Applied Mathematics Commons^™

A Mathematical Model Of A Corrosion System Containing Inhibitors, Abigael Frey

Williams Honors College, Honors Research Projects

A two dimensional model is developed to describe how organic and inorganic inhibitors slows down the corrosion damage of a coated metal plate that contains a defect. The model contains a metal covered on one side by a coating that contains organic and inorganic inhibitors, electrolytes that are on the outside of the coating, and a small defect in the coating. The defect is an area where the coating is more porous and allows the electrolytes to leak in faster. In this model the organic inhibitor is presumed to be dissolved into the coating and the inorganic inhibitor is released …

Boundization, Closure And Convergence For The Ultra Extended Complex Banach And Hilbert Spaces With Applications, Salah Hamad

Graduate Theses, Dissertations, and Problem Reports (ETD)

We study Boundization, Closure and Convergence of Complex Banach and Hilbert spaces. We augment a Banach space with elements “infinity” and turn the augmented set into a metric space by appropriate distance functions. This new metric space is called the Ultra Extended Banach Space. A new family of bijections, motivated by nonlinear projections, take an Ultra Extended Banach Space into bounded subsets of a “larger” Banach space. We compare the family of new metrics induced and show which ones are equivalent and which ones are unexpectedly not equivalent. Some applications are provided.

High-Order Integral Equation Methods For Quasi-Magnetostatic And Corrosion-Related Field Analysis With Maritime Applications, Robert Pfeiffer

Theses and Dissertations--Electrical and Computer Engineering

This dissertation presents techniques for high-order simulation of electromagnetic fields, particularly for problems involving ships with ferromagnetic hulls and active corrosion-protection systems.

A set of numerically constrained hexahedral basis functions for volume integral equation discretization is presented in a method-of-moments context. Test simulations demonstrate the accuracy achievable with these functions as well as the improvement brought about in system conditioning when compared to other basis sets.

A general method for converting between a locally-corrected Nyström discretization of an integral equation and a method-of-moments discretization is presented next. Several problems involving conducting and magnetic-conducting materials are solved to verify the accuracy …

Penalized Mixed-Effects Ordinal Response Models For High-Dimensional Genomic Data In Twins And Families, Amanda E. Gentry

Theses and Dissertations

The Brisbane Longitudinal Twin Study (BLTS) was being conducted in Australia and was funded by the US National Institute on Drug Abuse (NIDA). Adolescent twins were sampled as a part of this study and surveyed about their substance use as part of the Pathways to Cannabis Use, Abuse and Dependence project. The methods developed in this dissertation were designed for the purpose of analyzing a subset of the Pathways data that includes demographics, cannabis use metrics, personality measures, and imputed genotypes (SNPs) for 493 complete twin pairs (986 subjects.) The primary goal was to determine what combination of SNPs and …

Delay Differential Equations And Their Application To Micro Electro Mechanical Systems, Asset Ospanov

Theses and Dissertations

Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic solution for this equation is …

Optimal Supply Delivery Under Military Specific Constraints, Talena Fletcher

College of Graduate Studies: Theses & Dissertations

Through-out military history, the need to safely and effectively allocate resources to various military operations was a task of extreme importance. Satisfying the needs of multiple consumers by optimally pairing with appropriate suppliers falls into the category of vehicle routing problems (VRP), which has been intensively studied over the years. In general, finding the optimal solution to VRP is known to be NP-hard. The proposed solutions rely on mathematical programming and the size of the problems that can be optimally solved is typically limited. In military settings, balancing the needs of multiple consumers with the current operational environment has always …

Blow Up Solution Of Bose-Einstein Condensates With Anisotropic Trapping Potential And Rotation, Christopher Leonard

College of Graduate Studies: Theses & Dissertations

In this paper we will analyze a nonlinear Schrodinger equation with quadratic anisotropic trapping potential used to describe a Bose-Einstein condensate. We will find sufficient condition for the global existence of the solution and for the blow up result using physical properties associated to the equation such as the mass, energy, and angular momentum along with some other identities related to the equation. We will finish the thesis with showing some graphical representations describing the solution of the equation.

Developing A Cyberterrorism Policy: Incorporating Individual Values, Osama Bassam J. Rabie

Theses and Dissertations

Preventing cyberterrorism is becoming a necessity for individuals, organizations, and governments. However, current policies focus on technical and managerial aspects without asking for experts and non-experts values and preferences for preventing cyberterrorism. This study employs value focused thinking and public value forum to bare strategic measures and alternatives for complex policy decisions for preventing cyberterrorism. The strategic measures and alternatives are per socio-technical process.

Models For High Dimensional Spatially Correlated Risks And Application To Thunderstorm Loss Data In Texas, Tobias Merk

Masters Theses

"Insurance claims caused by natural disasters exhibit spatial dependence with the strength of dependence being based on factors such as physical distance and population density, to name a few. Accounting for spatial dependence is therefore of crucial importance when modeling these types of claims. In this work, we present an approach to assess spatially dependent insurance risks using a combination of linear regression and factor copula models. Specifically, in loss modeling, observed dependence patterns are highly nonlinear, thus copula-based models seem appropriate since they can handle both linear and nonlinear dependence. The factor copula approach for estimating the spatial dependence …

Copula Theory And Regression Analysis, Mayooran Thevaraja

All Graduate Theses, Dissertations, and Other Capstone Projects

Researchers are often interested to study in the relationships between one variable and several other variables. Regression analysis is the statistical method for investigating such relationship and it is one of the most commonly used statistical Methods in many scientific fields such as financial data analysis, medicine, biology, agriculture, economics, engineering, sociology, geology, etc. But basic form of the regression analysis, ordinary least squares is not suitable for actuarial applications because the relationships are often nonlinear and the probability distribution of the response variable may be non-Gaussian distribution. One of the method that has been successful in overcoming these challenges …

A Mixed Finite Element Method For The Coupling Of Linear Elasticity And Stokes Flow, Maranda Bean

Open Access Theses & Dissertations

The complex interaction between fluids and structures require the coupling the laws concerning structure mechanics and fluid dynamics and are of vital importance to many scientific and engineering fields. We propose a method for modeling the coupling of a linearly elastic solid and slow fluid flow modeled by Stokes equations. The model equations are expressed in terms of displacement, velocity and stress. With these primary variables, we use a single mixed finite element space based on the Hellinger-Reissner variational principle for linear elasticity to discretize the resulting system spatially. This results in more accurate approximations for stress than those obtained …

Inclusion Of Blocking Power For A Complete Voting Power Analysis In The Imf, Shiwani Varal

Senior Independent Study Theses

The International Monetary Fund (IMF) calculates the voting power of a country by dividing the total of one member's votes by the total of all members' votes. This method of calculating the power of a state judges power as voting weight. However, voting weights are the total number of votes a country has in an institution, while voting power is the influence a country has on a policy decision. A better approach to calculate this voting power within an institution is by using voting power indices. However, literature only calculates the winning power, while voting power is defined as the …

Sports Analytics With Computer Vision, Colby T. Jeffries

Senior Independent Study Theses

Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …

Using A Coupled Bio-Economic Model To Find The Optimal Phosphorus Load In Lake Tainter, Wi, Mackenzie Jones

Williams Honors College, Honors Research Projects

In Dunn County, Wisconsin the lakes suffer from algae blooms due to excess phosphorus runoff. A coupled bio-economic model is studied with the intent of finding the optimal level of phosphorus that should be allowed into the lake depending on certain biologic and economic parameters. We model the algae and phosphorus concentration in the lake over time based off the phosphorus input. Community welfare is modeled by comparing the costs and benefits of phosphorus fertilizer. This model is proposed to find the phosphorus level that maximizes community welfare and then determine how certain environmental and social change initiatives will affect …

Nonlinear Coupled Effects In Nanomaterials, Sia Bhowmick

Theses and Dissertations (Comprehensive)

Materials at the nanoscale have different chemical, structural, and optoelectrical properties compared to their bulk counterparts. As a result, such materials, called nanomaterials, exhibit observable differences in certain physical phenomena. One such resulting phenomenon called the piezoelectric effect has played a crucial role in miniature self-powering electronic devices called nanogenerators which are fabricated by using nanostructures, such as nanowires, nanorods, and nanofilms. These devices are capable of harvesting electrical energy by inducing mechanical strain on the individual nanostructures. Electrical energy created in this manner does not have environmental limitations. In this thesis, important coupled effects, such as the nonlinear piezoelectric …

Adaptive Methods For Point Cloud And Mesh Processing, Zinat Afrose

Computational Modeling & Simulation Engineering Theses & Dissertations

Point clouds and 3D meshes are widely used in numerous applications ranging from games to virtual reality to autonomous vehicles. This dissertation proposes several approaches for noise removal and calibration of noisy point cloud data and 3D mesh sharpening methods. Order statistic filters have been proven to be very successful in image processing and other domains as well. Different variations of order statistics filters originally proposed for image processing are extended to point cloud filtering in this dissertation. A brand-new adaptive vector median is proposed in this dissertation for removing noise and outliers from noisy point cloud data.

The major …

The Use Of Item Response Theory In Survey Methodology: Application In Seat Belt Data, Mark K. Ledbetter, Norou Diawara, Bryan E. Porter

Mathematics & Statistics Faculty Publications

Problem: Several approaches to analyze survey data have been proposed in the literature. One method that is not popular in survey research methodology is the use of item response theory (IRT). Since accurate methods to make prediction behaviors are based upon observed data, the design model must overcome computation challenges, but also consideration towards calibration and proficiency estimation. The IRT model deems to be offered those latter options. We review that model and apply it to an observational survey data. We then compare the findings with the more popular weighted logistic regression. Method: Apply IRT model to the observed data …

Numerical Simulation For A Rising Bubble Interacting With A Solid Wall: Impact, Bounce, And Thin Film Dynamics, Changjuan Zhang, Jie Li, Li-Shi Luo, Tiezheng Qian

Mathematics & Statistics Faculty Publications

Using an arbitrary Lagrangian-Eulerian method on an adaptive moving unstructured mesh, we carry out numerical simulations for a rising bubble interacting with a solid wall. Driven by the buoyancy force, the axisymmetric bubble rises in a viscous liquid toward a horizontal wall, with impact on and possible bounce from the wall. First, our simulation is quantitatively validated through a detailed comparison between numerical results and experimental data. We then investigate the bubble dynamics which exhibits four different behaviors depending on the competition among the inertial, viscous, gravitational, and capillary forces. A phase diagram for bubble dynamics has been produced using …

Computational Investigation Of Energetic Materials: Influence Of Intramolecular And Intermolecular Interactions On Sensitivity, Ashley Lauren Shoaf

Chemistry & Biochemistry Theses & Dissertations

The development of novel high energy density materials (HEDMs) with superior energetic properties depends on characterizing how and why detonation occurs. Detonation is highly energetic and a nearly instantaneous process, making experimental studies challenging; thus, computational modeling through density functional theory (DFT) and molecular dynamics (MD) can be used to propose weakened, or activated, bonds that break to initiate explosive decomposition, termed trigger bonds. Bond activation is characterized by the Wiberg bond index (WBI), a measure of interatomic electron density. Trigger bonds in HEDMs are commonly found in explosophores, functional groups that contribute to energetic potential such as X-NO_{2 …}

Application Of Evolutionary Network Concept In Structuring Mathematics Curriculum, Aditi Mitra

College of Graduate Studies: Theses & Dissertations

Phylogenetic tree and in general, evolutionary network, has found its application well beyond the biological fields and has even percolated into recent high demanding areas, such as data mining and social media chain reactions. An extensive survey of its current applications are presented here. An attempt has been made to apply the very concept in the mathematics course curriculum inside a degree program. Various features of the tree structure are identified within the curriculum network. To highlight various key components and to enhance the visual effect, several diagrams are presented. The combined effect of these diagram provides a sense of …