Digital Commons Network^™

Reciprocity-Based Transfer Function Techniques For Acoustic Source Reconstruction, Spring Isolator Characterization And Structural Damping Assessment, David Pum Thian Lal Paite Neihguk

Theses and Dissertations--Mechanical and Aerospace Engineering

Reciprocity implies that a system responds identically when the source and receiver positions are interchanged. This dissertation applies this principle to address three practical challenges in noise and vibration characterization, where conventional approaches are limited by inaccessible interfaces, constrained excitation conditions, or metrics that do not fully capture vibroacoustic behavior.

The first study develops and validates an inverse method to characterize ducted acoustic sources using acoustic free velocity. Acoustic reciprocity is applied to simplify transfer function measurements. The method is extended to large cross-section ducts, where the source is reconstructed as a collection of point sources along a plane. Validation …

Using Camera-Based Unmarked Spatial Capture-Recapture Modeling To Estimate Reintroduced Elk (Cervus Canadensis) Population Parameters And Distribution In Southeastern Kentucky, Claire Marie Muia

Theses and Dissertations--Forestry and Natural Resources

Estimation of population parameters is important for wildlife management decisions. Elk reintroduced to southeastern Kentucky experienced early irruptive population growth and are currently monitored using a statewide harvest-based statistical population reconstruction model (SPR) across the Kentucky Elk Restoration Zone (KERZ). Because the SPR model is spatially coarse and difficult to scale to the smaller management units comprising the KERZ, we conducted a spatially explicit capture-recapture study using a clustered camera-trapping array deployed for 10 weeks from June–August 2024 to estimate elk population parameters within Management Unit 4. Due to a lack of resights of GPS-marked elk, population parameters were estimated …

Understanding Knowledge And Perceptions Of The Beef Industry On A Land-Grant University Campus, Allison E. Reaves

Theses and Dissertations--Community & Leadership Development

A well-researched phenomenon in the agricultural industry is the effects of constant innovation coupled with an increasing divide between producer and consumer. This issue has been presented as especially prevalent within animal agriculture and the beef industry, a predominant concern considering Kentucky’s agricultural commodities. This study (n = 31) utilized a mixed-methods approach to understand the knowledge, perceptions, and behavior of beef consumers on a land-grant university campus. Methodologies included Python’s DeepFace emotion recognition, semi-structured interviews, and the JMALI agricultural literacy assessment. Findings revealed participants to be below expected agricultural literacy levels of high school graduates (M=11), with no …

Wastewater Surveillance For Sars-Cov-2 In Rural Kentucky, 2021–2023, James W. Keck, Reuben Adatorwovor, Ann Noble, Savannah Tucker, William Strike, Soroosh Torabi, Mohammad Dehghan Banadaki, Blazan Mijatovic, Steven K. Roggenkamp, Donna Mcneil, Lindell Ormsbee, Scott M. Berry

Family and Community Medicine Faculty Publications

Wastewater testing for SARS-CoV-2 provided useful public health information during the COVID-19 pandemic yet was underutilized in rural communities. We addressed this gap by implementing wastewater surveillance and assessing its performance in 10 communities in Eastern Kentucky. We collected wastewater samples 1–2 times weekly at 10 wastewater treatment plants (WWTPs) from May 2021 until April 2023 and measured SARS-CoV-2 RNA concentrations using polymerase chain reaction testing. We calculated time-lagged correlations between wastewater concentrations and county-level reported COVID-19 cases by site. We developed a generalized linear model to estimate COVID-19 incidence from wastewater SARS-CoV-2 concentrations. The 10 participating WWTPs served 2430 …

Adsorptive Gas Sensor Response Forecasting To Enable Breath-By-Breath Analysis, Samuel Bellaire, Samir Ahmed Rawashdeh, Kirby P. Mayer, Jamie L. Sturgill

Physical Therapy Faculty Publications

MOS gas sensors have proven to be useful in electronic noses, which utilize these sensors to detect volatile organic compounds in human breath to detect various lung diseases. Unfortunately, the long settling time of MOS gas sensors is ill-suited to measuring human breath, where complete breathing cycles are often shorter than 5 s. Existing studies circumvent this limitation by collecting gas samples and injecting them into a sealed chamber to react with the sensors. However, it would be convenient if breath-by-breath analysis could be conducted without the need to store breath samples. To accomplish this, we present a novel forecasting …

Body Mass Index Has No Impact On Complications And Mortality For Patients With Stage Iv Pancreatic Ductal Adenocarcinoma, Ren Bryant, Hannah Darnell, Megan Hall, Kelsey N. Karnik, Kristen J. Mcquerry, Ruben R. Plentz

Biostatistics Faculty Publications

Background: Pancreatic ductal adenocarcinoma (PDAC) is one of the leading causes of United States (USA) cancer death. Overweight and obesity developing into a growing global medical and socio-economic problem, affecting approximately 42% of adults in the USA population. The aim of our analysis was to evaluate the influence of overweight and obesity on complications and clinical outcome in patients with stage IV PDAC.

Methods: We retrospectively reviewed electronic health records of patients diagnosed with stage IV PDAC (n=162) who followed with the University of Kentucky from January 2017–October 2024. Comparisons were based on the body mass index (BMI): low BMI …

A Simple Statistical Tool To Correct The Daily Temperature Effect On Dielectric Soil Matric Potential Sensor Readings, Sebastián Bravo Peña, Meindert Commelin, Ole O. Wendroth

Plant and Soil Sciences Faculty Publications

High-resolution time series recorded by soil water dielectric sensors are often affected by other processes. Dielectric soil matric potential sensors, such as the TEROS 21, exhibit temperature sensitivity, resulting in deviations of readings from the true value due to soil temperature fluctuations. However, methods for correcting this effect remain limited. The objective of this study was to create a straightforward, scale-based statistical approach to mitigate the influence of daily temperature oscillations on matric potential dielectric readings. The temperature sensitivity correction function (TSCF) identifies, quantifies, and smooths diurnal fluctuations caused by soil temperature dynamics. We provide a detailed description of the …

Cultus: Eco-Phenomenology In The Work Of John Steinbeck, Robinson Jeffers, And Jack London, Carter D. Johnson

Theses and Dissertations--English

In the face of increasingly dire environmental crises, proposed solutions have gravitated toward imperatives for faster, cleaner, and more efficient technologies and resources. While practical solutions are necessary, they are entirely insufficient to deal with an underlying issue driving environmental degradation: unbridled instrumental reason. In this dissertation, I suggest a theoretical posture, cultus, which attempts to balance the necessity of instrumental action with the guiding counterweight of receptivity. Furthermore, I argue that such personal receptivity is uniquely fostered in aesthetic experiences, attuning the individual to the non-identical and renewing a relationship of care.

I examine the life and work of …

Federated Data Engineering And Learning For Edge Intelligence Systems, Afsaneh Mahanipour

Theses and Dissertations--Computer Science

The rapid proliferation of Internet of Things (IoT) devices and cyber–physical systems (CPS) in domains such as smart healthcare, intelligent transportation, and industrial automation has led to unprecedented volumes of heterogeneous data. While advances in deep learning and large-scale foundation models have enabled powerful data-driven decision making, their deployment in real-world distributed environments remains fundamentally constrained by limited computation, communication bandwidth, energy resources, and data privacy requirements. This dissertation addresses these challenges by developing novel federated learning frameworks and efficient federated data-processing pipelines that make large-scale artificial intelligence practical, scalable, and trustworthy in resource-constrained settings. This dissertation identifies data preprocessing …

Multi-Objective Optimization Of Energy Costs And Ev Battery Health In V2g Enabled Homes, Dzifa M. Hodey

Theses and Dissertations--Computer Science

Electric vehicles (EVs) and rooftop solar photovoltaic (PV) systems are increasingly being integrated into residential settings, creating new opportunities for vehicle-to-grid (V2G) and vehicle-to-home (V2H) operations. In these systems, the EV battery functions as a controllable energy storage unit that can charge from the grid or PV and discharge energy to supply household load or export to the grid for a profit. By intelligently scheduling this bidirectional power exchange, households can reduce electricity costs and enhance PV utilization. Realizing these benefits requires optimization strategies that balance cost reduction with EV battery health preservation. However, existing V2G/V2H studies largely emphasize cost …

Toward Efficient And Scalable Scientific Data Management Through Quality-Oriented Data Compression, Pu Jiao

Theses and Dissertations--Computer Science

Scientific simulations and instruments now produce data at rates that overwhelm the storage, memory, and network subsystems of modern high-performance computing (HPC) facilities. Error-bounded lossy compression reduces data movement costs while bounding reconstruction error, yet three barriers limit its adoption in mission-critical workflows: existing compressors cannot guarantee the accuracy of domain-specific quantities of interest (QoIs) derived from compressed data; compression-induced artifacts such as posterization, blocking, and interpolation banding erode user confidence in decompressed fields; and significant compressibility in the quantization index arrays of interpolation-based pipelines remains unexploited. This dissertation addresses all three barriers through four contributions, with the artifact barrier …

Advancing Task-Oriented Dialog Systems: Scalability, Generalization, And Evaluation, Adib Mosharrof

Theses and Dissertations--Computer Science

Task-oriented dialog (TOD) systems enable conversational interfaces for complex tasks like flight booking and restaurant reservations. However, deploying TOD systems at scale faces three critical barriers: scalability, generalization, and evaluation. Scalability is primarily restricted by the human-annotation bottleneck, as current systems depend on vast quantities of manually labeled data for every new domain, making deployment prohibitively expensive. Generalization remains a persistent challenge, as systems optimized for known domains often suffer significant performance degradation when encountering new, unseen ones. Existing evaluation metrics measure response quality and fluency, but fail to measure functional task success. As TOD systems are deployed across diverse …

Alexander Duals Of Symmetric Simplicial Complexes And Stanley-Reisner Ideals, Ayah Almousa, Kaitlin Bruegge, Martina Juhnke-Kubitzke, Uwe Nagel, Alexandra Pevzner

Mathematics Faculty Publications

Given an ascending chain (I_n)_n∈N of Sym-invariant squarefree monomial ideals, we study the corresponding chain of Alexander duals (I_n^∨)_n∈N. Using a novel combinatorial tool, which we call avoidance up to symmetry, we provide an explicit description of the minimal generating set up to symmetry in terms of the original generators. Combining this result with methods from discrete geometry, this enables us to show that the number of orbit generators of I_n^∨ is given by a polynomial in n for sufficiently large n. The same is true for …

The Effects Of Systematic Instructional Interventions On Functional Communication, Vocational Independence, And Academic Performance For High School Students With Autism In A Self-Contained Special Education Setting, Sarah O. Shalash

University of Kentucky Master's Theses

This project evaluated the effects of systematic instruction on functional communication, vocational independence, and functional mathematics for three high school students with autism in a self-contained special education classroom using three A–B single-case designs. Interventions included a system of least prompts for AAC requesting and vocational task completion and constant time delay for a functional timer-setting task. Student performance was measured as the percentage of independently completed responses across instructional sessions. Student T demonstrated meaningful improvement in independent AAC requesting and reached 75% independence in the final session. Student B demonstrated emerging improvement in timer-setting performance and reached 60% independence …

Effective Deep Learning Architectures For Structured Data Analysis And Generation, Md Atik Ahamed

Theses and Dissertations--Computer Science

The effective utilization of structured data is fundamental to modern machine learning, yet it presents distinct challenges in both predictive analysis and generative modeling. Traditional deep learning architectures, particularly Transformers, often suffer from quadratic computational complexity when processing long sequences. This dissertation addresses these limitations by introducing novel architectures based on State-Space Models (SSMs) and Diffusion Models. In the area of predictive analysis, we focus on overcoming the computational bottlenecks of attention mechanisms for tabular and time-series data. First, we introduce MambaTab, a selective state-space architecture designed for efficient tabular classification. By leveraging the linear complexity of SSMs, MambaTab significantly …

Different Destinations: Clarifying And Addressing Pipeline Problems For Women In Academic Archaeology, Scott R. Hutson, Jaycee Castro, Bruno Athie Teruel

Anthropology Faculty Publications

In STEM fields, women tend to leak out of the pipeline to the professoriate. In archaeology, however, robust databases and chronological control reveal that there is no leakage from earning a PhD to tenure-track positions. Nor is there a leak from assistant professor to associate professor. Nevertheless, men get hired as faculty in PhD programs more often than women. This is important because PhD programs are research-intensive and train future leaders. Furthermore, women PhD students have women as advisers more than often men and report advantages to this arrangement. Yet with fewer women faculty in PhD programs, women mentors are …

Chirp Imaging In Extant Lakes And Reservoirs, Kevin L. Woller, Edward W. Woolery, Eva C. Lyon, Michael M. Mcglue

Earth and Environmental Sciences Faculty Publications

Compressed high-intensity radiated pulse (CHIRP) acoustic reflection data acquired in lakes and other shallow water bodies can provide detailed imaging that is valuable for environmental and engineering geology applications well below the sub-bottom floors. However, it is often unclear to non-specialists which acquisition settings should be considered to achieve optimal imaging quality when beginning a new survey, particularly in an unfamiliar environment. We review fundamental concepts for optimizing signal design using coincident CHIRP lines from two extant glacial lakes in the eastern Sierra Nevada of California: Convict Lake and June Lake. As part of the optimization process, seismic data were …

Anuran Occupancy Of Created Wetlands Within Reforested Legacy Surface Mines In Kentucky And West Virginia, Jillian C. Newman, Steve Price, Jacquelyn C. Guzy, Joshua Castle, John J. Cox, Jeffery L. Larkin, Christopher D. Barton

Forestry and Natural Resources Faculty Publications

Restoration of habitat is an important component of wildlife management. Surface coal mining has altered forest cover in the Central Appalachians, and most reclamation activities on previously mined lands result in non-native grasslands or shrub lands. The Forestry Reclamation Approach (FRA), which emphasizes non-native vegetation removal, soil decompaction, planting of native trees and shrubs, and, in some cases, wetland creation represents an alternative to grassland-based reclamation that may promote forest-associated wildlife on legacy surface mines. We used automated recording units to evaluate the response of anurans to created wetlands and the FRA in Kentucky and West Virginia, USA. We used …

Deep Crustal Boundaries As Fluid Conduits: A Geochemical Investigation Of Mvt Mineralization In Kentucky And Beyond, Dairian Boddy M. Boddy

Theses and Dissertations--Earth and Environmental Sciences

Critical minerals are vital to the United States economy and national security, yet their supply chains are at risk. Common minerals in Mississippi Valley-type (MVT) deposits, such as sphalerite, galena, fluorite, and barite, host critical metals such as barium, gallium, germanium, and zinc, which are essential for energy technologies. An investigation of three MVT mineral districts in Kentucky elucidated previously unrecognized systematics, genetic relationships, and sources of ore components using stable and radiogenic isotope geochemistry, particularly from galena, sphalerite, barite, and gangue minerals (e.g., carbonates). The localization and dominant type of mineralization in each district are potentially influenced by deep …

Stochastic Mechanical Mesoscale Modeling Of Cylindrical Cavities In Metallic Foams, Mujan N. Seif, Alexandre Martin, Matthew J. Beck

Mechanical Engineering Faculty Publications

Aluminum foam is a critical component of state-of-the-art micrometeoroid and orbital debris shielding. However, its randomly oriented constituent ligaments create significant variability in properties at different length scales. Previous efforts have thoroughly characterized the statistical implications of micro- to macro-scale-length transitions on the homogenized elastic behavior of damage-free, pre–micrometeroid and orbital debris (MMOD) strike structures. In this work, the properties of the residual material post MMOD impact are assessed by introducing cylindrical cavities representing the damage track. It was observed that configuring the cavity parallel to the through-the-thickness direction transformed a nominally isotropic foam into an anisotropic (transverse isotropic) material, …

Insights From And Future Directions For A Nationwide Science And Engineering Education Collaboration In Stratospheric Ballooning, Beth A. Covitt, Angela C. Des Jardins, Erick P. Agrimson, Jason T. Ash, Sean C.C. Bailey, Katelyn A. Barber, Mike J. Bastidas, Edgar A. Bering, Matthew T. Bernards, Anthony Choi, Nicholas B. Conklin, Jacqueline K.Q. Do, Montana Etten-Bohm, William F. Finney, James A. Flaten, Jeffrey M. Freedman, Rachel H. Humphrey, Eric P. Kelsey, Hunmin Kim, Christopher L. Lee, Wookwon Lee, Jared W. Marquis, Justin R. Minder, Jani M. Pallis, David J. Pawlowski, Chong Qiu, Joanna H. Rivers, Jason A. Ruszkowski, Jillian B. Schmidt, Thomas G. Sharp, Paul E. Slaboch, Suzanne W. Smith

Mechanical Engineering Faculty Publications

The Nationwide Eclipse Ballooning Project (NEBP) engaged 53 teams of students from across the United States to fly experiments on high-altitude balloons for the 2023 annular and 2024 total solar eclipses. By many measures, NEBP was a successful project. However, the teams did encounter challenges. To better understand what could be improved for similar future projects, this study engaged project partners in examining strengths, challenges, and recommendations across four topics: project structure, education and research approach, broadening participation, and funding. Analysis of the topics was completed through written comments followed by remote focus group discussions. The project director and evaluator …

Field-Scale Evaluation Of Satellite- Derived Vegetation Indices And Image Timing For In-Season Nitrogen Management In Corn, Ana Morales-Ona, Katsutoshi Mizuta, James J. Camberato, Robert Nielsen, Yuxin Miao, Davide Cammarano, German Mandrini, Daniel Quinn

Plant and Soil Sciences Faculty Publications

Introduction: Traditional methods to determine the agronomic optimum nitrogen rate (AONR) for corn (Zea mays L.) rely on grain yield data, limiting in-season decision-making for nitrogen (N) management. Vegetation indices (VIs) derived from satellite imagery can serve as proxies for grain yield and help estimate in-season AONR, enabling timely sidedress applications. This study aimed to (1) quantify how VI–yield relationships vary during the vegetative period across fields with different tillage systems and crop residue; (2) determine whether VI–N response curves can be used to estimate AONR (AONRvi); and (3) assess the accuracy of AONRvi relative to yield-based AONR (AONRy). …

Feasibility, Acceptability, And Preliminary Efficacy Of A Pilot Study To Integrate Buprenorphine Into A Harm-Reduction Drop-In-Center In Kampala, Uganda, Julia Dickson-Gomez, Sergey Tarima, Wamala Twaibu, Dan Katende, Latifah Kyeswa, Laura Glasman, Arthur Kiconco, Sarah Krechel, Bryan Johnston, Moses Ogwal, Brian Byamah Mutamba, Peter Mudiope, Stella Alamo, Rhoda Wanyenze, Geofrey Musinguzi

Biostatistics Faculty Publications

Illicit drug use has been increasing rapidly in Sub-Saharan Africa in the past decade. However, until recently HIV prevention has largely ignored people who inject drugs and medications to treat opioid use disorder (MOUD) were largely absent. This paper reports results of a pilot intervention that integrated buprenorphine into a harm-reduction drop-in-center for people with opioid use disorder (OUD) in Kampala, Uganda. We collected implementation outcomes and changes in self-reported drug use after buprenorphine initiation. We conducted qualitative interviews with a subset of 14 participants who had initiated buprenorphine. Sixty-two participants were screened for OUD, of whom 57 were eligible …

Artificial Intelligence In Biomedical Team Science: Perceptions, Practices, And Training Needs, Emily Slade, Kelsey N. Karnik, Caitline Phan, Megan E. Hall, Yana Feygin, Kristen J. Mcquerry

Biostatistics Faculty Publications

Introduction: Artificial intelligence (AI) is increasingly used in biomedical research, yet limited empirical work has described how researchers use AI tools on collaborative research teams and how they view their role within team-based research. This study examines researchers’ experience with and attitudes toward AI use in collaborative research environments.

Methods: A cross-sectional survey was administered to 178 investigators engaged in collaborative research at the University of Kentucky. Questions assessed AI use across research and communication tasks, team-related decision-making practices, perceived benefits and concerns, and preferences for training and frameworks.

Results: Thirty-nine participants responded (22%). AI use was heterogeneous: 26% had …

Narrowing The K-12 Excellence Gap In Kentucky Schools: Lessons On High Achievement From High Achievers, Jimmy M. W. Bartlett, Johnathan K. Hurley

MPA/MPP/MPFM Capstone Projects

Disparities in high-level academic achievement – known as excellence gaps – remain a persistent equity challenge in K–12 education, particularly in access to advanced mathematics learning. This study examines school-level practices associated with narrower excellence gaps in Kentucky public schools. Principals of schools demonstrating higher-than-expected advanced achievement and relatively small gaps by gender and economic status were invited to semi-structured interviews. The interviews cover seven schools, spanning grade levels and other characteristics. Guided by the Excellence Gap Intervention Model, a hybrid inductive–deductive thematic analysis reveals that narrower excellence gaps are not driven by isolated programs or policy mandates, but by …

Stochastic Mechanical Mesoscale Modeling Of Cylindrical Cavities In Metallic Foams, Mujan N. Seif, Alexandre Martin, Matthew J. Beck

Chemical and Materials Engineering Faculty Publications

Aluminum foam is a critical component of state-of-the-art micrometeoroid and orbital debris shielding. However, its randomly oriented constituent ligaments create significant variability in properties at different length scales. Previous efforts have thoroughly characterized the statistical implications of micro- to macro-scale-length transitions on the homogenized elastic behavior of damage-free, pre–micrometeroid and orbital debris (MMOD) strike structures. In this work, the properties of the residual material post MMOD impact are assessed by introducing cylindrical cavities representing the damage track. It was observed that configuring the cavity parallel to the through-the-thickness direction transformed a nominally isotropic foam into an anisotropic (transverse isotropic) material, …

The Impact Of Congenital Heart Disease On The Timing Of Alzheimer's Disease In Down Syndrome, Julianne G. Clina, Brian C. Helsel, Sigan L. Hartley, David A. White, Victoria L. Fleming-Batayneh, Benjamin Handen, Bradley Christian, Elizabeth Head, Mark Mapstone, Christy L. Hom, Beau Ances, Jeffrey Burns, H. Diana Rosas, Florence Lai, Sharon Krinsky Mchale, Joseph H. Lee, Frederick A. Schmitt, Jordan Harp, Ira T. Lott, Shahid Zaman, Lauren T. Ptomey

Neurology Faculty Publications

INTRODUCTION: The incidence of Alzheimer's disease (AD) in Down syndrome (DS) exceeds 90%. Approximately 50% of people with DS have congenital heart disease (CHD). Having CHD increases risk for early-onset AD in populations without DS, but it is unclear if CHD influences AD in DS. METHODS: Data from the Alzheimer Biomarker Consortium-Down Syndrome (ABC-DS) were used. Participants with CHD (n = 82, mean age = 39.9 ± 8.5 years, 97.6% White race) were age- and sex-matched to participants without CHD (n = 82, mean age = 40.5 ± 8.1 years, 98.8% White race). Cognitive assessments and Centiloid load (CL) (positron …

Climate Change Effects On Biomass And Greenhouse Gas Emissions Are Ameliorated By Nontoxic Endophytes In Southeastern Usa Transition Zone Tall Fescue Pastures, Rebecca Kay Mcgrail, Jonathan D. Moore, A. Elizabeth Carlisle, Jim A. Nelson, Rebecca L. Mcculley

Plant and Soil Sciences Faculty Publications

Background: The plant–microbe interaction between tall fescue and its endophyte Epichloë coenophiala can affect ecosystem responses to changing rainfall patterns and increasing temperatures. Endophyte-infected (E+) stands often exhibit improved stress tolerance and differing soil greenhouse gas (GHG) emissions compared to endophyte-free (E−) stands. However, it is unknown if mammalian nontoxic endophyte (NTE) strains introduced into some tall fescue cultivars confer differing stress tolerances or reduce soil GHG emissions.

Methods: We quantified the impact of fescue-NTE symbioses in Jesup and Texoma on biomass and GHG emissions in response to increased temperature (+3°C) and altered precipitation (50% lengthened interval between events) using …

A Global Synthesis Of Fragipan Silicon Concentrations And Relationships With Soil Physicochemical Properties As A Function Of Soil Parent Materials, Christopher Shepard

Plant and Soil Sciences Faculty Publications

Fragipans are dense, brittle subsurface horizons that restrict root growth and limit water-holding capacity. A common factor in these soils is a binding agent, potentially either phyllosilicate clay bridging, amorphous aluminosilicate/silica, or silica sorbed to Fe oxides. Others have suggested that no binding agent is present within these soil horizons and that the arrangement of individual particles is solely responsible for these horizons. In this article, a secondary data synthesis was utilized to demonstrate that silicon (Si) accumulation is a key pedogenic process in loess-derived fragipan horizons, but not in all fragipans. The average dithionite-extractable Si (Si_d) content …

Eigenvalue Spacing Distributions And The Weak Disorder Limit For Random Schrodinger Operators, Kyle E. Hammer

Theses and Dissertations--Mathematics

We study a collection of discrete Schrodinger Operators with random potentials through the lens of global and local eigenvalue spacings. We discuss the three models: the standard scaled disorder Anderson Model, the Anderson-Bernoulli Polymer Model, and the Discrete Fractional Laplacian Anderson Model. First, we discuss the scaled disorder case using the invariant measure and its application to the density of states in the weak disorder limit. We also prove the limit of the local and global eigenvalue spacings in the non random case, and demonstrate numerically how randomness affects the eigenvalue spacings. We then discuss a special family of random …