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 …

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 …

Pseudo-Companion Matrices For Polynomial Systems, Melinda Kleczynski

Dissertations, Master's Theses and Master's Reports

Roots of a scalar polynomial in one variable are frequently found by computing the eigenvalues of the standard companion matrix. In this exploratory work, we introduce the pseudo-companion matrix for finding roots of multivariable polynomial systems. In some cases, a perturbation of the polynomial system is used for the matrix construction, yielding approximate roots of the original polynomial system. The coordinates of the roots, or their approximations, are obtained from the eigenvectors of this matrix. In this thesis, we describe the process of constructing the pseudo-companion matrix and computing the polynomial roots using illustrative examples.

High Accuracy Methods And Regularization Techniques For Fluid Flows And Fluid-Fluid Interaction, Mustafa Aggul

Dissertations, Master's Theses and Master's Reports

This dissertation contains several approaches to resolve irregularity issues of CFD problems, including a decoupling of non-linearly coupled fluid-fluid interaction, due to high Reynolds number. New models present not only regularize the linear systems but also produce high accurate solutions both in space and time. To achieve this goal, methods solve a computationally attractive artificial viscosity approximation of the target problem, and then utilize a correction approach to make it high order accurate. This way, they all allow the usage of legacy code | a frequent requirement in the simulation of fluid flows in complex geometries. In addition, they all …

Optimization And Control Of An Array Of Wave Energy Converters, Jianyang Lyu

Dissertations, Master's Theses and Master's Reports

This study explored optimal configuration of both the array layout and the dimension of each WEC in the array. The array contains heaving buoys with full interaction and exact hydrodynamics. Optimization of dimension was done on each WEC in the array with a given optimal layout, and a higher q-factor was achieved. Both impedance matching optimal control and derivative control were employed, which provides both theoretical maximum energy and a more realistic case. Then the work was expanded to optimization of both the array layout and the dimension of each WEC in the array. An average of 39.21% higher q-factor …

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 …

Money Matters: An Analysis Of Campaign Finance In United States House Of Representatives Elections, 2010-2016, Destiny Leitz

Honors Program Theses

Money in politics is the single largest threat to the democratic system in the United States. It influences everything in politics, from the candidates to the issues debated. Every American knows that running for office requires large amounts of funding, and being elected requires even more. People worry that only the wealthiest voices are being heard; of course, candidates who depend on money from wealthy donors for campaign strength would never support unfavorable policies for their donors. Clearly, money in politics threatens the core democratic principles upon which America was founded. However, few people discuss whether the money really makes …

Exploration Of Counter Examples Of Balanced Sets, Jake Allen Weber

Honors Program Theses

Mathematicians are often intrigued with patterns, many times finding themselves looking for pieces of structure within a data set. This research project is no different in that we have explored our vast data set for substructure.

Our goal is to identify the following: how many data points are necessary to guarantee our set has a balanced set/substructure? Naturally rephrasing the previous question, we also ask ourselves what is the largest set that does not have a balanced subset/substructure? This alternate phrasing set us down our current path. We focused on the largest sets with no balanced substructure and what they …

Decoding Book Barcode Images, Yizhou Tao

CMC Senior Theses

This thesis investigated a method of barcode reconstruction to address the recovery of a blurred and convoluted one-dimensional barcode. There are a lot of types of barcodes used today, such as Code 39, Code 93, Code 128, etc. Our algorithm applies to the universal barcode, EAN 13. We extend the methodologies proposed by Iwen et al. (2013) in the journal article "A Symbol-Based Algorithm for Decoding barcodes." The algorithm proposed in the paper requires a signal measured by a laser scanner as an input. The observed signal is modeled as a true signal corrupted by a Gaussian convolution, additional noises, …

Validation Of A Lottery, Xiaona Zhou

Publications and Research

The NY Pick 4 lottery consists of four "randomly" chosen digits from 0 to 9. For this to be fair, each digit should be equally likely to occur. To determine whether this is the case, a Chi-squared goodness of fit test will be applied to historical data. This provides a quantitative way of measuring how well the observed frequency of digits matches our expectations of a fair lottery. The Chi-squared distribution gives us a number beyond which we reject fairness. However, there is another possibility. If the difference between the fair model and the observed frequency is too small, that …

Wildfire Emissions In The Context Of Global Change And The Implications For Mercury Pollution, Aditya Kumar

Dissertations, Master's Theses and Master's Reports

Wildfires are episodic disturbances that exert a significant influence on the Earth system. They emit substantial amounts of atmospheric pollutants, which can impact atmospheric chemistry/composition and the Earth’s climate at the global and regional scales. This work presents a collection of studies aimed at better estimating wildfire emissions of atmospheric pollutants, quantifying their impacts on remote ecosystems and determining the implications of 2000s-2050s global environmental change (land use/land cover, climate) for wildfire emissions following the Intergovernmental Panel on Climate Change (IPCC) A1B socioeconomic scenario.

A global fire emissions model is developed to compile global wildfire emission inventories for major atmospheric …

Positive Definite Functions And Dual Pairs Of Locally Convex Spaces, Daniel Alpay, Saak Gabriyelyan

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.

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 …

Effect Of Neuromodulation Of Short-Term Plasticity On Information Processing In Hippocampal Interneuron Synapses, Elham Bayat Mokhtari

Graduate Student Theses, Dissertations, & Professional Papers

Neurons convey information about the complex dynamic environment in the form of signals. Computational neuroscience provides a theoretical foundation toward enhancing our understanding of nervous system. The aim of this dissertation is to present techniques to study the brain and how it processes information in particular neurons in hippocampus.

We begin with a brief review of the history of neuroscience and biological background of basic neurons. To appreciate the importance of information theory, familiarity with the information theoretic basics is required, these basics are presented in Chapter 2. In Chapter 3, we use information theory to estimate the amount of …

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 …

Multiclass Classification Using Support Vector Machines, Duleep Prasanna W. Rathgamage Don

College of Graduate Studies: Theses & Dissertations

In this thesis, we discuss different SVM methods for multiclass classification and introduce the Divide and Conquer Support Vector Machine (DCSVM) algorithm which relies on data sparsity in high dimensional space and performs a smart partitioning of the whole training data set into disjoint subsets that are easily separable. A single prediction performed between two partitions eliminates one or more classes in a single partition, leaving only a reduced number of candidate classes for subsequent steps. The algorithm continues recursively, reducing the number of classes at each step until a final binary decision is made between the last two classes …

On Modeling Quantities For Insurer Solvency Against Catastrophe Under Some Markovian Assumptions, Daniel Jefferson Geiger

Doctoral Dissertations

"Insurance companies sometimes face catastrophic losses, yet they must remain solvent enough to meet the legal obligation of covering all claims. Catastrophes can result in large damages to the policyholders, causing the arrival of numerous claims to insurance companies at once. Furthermore, the severity of an event could impact the time until the next occurrence. An insurer needs certain levels of startup capital to meet all claims, and then must have adequate reserves on a continual basis, even more so when catastrophes occur. This work examines two facets of these matters: for an infinite time horizon, we extend and develop …

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 …

A Two-Dimensional Finite Element Model Of The Grain Boundary Based On Thermo-Mechanical Strain Gradient Plasticity, Yooseob Song, George Z. Voyiadjis

Civil Engineering Faculty Publications

In this work, a two-dimensional finite element model for the grain boundary flow rule is developed based on the thermo-mechanical gradient-enhanced plasticity theory. The proposed model is temperature-dependent. A special attention is given to physical and micromechanical nature of dislocation interactions in combination with thermal activation on stored and dissipated energy. Thermodynamic conjugate microforces are decomposed into energetic and dissipative components. Correspondingly, two different grain boundary material length scales are present in the proposed model. Finally, numerical examples are solved in order to explore characteristics of the proposed grain boundary flow rule.

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 …

Derivation Of The Hellinger-Reissner Variational Form Of The Linear Elasticity Equations, And A Finite Element Discretization, Bram Fouts

REU Final Reports

In this paper we are going to derive the linear elasticity equations in the Strong Form to the Hellinger Reissner Form. We find a suitable solution to solve our stress tensor. Then we will use finite element discretization from. We will run tests on a unit cube and multiple other shapes, which are described at the end. We view the different magnitudes of the displacement vector of each shape.

Wavelet Anova Bisection Method For Identifying Simulation Model Bias, Andrew D. Atkinson, Raymond R. Hill, Joseph J. Pignatiello Jr., G. Geoffrey Vining, Edward D. White, Eric Chicken

Faculty Publications

High-resolution computer models can simulate complex systems and processes in order to evaluate a solution quickly and inexpensively. Many simulation models produce dynamic functional output, such as a set of time-series data generated during a process. These computer models require verification and validation (V&V) to assess the correctness of these simulations. In particular, the model validation effort evaluates if the model is an appropriate representation of the real-world system that it is meant to simulate. However, when assessing a model capable of generating functional output, it is useful to learn more than simply whether the model is valid or invalid. …

Particle Filters For State Estimation Of Confined Aquifers, Graeme Field

UNF Graduate Theses and Dissertations

Mathematical models are used in engineering and the sciences to estimate properties of systems of interest, increasing our understanding of the surrounding world and driving technological innovation. Unfortunately, as the systems of interest grow in complexity, so to do the models necessary to accurately describe them. Analytic solutions for problems with such models are provably intractable, motivating the use of approximate yet still accurate estimation techniques. Particle filtering methods have emerged as a popular tool in the presence of such models, spreading from its origins in signal processing to a diverse set of fields throughout engineering and the sciences including …

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 …

Weighted Inequalities For Dyadic Operators Over Spaces Of Homogeneous Type, David Edward Weirich

Mathematics & Statistics ETDs

A so-called space of homogeneous type is a set equipped with a quasi-metric and a doubling measure. We give a survey of results spanning the last few decades concerning the geometric properties of such spaces, culminating in the description of a system of dyadic cubes in this setting whose properties mirror the more familiar dyadic lattices in R^n . We then use these cubes to prove a result pertaining to weighted inequality theory over such spaces. We develop a general method for extending Bellman function type arguments from the real line to spaces of homogeneous type. Finally, we uses this …

An Application Of M-Matrices To Preserve Bounded Positive Solutions To The Evolution Equations Of Biofilm Models, Richard S. Landry Jr.

LSU New Orleans Theses and Dissertations

In this work, we design a linear, two step implicit finite difference method to approximate the solutions of a biological system that describes the interaction between a microbial colony and a surrounding substrate. Three separate models are analyzed, all of which can be described as systems of partial differential equations (PDE)s with nonlinear diffusion and reaction, where the biological colony grows and decays based on the substrate bioavailability. The systems under investigation are all complex models describing the dynamics of biological films. In view of the difficulties to calculate analytical solutions of the models, we design here a numerical technique …

Mathematical Formulation Of Fusion Energy Magnetohydrodynamics, Nikolaos I. Xiros

LSU New Orleans Theses and Dissertations

Chapter 1 presents the basic principles of Controlled Thermonuclear Fusion, and the approaches to achieve nuclear fusion on Earth. Furthermore, the basic components of the Tokamak, the reactor which will house the fusion reaction, are analyzed. Finally, the chapter ends with a discussion on how the present thesis is related to the Controlled Thermonuclear Fusion. Chapter 2 introduces briefly the basic concepts of the Electromagnetic and Magnetohydrodynamic theories as well as MHD turbulence. Chapter 3 presents a first glance in OpenFOAM CFD library. Chapter 4 introduces the Orszag-Tang vortex flow, which is a benchmark test case for MHD numerical models. …

Underwater Acoustic Signal Analysis Toolkit, Kirk Bienvenu Jr

LSU New Orleans Theses and Dissertations

This project started early in the summer of 2016 when it became evident there was a need for an effective and efficient signal analysis toolkit for the Littoral Acoustic Demonstration Center Gulf Ecological Monitoring and Modeling (LADC-GEMM) Research Consortium. LADC-GEMM collected underwater acoustic data in the northern Gulf of Mexico during the summer of 2015 using Environmental Acoustic Recording Systems (EARS) buoys. Much of the visualization of data was handled through short scripts and executed through terminal commands, each time requiring the data to be loaded into memory and parameters to be fed through arguments. The vision was to develop …

A Statistical Study Of Student Success In The Bgsu Honors College, Sarah Hercules

Honors Projects

Higher education has long tried to find the best measures to predict student success. Different colleges often have different guidelines, requiring different criteria to be evaluated. The BGSU Honors College has struggled with retention and recruitment of underrepresented students with their current admission criteria. This analysis studies different measures of student success such as BGSU GPA and number of completed Honors credits for high-achieving BGSU students who enrolled from Fall 2013 through Fall 2016 to find the best predictors of student success through regression analysis. Throughout this paper, the impact of ethnicity, gender, the college of a student’s program, high …