severely ill posed, and currently only low resolution reconstructions are possible, particularly when using an unmodulated direct current (DC) source.
In this work, the well posedness of the forward …

Modeling The Curvature Of A Ferrofluid Interface Using A Height Function Method, Holly Timme

Theses, Dissertations and Culminating Projects

The behavior of an interface embedded in a fluid is central to a wide range of biological, chemical, environmental and physical problems and engineering processes. Modeling the evolution of a fluid interface is thus a critical and important problem. In many instances, including two-phase (e.g. liquid-gas) flows, the interface is an internal boundary within a PDE model. A model of the interface properties and its evolution is then typically performed by numerical computation, within the framework of the PDE solution method, such as finite differences (FD). Volume of Fluid (VOF) is a simple FD based method which exhibits excellent volume …

Robust Parameter Estimation In The Weibull And The Birnbaum-Saunders Distribution, Jing Zhao

All Theses

This paper concerns robust parameter estimation of the two-parameter Weibull distribution and the two-parameter Birnbaum-Saunders distribution. We use the proposed method to estimate the distribution parameters from (i) complete samples with and without contamination (ii) type-II censoring samples, in both distributions. Also, we consider the maximum likelihood estimation and graphical methods to compare the maximum likelihood estimation and graphical method with the proposed method based on quantile. We find the advantages and disadvantages for those three different methods.

Branching Rules For Minimum Congestion Multi-Commodity Flow Problems, Cameron Megaw

All Theses

In this paper, we examine various branch and bound algorithms for a minimum congestion origin-destination integer multi-commodity flow problem.
The problem consists of finding a routing such that the congestion of the most congested arc is minimum. For our implementation, we assume that all demands are known a priori.
We provide a mixed integer linear programming formulation of our problem and propose various new branching rules to solve the model. For each rule, we provide theoretical and experimental proof of their effectiveness.
In order to solve large instances, that more accurately portray real-world applications, we outline a path formulation model …

A Set Of Tournaments With Many Hamiltonian Cycles, Hayato Ushijima-Mwesigwa

All Theses

For a random tournament on $3^n$ vertices, the expected number of Hamiltonian cycles is known to be $(3^n -1)!/2^{3^n}$. Let $T_1$ denote a tournament of three vertices $ {v_1, v_2, v_3}$. Let the orientation be such that there are directed edges from $v_1 $to $v_2$ , from $v_2$ to $v_3$ and from $v_3$ to $ v_1$. Construct a tournament $T_i$ by making three copies of $T_{i-1}$, $T_{i-1}'$, $T_{i-1}''$ and $T_{i-1}'''$. Let each vertex in $T_{i-1}'$ have directed edges to all vertices in $T_{i-1}''$, similarly place directed edges from each vertex in $T_{i-1}''$ to all vertices in $T_{i-1}'''$ and from $T_{i-1}'''$ …

Local Polynomial Regression With Application To Sea Surface Temperatures, Michael Finney

All Theses

Our problem involves methods for determining the times of a maximum or minimum for a general mean function in time series data. The methods explored here involve polynomial smoothing. In theory, the methods calculate a general number of derivatives of the estimated polynomial. Using these techniques, we wish to find a balance between error, variance, and complexity and apply it to a time series of sea surface temperatures. We will first explore the theory behind the method and then find a way to optimally apply it to our data.

Decay Estimates For Nonlinear Wave Equations With Variable Coefficients, Michael Jacob Roberts

Masters Theses

We studied the long time behavior of solutions of nonlinear wave equations with variable coefficients and an absorption nonlinearity. Such an equation appears in models for traveling waves in a non-homogeneous gas with damping that changes with position. We established decay estimates of the energy of solutions. We found three different regimes of decay of solutions depending on the exponent of the absorption term. We show the existence of two critical exponents. For the exponents above the larger critical exponent, the decay of solutions of the nonlinear equation coincides with that of the corresponding linear problem. For exponents below the …

Numerical Analysis Of First And Second Order Unconditional Energy Stable Schemes For Nonlocal Cahn-Hilliard And Allen-Cahn Equations, Zhen Guan

Doctoral Dissertations

This PhD dissertation concentrates on the numerical analysis of a family of fully discrete, energy stable schemes for nonlocal Cahn-Hilliard and Allen-Cahn type equations, which are integro-partial differential equations (IPDEs). These two IPDEs -- along with the evolution equation from dynamical density functional theory (DDFT), which is a generalization of the nonlocal Cahn-Hilliard equation -- are used to model a variety of physical and biological processes such as crystallization, phase transformations, and tumor growth. This dissertation advances the computational state-of-the-art related to this field in the following main contributions: (I) We propose and analyze a family of two-dimensional unconditionally energy …

Further Applications Of Higher-Order Markov Chains And Developments In Regime-Switching Models, Xiaojing Xi

Electronic Thesis and Dissertation Repository

We consider a higher-order hidden Markov models (HMM), also called weak HMM (WHMM), to capture the regime-switching and memory properties of financial time series. A technique of transforming a WHMM into a regular HMM is employed, which in turn enables the development of recursive filters. With the use of the change of reference probability measure methodology and EM algorithm, a dynamic estimation of model parameters is obtained. Several applications and extensions were investigated. WHMM is adopted in describing the evolution of asset prices and its performance is examined through a forecasting analysis. This is extended to the case when the …

A Real Options Valuation Of Renewable Energy Projects, Natasha Burke

Electronic Thesis and Dissertation Repository

Due to climate change concerns, high oil prices and nuclear dangers there is increasing support for renewable energy. At the forefront of the debate for government support of renewable energy are wind energy and biofuels. Used primarily for power generation and transportation, respectively, there have been many debates surrounding the reliability and efficiency of these resources. These debates often address the uncertainty in the economic value of the resource through time, however it is often difficult to quantify this uncertainty, which stems from the random behavior of prices and the unpredictable nature of the resource itself.

In this thesis we …