Digital Commons Network^™

Theoretical And Computational Modeling Of Contaminant Removal In Porous Water Filters, Aman Raizada

Theses and Dissertations

Contaminant transport in porous media is a well-researched problem across many scientific and engineering disciplines, including soil sciences, groundwater hydrology, chemical engineering, and environmental engineering. In this thesis, we attempt to tackle this multiscale transport problem using the upscaling approach, which leads to the development of macroscale models while considering a porous medium as an averaged continuum system.

First, we describe a volume averaging-based method for estimating flow permeability in porous media. This numerical method overcomes several challenges faced during the application of traditional permeability estimation techniques, and is able to accurately provide the complete permeability tensor of a porous …

Regime-Switching Jump Diffusion Processes With Countable Regimes: Feller, Strong Feller, Irreducibility And Exponential Ergodicity, Khwanchai Kunwai

Theses and Dissertations

This work is devoted to the study of regime-switching jump diffusion processes in which the switching component has countably infinite regimes. Such processes can be used to model complex hybrid systems in which both structural changes, small fluctuations as well as big spikes coexist and are intertwined. Weak sufficient conditions for Feller and strong Feller properties and irreducibility for such processes are derived; which further lead to Foster-Lyapunov drift conditions for exponential ergodicity. Our results can be applied to stochastic differential equations with non-Lipschitz coefficients. Finally, an application to feedback control problems is presented.

Two Counting Problems In Geometric Triangulations And Pseudoline Arrangements, Ritankar Mandal

Theses and Dissertations

The purpose of this dissertation is to study two problems in combinatorial geometry in regard to obtaining better bounds on the number of geometric objects of interest: (i) monotone paths in geometric triangulations and (ii) pseudoline arrangements.

\medskip(i) A directed path in a graph is monotone in direction of $\mathbf{u}$ if every edge in the path has a positive inner product with $\mathbf{u}$. A path is monotone if it is monotone in some direction. Monotone paths are studied in optimization problems, specially in classical simplex algorithm in linear programming. We prove that the (maximum) number of monotone paths in a …

The Gini Index In Algebraic Combinatorics And Representation Theory, Grant Joseph Kopitzke

Theses and Dissertations

The Gini index is a number that attempts to measure how equitably a resource is distributed throughout a population, and is commonly used in economics as a measurement of inequality of wealth or income. The Gini index is often defined as the area between the "Lorenz curve" of a distribution and the line of equality, normalized to be between zero and one. In this fashion, we will define a Gini index on the set of integer partitions and prove some combinatorial results related to it; culminating in the proof of an identity for the expected value of the Gini index. …

Development Of Novel Compound Controllers To Reduce Chattering Of Sliding Mode Control, Mehran Rahmani

Theses and Dissertations

The robotics and dynamic systems constantly encountered with disturbances such as micro electro mechanical systems (MEMS) gyroscope under disturbances result in mechanical coupling terms between two axes, friction forces in exoskeleton robot joints, and unmodelled dynamics of robot manipulator. Sliding mode control (SMC) is a robust controller. The main drawback of the sliding mode controller is that it produces high-frequency control signals, which leads to chattering. The research objective is to reduce chattering, improve robustness, and increase trajectory tracking of SMC. In this research, we developed controllers for three different dynamic systems: (i) MEMS, (ii) an Exoskeleton type robot, and …

Applications Of A U-Net Variant Neural Network: Image Classification For Vegetation Component Identification In Outdoors Images And Image To Image Translation Of Ultrasound Images, Adam Honts

Theses and Dissertations

Convolutional Neural Networks have been applied in many image applications, for both supervised and unsupervised learning. They have shown their ability to be used in an array of diverse use cases which include but are not limited to image classification, segmentation, and image enhancement tasks. We make use of Convolutional Neural Networks' ability to perform well in these situations and propose an architecture for a Convolutional Neural Network based on a network known as U-Net. We then apply our proposed network to two different tasks, a vegetation classification task for images of outdoors environment, and an image to image translation …

Exploring The Division Algorithm In Euclidean Domains With Exploding Dots, Nicholas Johnson

Theses and Dissertations

We will give an overview of the representation of place value and arithmetic known as Exploding Dots and use this idea to explore the division algorithm. It is well-known that the ring of integers, the ring of polynomials, and the ring of Gaussian integers are all examples of Euclidean domains and therefore possess a division algorithm. Exploding Dots beautifully illustrates how one can perform division in any base and how this naturally leads us to division of polynomials. We will show how this same idea of having a “base machine” can be used to perform division in the Gaussian integers. …

Examining Virtual Mathematics Instruction: A Comparative Case Study Of In-Service Elementary Teachers With Mathematics Anxiety And Mathematics Teaching Self-Efficacy, Telashay Swope-Farr

Theses and Dissertations

Mathematics Anxiety (MA) and Mathematics Teaching Self-Efficacy (MTSE) have been reported as factors related to teachers’ mathematics instruction. This study investigated MA and MTSE in in-service elementary teachers’ virtual mathematics instruction. A comparative case study design was used to understand the relationship between MA, MTSE, and their virtual mathematics instructional practices. Two in-service elementary teachers from an urban public charter school district in a large metropolitan city in the Midwest participated. I employed qualitative methods to examine the results from the Abbreviated Mathematics Anxiety Rating Scale (AMAS), an adapted version of a researcher-developed instrument called the Mathematics Teaching and Mathematics …