Mathematics Commons^™

Instabilities In Newtonian Films And Nematic Liquid Crystal Droplets, Te-Sheng Lin

Dissertations

The instabilities of Newtonian films and nematic liquid crystal droplets within the framework of the long wave (lubrication) approximation are studied. For Newtonian films, it is found that, under destabilizing gravitational force, a contact line, modeled by a commonly used precursor film model, leads to free surface instabilities without any additional natural or imposed perturbations. In addition, there is a coupling between the surface instabilities and the transverse (fingering) instabilities which leads to complex behavior. All the observed phenomena are characterized by a single parameter D = (3Ca)^1/3 cot α where Ca is the capillary number and …

Mathematical Models Of Combustion At High Pressure, Daniel Fong

Dissertations

In this dissertation, we develop new mathematical theories of flame propagation that are valid at elevated, or extreme, pressures. Of particular interest is the regime of burning in which the pressure exceeds the critical pressure of the species undergoing chemical reaction. Fluids and flames are known to behave differently under these extreme conditions as opposed to atmospheric pressure. The focus of this dissertation is to investigate these differences by deriving reduced models that contain the unique features.

In the first part of this dissertation, we analyze the structure of laminar diffusion flames at high pressure in the limit of large …

Function Estimation Of Irregularly Spaced Data With Long Memory Dependence, Rosalie Michelle Wheeler

Dissertations

We examine the problem of estimating an underlying function from collected data. The methods considered include parametric regression, density estimation, kernel estimation, wavelet regression, and specific results from when our underlying function f\left(x\right) is a member of the Besov or the Triebel spaces. Then we consider the problem of long memory error in several settings, including data which is equally spaced, data which is unequally spaced, and data which is a member of the Holder class and several other spaces. Ultimately we focus on three different problems. The first involves using linear interpolation or local averaging to account for the …

Partial Connectivity In Wireless Sensor Networks, Robert Andre Murphy

Dissertations

Given a bounded region of the 2-dimensional plane, a discrete set of nodes is distributed throughout according to a Poisson point process. Given some fixed, finite, real number, two nodes are said to connect and form an edge if their mutual distance is less than this number. Let G be the graph of all such edges over the set of generated nodes and let C be any set of mutually connected nodes. It is shown that there is a critical mutual distance such that at least half of all generated nodes are mutually connected to form a connected cluster. Now, …

Geometric Structures On Matrix-Valued Subdivision Schemes, James J. Smith

Dissertations

Surface subdivision schemes are used in computer graphics to generate visually smooth surfaces of arbitrary topology. Applications in computer graphics utilize surface normals and curvature. In this paper, formulas are obtained for the first and second partial derivatives of limit surfaces formed using 1-ring subdivision schemes that have 2 by 2 matrix-valued masks. Consequently, surface normals, and Gaussian and mean curvatures can be derived. Both quadrilateral and triangular schemes are considered and for each scheme both interpolatory and approximating schemes are examined. In each case, we look at both extraordinary and regular vertices. Every 3-D vertex of the refinement polyhedrons …

The Effects Of Periodic And Non-Periodic Inputs On The Dynamics Of A Medial Entorhinal Cortex Layer Ii Stellate Cell Model, Dongwook Kim

Dissertations

Various neuron types exhibit sub-threshold and firing frequency resonance in which the sub-threshold membrane potential or firing frequency responses to periodic inputs peak at a preferred frequency (or frequencies). Previous experimental work has shown that medial entorhinal cortex layer II stellate cells (SCs) exhibit sub-threshold and firing frequency resonance in the theta frequency band (4 - 10 Hz). In this thesis we seek to understand the biophysical and dynamic mechanism underlying these phenomena and how they are related. We studied the effects of sinusoidal current and synaptic conductance inputs at various frequencies, with and without noise, on the supra-threshold dynamics …

Energy Propagation In Jammed Granular Matter, Xiaoni Fang

Dissertations

The systems built from dense granular materials are very important due to their relevance to a number of technological and other fields. However, they are difficult to study in particular due to a lack of accurate continuum description. In this work, studies on these systems are presented using discrete element simulations that model the granular particles as soft, elastic, and frictional disks which interact when in contact. These simulations are used for the purpose of analyzing a few granular systems with the main emphasis on understanding phenomena of energy and force propagation.

Analysis of energy propagation in a two-dimensional disordered …

Confidence Bands For Survival Functions Under Semiparametric Random Censorship Models, Peixin Zhang

Dissertations

In medical reports point estimates and pointwise confidence intervals of parameters are usually displayed. When the parameter is a survival function, however, the approach of joining the upper end points of individual interval estimates obtained at several points and likewise for the lower end points would not produce bands that include the entire survival curve with a given confidence. Simultaneous confidence bands, which allow confidence statements to be valid for the entire survival curve,would be more meaningful

This dissertation focuses on a novel method of developing one-sample confidence bands for survival functions from right censored data. The approach is model- …

High-Order Adaptive Methods For Computing Invariant Manifolds Of Maps, Jacek K. Wrobel

Dissertations

The author presents efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve/surface, he proposes using higher-order interpolation/approximation techniques from geometric modeling. He uses B´ezier curves/triangles, fundamental objects in curve/surface design, to create adaptive methods. The methods are based on tolerance conditions derived from properties of B´ezier curves/triangles. The author develops and tests the methods for an ordinary parametric curve; then he adapts these methods to invariant manifolds of planar maps. Next, he develops and tests the …

Markovian And Stochastic Differential Equation Based Approaches To Computer Virus Propagation Dynamics And Some Models For Survival Distributions, Lianzhe Xu

Dissertations

This dissertation is divided in two Parts. The first Part explores probabilistic modeling of propagation of computer 'malware' (generally referred to as 'virus') across a network of computers, and investigates modeling improvements achieved by introducing a random latency period during which an infected computer in the network is unable to infect others. In the second Part, two approaches for modeling life distributions in univariate and bivariate setups are developed.

In Part I, homogeneous and non-homogeneous stochastic susceptible-exposed-infectious- recovered (SEIR) models are specifically explored for the propagation of computer virus over the Internet by borrowing ideas from mathematical epidemiology. Large computer …

Sequential Bayesian Filtering For Spatial Arrival Time Estimation, Rashi Jain

Dissertations

Locating and tracking a source in an ocean environment as well as estimating environmental parameters of a sound propagation medium is of utmost importance in underwater acoustics. Matched field processing is often the method of choice for the estimation of such parameters. This approach, based on full field calculations, is computationally intensive and sensitive to assumptions on the structure of the environment. As an alternative, methods that use only select features of the acoustic field for source localization and environmental inversion have been proposed. The focus here is on inversion using arrival times of identified paths within recorded time-series. After …

Uniform Heating Of Thin Ceramic Slabs In A Multimode Microwave Cavity, Shuchi Agrawal

Dissertations

Two-dimensional reaction diffusion equations, which contain a functional and an inhomogeneous source term, are good models for describing microwave heating of thin ceramic slabs and cylinders in a multi mode, highly resonant cavity. A thin ceramic slab situated in a TEN03 rectangular cavity modeled in the small Biot number limit and a thin silicon wafer situated in a TM101 cylindrical cavity modeled in the small fineness ratio limit are studied to gain insight into the dynamics of the heating process. The evolution of temperature is governed by a two-dimensional reaction diffusion equation and a spatially non-homogeneous reaction term. Numerical methods …

Asymptotic And Numerical Analysis Of Time-Dependent Wave Propagation In Dispersive Dielectric Media That Exhibit Fractional Relaxation, Matthew Frank Causley

Dissertations

This dissertation addresses electromagnetic pulse propagation through anomalously dispersive dielectric media. The Havriliak-Negami (H-N) and Cole-Cole (C-C) models capture the non-exponential nature of such dielectric relaxation phenomena, which is manifest in a variety of dispersive dielectric media. In the C-C model, the dielectric polarization is coupled to the time-dependent Maxwell's equations by a fractional differential equation involving the electric field. In the H-N case, a more general pseudo-fractional differential operator describes the polarization.

The development and analysis of a robust method for implementing such models is presented, with an emphasis on algorithmic efficiency. Separate numerical schemes are presented for C-C …

Numerical And Asymptotic Modeling Of Evolving Nonlinear Ocean Surface Wave Fields, Matt Malej

Dissertations

The main focus of this dissertation is the asymptotic and numerical modeling of nonlinear ocean surface wave fields. In particular, a development of an accurate numerical model for the evolution of nonlinear ocean waves, including extreme waves known as Rogue/Freak waves. Due to their elusive and destructive nature, the media often portrays Rogue waves as unimaginatively huge and unpredictable monsters of the sea. To address these concerns, derivations of asymptotically reduced models, based on the small wave steepness assumption, are presented and their corresponding numerical simulations via a Fourier pseudo-spectral method are discussed. The simulations are initialized with a well-known …

Some Contributions To Modeling Usage Sensitive Warranty Servicing Strategies And Their Analyses, Rudrani Banerjee

Dissertations

Providing a warranty as a part of a product's sale is a common practice in industry. Parameters of such warranties (e.g., its duration limits, intensity of use) must be carefully specified to ensure their financial viability. A great deal of effort has been accordingly devoted in attempts to reduce the costs of warranties via appropriately designed strategies to service them. many such strategies, that aim to reduce the total expected costs of the warrantor or / and are appealing in other ways such as being more pragmatic to implement - have been suggested in the literature. Design, analysis and optimization …

Using Feed-Forward Networks To Infer The Activity Of Feedback Neuronal Networks, Xinxian Huang

Dissertations

The nervous system is one of the most important organ systems in a multicellular body. Animals, including human beings perceive, learn, think and deliver motion instructions through their nervous system. The basic structural units of the nervous system are individual neurons which constitute different neuronal networks with distinct functions. In each network, constituent neurons are coupled with different connection patterns, for example, some neurons send feed-forward information to the coupling neurons while others are mutually coupled. Because it is often difficult to analyze large interconnected feedback neuronal networks, it is important to derive techniques to reduce the complexity of the …

Pattern Formation In Oscillatory Systems, Hui Wu

Dissertations

Synchronization is a kind of ordinary phenomenon in nature, the study of it includes many mathematical branches. Phase space is one of the most powerful inventions of modern mathematical science. There are two variables, the position and velocity, that can describe the 2-dimensional phase space system. For example, the state of pendulum may be specified by its position and its velocity, so its phase space is 2-dimensional. The state of the system at a given time has a unique corresponding point in the phase space. In order to describe the motion of an oscillator, we can talk about its motion …

Modular And Graceful Edge Colorings Of Graphs, Ryan Jones

Dissertations

Abstract attached as separate file.

Hamiltonicity And Connectivity In Distance-Colored Graphs, Kyle C. Kolasinski

Dissertations

Abstract attached as separate file.

A Comparative Analysis Of The Origin And Divine Causation Of Death In Ancient Near Eastern Literature And In The Old Testament, Lazarus Castang

Dissertations

The present dissertation attempts a comparative analysis of both the origin of death in the creation accounts and the divine causation of death in the main flood accounts in the ancient Near Eastern (ANE) literature and the Hebrew Old Testament (OT). Both literatures are examined for their implicit or explicit conceptions of the origin and divine causation of death. The origin of death in the ANE literature is located in the Egyptian Osirian myth and the Mesopotamian Enki-Ninmah myth, Enûma Elish, Epic of Gilgamesh, and the Adapa legend. The divine causation of death is studied in the Eridu Genesis, Atra-Hasis …

The K-Cores Of A Graph, Allan Bickle

Dissertations

Full abstract attached as supplemental file.

Robust Interval Estimation Of A Treatment Effect In Observational Studies Using Propensity Score Matching, Scott F. Kosten

Dissertations

Estimating the treatment effect between a treatment group and a control group in an observational study is a challenging problem in statistics. Without random assignment of subjects, there are likely to be differences between the treatment group and control group on a set of baseline covariates. If one of these baseline covariates is correlated to the response variable, then the difference in sample means between the groups is likely to be a biased estimate of the true treatment effect.

Propensity score matching has become an increasingly popular strategy for reducing bias in estimates of the treatment effect. This reduction in …

A Numerical Study On The Propagation And Interaction Of Strongly Nonlinear Solitary Waves, Qiyi Zhou

Dissertations

We study numerically a strongly nonlinear long wave model for surface gravity waves propagating in both one and two horizontal dimensions. This model often referred to as the Su-Gardner or Green-Naghdi equations can be derived from the Euler equations under the assumption that the ratio between the characteristic wavelength and water depth is small, but no assumption on the wave amplitude is required. We first generalize the model to describe large amplitude one-dimensional solitary waves in the presence of background shear of constant vorticity. After computing the solitary wave solution of the strongly nonlinear model, the interaction between two solitary …

Computational Methods For Two-Phase Flow With Soluble Surfactant, Kuan Xu

Dissertations

A mathematical model is formulated and solved for the two-phase flow of a viscous drop or inviscid bubble in an immiscible, viscous surrounding fluid in the zero Reynold's number or Stokes flow limit. A surfactant that is present on the interface is also soluble in the exterior fluid, and the drop is deformed by an imposed linear flow. The geometry is two-dimensional and Cartesian.

The dissolved surfactant is considered in the physically realistic limit of large bulk Péclet number. That is, it convects and diffuses as a passive scalar in the bulk flow where the ratio of its convection to …

Local Radial Basis Function Methods For Solving Partial Differential Equations, Guangming Yao

Dissertations

Meshless methods are relatively new numerical methods which have gained popularity in computational and engineering sciences during the last two decades. This dissertation develops two new localized meshless methods for solving a variety partial differential equations.

Recently, some localized meshless methods have been introduced in order to handle large-scale problems, or to avoid ill-conditioned problems involving global radial basis function approximations. This dissertation explains two new localized meshelss methods, each derived from the global Method of Approximate Particular Solutions (MAPS). One method, the Localized Method of Approximate Particular Solutions (LMAPS), is used for elliptic and parabolic partial differential equations (PDEs) …

Studies Of Meson Mass Spectra In The Context Of Quark-Antiquark Bound States, Mallika Dhar

Dissertations

This dissertation deals with the computation of meson mass spectra in the context of quarkantiquark (q ¯ q) bound-state. Traditionally the q ¯ q bound-state problem is treated by solving the non-relativistic Schrödinger equation in position representation with a linear confining potential and a Coulomb-like attractive potential. For high energy, relativistic kinematics is necessary. It is well known that relativistic kinematics cannot be treated properly in position representation, but it can easily be handled in momentum representation. On the other hand, the linear potential and Coulomb-like potential have singularities in momentum-space and complicated subtraction procedure is necessary to treat the …

Dnagents: Genetically Engineered Intelligent Mobile Agents, Jeremy Otho Kackley

Dissertations

Mobile agents are a useful paradigm for network coding providing many advantages and disadvantages. Unfortunately, widespread adoption of mobile agents has been hampered by the disadvantages, which could be said to outweigh the advantages. There is a variety of ongoing work to address these issues, and this is discussed. Ultimately, genetic algorithms are selected as the most interesting potential avenue. Genetic algorithms have many potential benefits for mobile agents. The primary benefit is the potential for agents to become even more adaptive to situational changes in the environment and/or emergent security risks. There are secondary benefits such as the natural …

Relativistic Studies Of The Charmonium And Bottomonium Systems Using The Sucher Equation, Charles Martin Werneth

Dissertations

In this dissertation, bound states of quarks and anti-quarks (mesons) are studied with a relativistic equation known as the Sucher equation. Prior to the work in this dissertation, the Sucher equation had never been used for meson mass spectra. Furthermore, a full angular momentum analysis of the Sucher equation has never been studied. The Sucher equation is a relativistic equation with positive energy projectors imposed on the interaction. Since spin is inherent to the equation, the Sucher equation is equivalent to a relativistic Schrödinger equation with a spin-dependent effective potential. Through a complete general angular momentum analysis of the equation, …

Modeling With Bivariate Geometric Distributions, Jing Li

Dissertations

This dissertation studied systems with several components which were subject to different types of failures. Systems with two components having frequency counts in the domain of positive integers, and the survival time of each component following geometric or mixture geometric distribution can be classified into this category. Examples of such systems include twin engines of an airplane and the paired organs in a human body. It was found that such a system, using conditional arguments, can be characterized as multivariate geometric distributions. It was proved that these characterizations of the geometric models can be achieved using conditional probabilities, conditional failure …

Option Pricing And Stable Trading Strategies In The Presence Of Information Asymmetry, Anirban Dutta

Dissertations

Pricing derivatives is one of the central issues in mathematical finance. The seminal work of Black, Scholes and Merton has been the cornerstone of option pricing since their introduction in 1973. Their work influenced the pricing theory of other derivatives as well.

This derivative pricing theory has two primary shortcomings. Firstly, the theoretical pricing in such theories are not accompanied by a stable trading strategy. Secondly, they often assume that the market agents use a uniform model for the underlying instrument and that the market prices of the derivatives reveal all the information about the underlying instrument.

Theoreticians like Grossman …