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Articles 481 - 510 of 3168
Full-Text Articles in Physical Sciences and Mathematics
Evaluation Of Polymerization Condition Reactions Of Methyl Vinyl Ketone For Hydrogen Storage, Rituborna Ghosh
Evaluation Of Polymerization Condition Reactions Of Methyl Vinyl Ketone For Hydrogen Storage, Rituborna Ghosh
Theses and Dissertations
Hydrogen is widely regarded as one of the most promising clean alternative fuel sources; however, its widespread adoption has been hindered by significant challenges related to storage and transportation. Various storage methods have been proposed and developed, with continuous advancements being made to address these issues. Among the most effective solutions is the utilization of polymers, which serve as safe and efficient hydrogen storage media. This work investigated the polymerization of methyl vinyl ketone using different ratio of monomer: initiator and monomer: crosslinker using N,N′-methylenebisacrylamide (MBA) as crosslinker and ammonium persulfate (APS) as initiator in a free radical polymerization mechanism. …
Theoretical Insights And Analysis Into Luneburg Lens, Aram Flores
Theoretical Insights And Analysis Into Luneburg Lens, Aram Flores
Theses and Dissertations
Advancements in wireless communications necessitate innovative antenna designs for radar systems and satellite communications. The Luneburg lens, theorized by Rudolf Luneburg in 1944, is a gradient-index lens capable of focusing electromagnetic waves onto a point on its surface, offering potential improvements in antenna gain and performance. Access to the lenses, courtesy of Assured Space Access Incorporated, enabled me to research the lenses response, and specific design details remain confidential. Practical assessments of 3D-printed Luneburg lenses of varying sizes are limited, including factors such as lens alignment and focal point offset. This study investigates the performance of 6-inch and 13.25-inch Luneburg …
Bayesian Lasso Regularized Quantile Regression And Its Applications, Priscilla Kissi-Appiah
Bayesian Lasso Regularized Quantile Regression And Its Applications, Priscilla Kissi-Appiah
Theses and Dissertations
Since the pioneering work of (Koenker and Bassett Jr 1978), quantile regression has been a popular regression technique that helps researchers investigate a whole distribution of the response variable. In addition, due to the quantile check loss function, it is robust against outliers and heavy-tailed distributions of the response variable and can provide a more comprehensive picture of modeling via exploring the conditional quantiles of the response variable. In this research, we study the lasso regularized quantile regression from a Bayesian perspective. We develop an efficient sampling algorithm to generate posterior samplings for making posterior inference by using a location-scale …
Examining Hispanic Beginning Farmers And Ranchers In The Rio Grande Valley Through A Community Capitals Framework, Perla Kimberly Schrock
Examining Hispanic Beginning Farmers And Ranchers In The Rio Grande Valley Through A Community Capitals Framework, Perla Kimberly Schrock
Theses and Dissertations
While existing literature addresses the experiences of beginning farmers and ranchers (BFR), there is a notable gap in research focused on Hispanic beginning farmers and ranchers (HBFR). This study aimed at exploring the unique experiences of HBFR in a predominantly Hispanic region, the Rio Grande Valley (RGV), employed the Community Capitals Framework (Flora et al., 2016). I conducted 16 semi-structured interviews with HBFR and local nonprofit organizations and federal employees, complemented by participant observations. Through thematic and content analysis of the interview transcripts, findings revealed valuable insights into the livelihoods of HBFR. Despite HBFR facing significant challenges, this study demonstrated …
Personal Exposure To Black Carbon: Impact Of Time-Activity Patterns And Environmental Factors On Exposure Levels, Sai Deepak Pinakana, Johnathan R. Gonzalez, Amit U. Raysoni
Personal Exposure To Black Carbon: Impact Of Time-Activity Patterns And Environmental Factors On Exposure Levels, Sai Deepak Pinakana, Johnathan R. Gonzalez, Amit U. Raysoni
School of Earth, Environmental, & Marine Sciences Faculty Publications
Black carbon (BC) is a critical environmental pollutant with significant implications for human health. This study aims to quantify personal exposure to BC by focusing on the influence of microenvironments and time-activity patterns in the Rio Grande Valley (RGV) region of South Texas, USA. Over eight days in March and April 2023, a portable aethalometer and GPS tracking instruments were used to measure BC exposure among a study participant, alongside recording the time spent in various microenvironments. The BC measurements were correlated to the time activity patterns to calculate BC inhaled dosage values thereby elucidating its impact on human health. …
Machine Learning Optimized Depolymerization Of Pet (Polyethylene Terephthalate) Via Glycolysis, Mehwash Aamir
Machine Learning Optimized Depolymerization Of Pet (Polyethylene Terephthalate) Via Glycolysis, Mehwash Aamir
Theses and Dissertations
Over 90% of the approximately 1 million PET bottles sold every minute end up in landfills or oceans, where they can persist for centuries. Plastic pollution urgently needs sustainable management and recycling solutions to mitigate the environmental impact of PET waste. From all techniques to recycle plastic waste, catalytic glycolysis stands out for its rapid reaction time, high monomer yields, lower costs, and enhanced durability.
In this work glycolysis of PET was evaluated under microwave conditions using 1,5,7-Triazabicyclo [4.4.0] dec5-ene (TBD) and 1,8-Diazabicyclo [5.4.0] undec-7-ene (DBU) as catalysts, being DBU as the best catalyst for further analysis. The effect of …
Microwave-Assisted Green Synthesis Of Spiroindolinopyranopyrazoles, Esther Owusu
Microwave-Assisted Green Synthesis Of Spiroindolinopyranopyrazoles, Esther Owusu
Theses and Dissertations
Green Chemistry, usually known as sustainable chemistry, is widely implemented worldwide to safeguard human health and the environment. Recent investigations in organic synthesis and chemical transformation have demonstrated that green chemistry techniques are significantly reducing both chemical waste and reaction time. In order to fulfill this ecological requirement, it is crucial to lessen the utilization of perilous solvents and noxious chemicals, while also creating innovative reaction methods that decrease the production of trash. The implementation of such methodologies can greatly enhance the field of green chemistry. A more environmentally friendly synthetic method was utilized to generate spiro chemicals and their …
The Temperature Versus Orbital Period Relation Of Am Cvns: Insights From Their Donors, Colin W. Macrie, Liliana Rivera Sandoval, Yuri Cavecchi, Tin Long Sunny Wong, Manuel Pichardo Marcano
The Temperature Versus Orbital Period Relation Of Am Cvns: Insights From Their Donors, Colin W. Macrie, Liliana Rivera Sandoval, Yuri Cavecchi, Tin Long Sunny Wong, Manuel Pichardo Marcano
Physics & Astronomy Faculty Publications
We studied the spectral energy distribution of 22 known AM CVns with orbital periods (Porb) larger than 35 minutes using multiwavelength public photometric data to estimate the effective temperature of the accreting white dwarf. We find an infrared (IR) excess in all systems when compared to a single blackbody, both when the disk should be extended and when it should be truncated by the accretor's magnetic field. This suggests a dominant contribution from the donor to the IR flux. When fitting two blackbodies, the temperature of the hot component decreases with Porb, as expected by evolutionary models. …
A Nursery Study Of The Interplay Between Soil Texture, Rooting Space, And Nurse Plants On Seedling Growth And Root Development In Woody Species Of Tamaulipan Thornscrub, Lance I. Santos
Theses and Dissertations
Reforestation attempts in semi-arid regions are plagued with seedling mortality. Blanket greenhouse practices may not be optimal, in addition, commensalism interactions between nurse plants are considered. To better understand the effects of soil texture and nurse plant interactions on growth and drought tolerance, two experiments were developed. For soil texture, Border palo verde seedlings were grown in different-sized plant bands with three soil types. To observe the effects of nurse plants, an experiment using guayacan, was developed using Texas Ebony, as a leguminous nurse plant. Plants were also exposed to a drought experiment. The results suggest that some soil textures …
Teachers’ Perceptions On The Impact And Effectiveness Of Certification Programs In Preparing And Retaining Educators, Teresa De Jesus Padilla
Teachers’ Perceptions On The Impact And Effectiveness Of Certification Programs In Preparing And Retaining Educators, Teresa De Jesus Padilla
Theses and Dissertations
Mathematics is integral to STEM fields, making math critically important for the stability and development of the nation. As a result, mathematics teachers have a crucial role in our society. A role whose importance needs the necessary support to accomplish its numerous responsibilities. However, research indicates that certification routes—traditional and alternative—often fail to adequately prepare math teachers for the challenges they face, leading to high turnover rates. This study explores the impact of these certification routes on teachers’ abilities to support student achievement, address diverse learning needs, and manage additional duties. Surveying secondary math teachers in the Rio Grande Valley, …
Anomaly Detection Using Unsupervised Machine Learning Algorithms: A Simulation Study, Edmund F. Agyemang
Anomaly Detection Using Unsupervised Machine Learning Algorithms: A Simulation Study, Edmund F. Agyemang
School of Mathematical & Statistical Sciences Faculty Publications
This study presents a comprehensive evaluation of five prominent unsupervised machine learning anomaly detection algorithms: One-Class Support Vector Machine (One-Class SVM), One-Class SVM with Stochastic Gradient Descent (SGD), Isolation Forest (iForest), Local Outlier Factor (LOF), and Robust Covariance (Elliptic Envelope). Through systematic analysis on a synthetically simulated dataset, the study assessed each algorithm’s predictive performance using accuracy, precision, recall, and F1 score specifically for outlier detection. The evaluation reveals that One-Class SVM, Isolation Forest, and Robust Covariance are more effective in identifying outliers in the synthetic simulated dataset, with Isolation Forest slightly outperforming the other algorithms in terms of balancing …
On Representations Of The Super-Yangian Of The Queer Lie Superalgebra, Elena Poletaeva
On Representations Of The Super-Yangian Of The Queer Lie Superalgebra, Elena Poletaeva
School of Mathematical & Statistical Sciences Faculty Publications
Let Q(n) be the queer Lie superalgebra. We determine conditions under which two 1-dimensional modules over the super-Yangian of Q(n) can be extended nontrivially. We describe the dual modules of the simple finite-dimensional modules over YQ(1) . We use these results to describe blocks in the subcategory of finite-dimensional YQ(1) -modules admitting the zero generalized central character.
Modelling Tinnitus Functional Index Reduction Using Supervised Machine Learning Algorithms, Edmund F. Agyemang
Modelling Tinnitus Functional Index Reduction Using Supervised Machine Learning Algorithms, Edmund F. Agyemang
School of Mathematical & Statistical Sciences Faculty Publications
This study aims to model the reduction in the Tinnitus Functional Index (TFI) utilizing supervised machine learning algorithms, focusing primarily on Ordinary Least Squares (OLS), K-Nearest Neighbor (KNN), Ridge, and Lasso regressions. Our analysis highlighted Group, ISI, and SWLS as significant predictors of TFI reduction, identified through the best subset selection and confirmed by both forward and backward selection criteria in the OLS regression. Notably, the shrinkage methods, Ridge and Lasso regressions, demonstrated superior performance compared to OLS and KNN, with the Ridge regression presenting the smallest test mean square error (MSE) of 318.30. This finding establishes the Ridge regression …
On The Lagrange And Hermite Quadrature Formula, Shuxia Li, Yonghong Chen
On The Lagrange And Hermite Quadrature Formula, Shuxia Li, Yonghong Chen
School of Mathematical & Statistical Sciences Faculty Publications
This paper builds on the error analysis method for Newton-Cotes quadrature formulas developed by D. R. Hayes and L. Rubin in 1970, which utilizes Lagrange interpolation polynomials. By adopting and extending their approach, this work derives the error estimate for Hermite interpolation quadrature. Specifically, we construct a polynomial P(x) analogous to the scaling function A(x) used by Hayes and Rubin, and prove its non-negativity over the interval. This allows us to establish a precise error formula for Hermite interpolation quadrature. The results provide a novel application of Hayes and Rubin's methodology, offering new insights …
Enhancing Student Learning Of The Physics Of The Human Eye In The Context Of Computer Vision Syndrome During Covid-19, Liang Zeng, Guang Zeng
Enhancing Student Learning Of The Physics Of The Human Eye In The Context Of Computer Vision Syndrome During Covid-19, Liang Zeng, Guang Zeng
Physics & Astronomy Faculty Publications
No abstract provided.
A B-Polynomial Approach To Approximate Solutions Of Pdes With Multiple Initial Conditions, Muhammad I. Bhatti, Md. Habibur Rahman
A B-Polynomial Approach To Approximate Solutions Of Pdes With Multiple Initial Conditions, Muhammad I. Bhatti, Md. Habibur Rahman
Physics & Astronomy Faculty Publications
In this article, we present a novel B-Polynomial Approach for approximating solutions to partial differential equations (PDEs), addressing the multiple initial conditions. Our method stands out by utilizing two-dimensional Bernstein polynomials (B-polynomials) in conjunction with their operational matrices to effectively manage the complexity associated with PDEs. This approach not only enhances the accuracy of solutions but also provides a structured framework for tackling various boundary conditions. The PDE is transformed into a system of algebraic equations, which are then solved to approximate the PDE solution. The process is divided into two main steps: First, the PDE is integrated to incorporate …
Bioconvection Dynamics In Rotating And Stationary Cone-Disk Systems, Puneet Rana, Mahanthesh Basavarajappa
Bioconvection Dynamics In Rotating And Stationary Cone-Disk Systems, Puneet Rana, Mahanthesh Basavarajappa
School of Mathematical & Statistical Sciences Faculty Publications
This work focuses on the study of bioconvection in a conical region of rotating and stationary cone-disk systems utilizing nanofluids involving gyrotactic micro-organisms. The flow geometry encompasses two different configurations, namely, rotating cone-disk system (RCDS) and stationary cone-disk system (SCDS). For RCDS, four unique configurations are considered: rotating cone static disk (Model-I), static cone rotating disk (Model-II), co-rotating cone-disk (Model-III), and counter-rotating cone-disk (Model-IV), while SCDS includes both swirling and non-swirling flow scenarios. A total of six different physical configurations that differ in boundary conditions are investigated. The mathematical model comprises Navier–Stokes, energy, nanoparticle volume fraction (NVF), and micro-organism density …
A Class Of Stable Nonlinear Non-Hermitian Skin Modes, Hamed Ghaemi-Dizicheh
A Class Of Stable Nonlinear Non-Hermitian Skin Modes, Hamed Ghaemi-Dizicheh
Physics & Astronomy Faculty Publications
The non-Hermitian skin effect (NHSE) is a well-known phenomenon in open topological systems that causes a large number of eigenstates to become localized at the boundary. Although many aspects of its theory have been investigated in linear systems, this phenomenon remains novel in nonlinear models. In the first step of this paper, we look at the conditions for the presence of quasi-skin modes in a semi-infinite, one-dimensional, nonlinear, nonreciprocal lattice. In the following phase, we explore the survival time of the quasi-skin mode in a finite nonlinear lattice with open edges. We study the dependency of the survival time on …
Medilink: A Secure Blockchain Framework For Multi-Institutional Healthcare, Jorge Castillo, Qian Chen
Medilink: A Secure Blockchain Framework For Multi-Institutional Healthcare, Jorge Castillo, Qian Chen
Informatics and Engineering Systems Faculty Publications
The use of Electronic Medical Records (EMRs) in the healthcare industry has proven to be critical for storing highly sensitive information. Disseminating and protecting healthcare data poses major challenges for the current healthcare information system. Blockchain technology provides solutions to these challenges with its inherited properties, such as decentralization, immutability, and transparency. This provides a unique opportunity to improve data sharing among stakeholders. We propose MediLink, a blockchain-based framework for secure collaborative medical storage. MediLink is designed to (1) protect EMR data from cyber attacks, (2) share healthcare information of patients with different stakeholders, and (3) enable the Internet of …
On The Total Perimeter Of Pairwise Disjoint Convex Bodies, Arseniy Akopyan, Alexey Glazyrin
On The Total Perimeter Of Pairwise Disjoint Convex Bodies, Arseniy Akopyan, Alexey Glazyrin
School of Mathematical & Statistical Sciences Faculty Publications
In this note we introduce a pseudometric on closed convex planar curves based on distances between normal lines and show its basic properties. Then we use this pseudometric to give a shorter proof of the theorem by Pinchasi that the sum of perimeters of 𝑘 convex planar bodies with disjoint interiors contained in a convex body of perimeter 𝑝 and diameter 𝑑 is not greater than 𝑝 + 2(𝑘 − 1)𝑑.
Red Harvester Ants Pogonomyrmex Barbatus (Smith, 1858) (Hymenoptera: Formicidae) Do Not Distinguish Between Sorghum Head Mold Symptomatic And Asymptomatic Seeds, Lilly Victoria Elliott-Vidaurri, Hannah J. Penn, Robin A. Choudhury
Red Harvester Ants Pogonomyrmex Barbatus (Smith, 1858) (Hymenoptera: Formicidae) Do Not Distinguish Between Sorghum Head Mold Symptomatic And Asymptomatic Seeds, Lilly Victoria Elliott-Vidaurri, Hannah J. Penn, Robin A. Choudhury
School of Earth, Environmental, & Marine Sciences Faculty Publications
Red harvester ants, Pogonomyrmex barbatus (Smith, 1858) (Hymenoptera: Formicidae), common in the Lower Rio Grande Valley of Texas, are known to gather seeds from areas around their nests and store the seeds inside their nests for later consumption. As these ants often nest in and near agricultural fields, some of these seeds may be from crops and may also be infected with fungal plant pathogens. These pathogens can degrade seed coats and may cause the seeds to rot within the ant nests, decreasing storage time and potentially spreading the pathogen to other stored seeds. We studied how head mold, a …
A Class Of Stable Nonlinear Non-Hermitian Skin Modes, Hamed Ghaemi-Dizicheh
A Class Of Stable Nonlinear Non-Hermitian Skin Modes, Hamed Ghaemi-Dizicheh
Physics & Astronomy Faculty Publications
The non-Hermitian skin effect (NHSE) is a well-known phenomenon in open topological systems that causes a large number of eigenstates to become localized at the boundary. Although many aspects of its theory have been investigated in linear systems, this phenomenon remains novel in nonlinear models. In the first step of this paper, we look at the conditions for the presence of quasi-skin modes in a semi-infinite, one-dimensional, nonlinear, nonreciprocal lattice. In the following phase, we explore the survival time of the quasi-skin mode in a finite nonlinear lattice with open edges. We study the dependency of the survival time on …
Place-Based Conservation In Coastal And Marine Ecosystems: The Importance Of Engagement With Underrepresented Communities, Viniece Jennings, Kelly M. San Antonio, Mya J. Brown, Lalah Choice, Queriah Simpson, Imani Ford, Hyun Jung Cho, Pedro Solis, Ashley Lacey, De’Marcus Robinson
Place-Based Conservation In Coastal And Marine Ecosystems: The Importance Of Engagement With Underrepresented Communities, Viniece Jennings, Kelly M. San Antonio, Mya J. Brown, Lalah Choice, Queriah Simpson, Imani Ford, Hyun Jung Cho, Pedro Solis, Ashley Lacey, De’Marcus Robinson
School of Earth, Environmental, & Marine Sciences Faculty Publications
Through the years, research has described the importance of community-based approaches in the management of coastal and marine ecosystems. Coastal and marine issues are multifaceted and require place-specific approaches developed in partnership with vulnerable communities who are impacted by environmental stressors. Place-based conservation, a management approach that focuses on unique, place-specific characteristics, and other similar methods. It considers the need to integrate human dimensions and location-centered approaches, which are often lacking in typical natural resource management. Meaningful engagement with underrepresented communities can holistically account for socioeconomic factors and cultural knowledge that inform best management practices. As the health of marine …
Teaching With Pedagogy And Empathy, Mamoona Muzammil, Muzammil Arshad, Washain Muzammil
Teaching With Pedagogy And Empathy, Mamoona Muzammil, Muzammil Arshad, Washain Muzammil
School of Integrative Biological & Chemical Sciences (Formerly Dept. of Chemistry)
Mental illness is common and can affect anyone. Each year the University welcomes students with Mental Health Issues. One in four adults in the US will experience a mental illness in their lifetime, however according to a NUS survey, eight out of ten students will experience a mental illness while in higher education. For some student’s mental illness can be a lifelong disability. Others can experience short term issues that emerge around difficult or stressful life events, while some students may be more at risk of experiencing mental illness in relation to their ethnicity, gender, sexuality or socio-economic background. Although …
Results From A Multi-Laboratory Ocean Metaproteomic Intercomparison: Effects Of Lc-Ms Acquisition And Data Analysis Procedures, Mak A. Saito, Jaclyn K. Saunders, Matthew R. Mcilvin, Erin M. Bertrand, John A. Breier, Margaret Mars Brisbin
Results From A Multi-Laboratory Ocean Metaproteomic Intercomparison: Effects Of Lc-Ms Acquisition And Data Analysis Procedures, Mak A. Saito, Jaclyn K. Saunders, Matthew R. Mcilvin, Erin M. Bertrand, John A. Breier, Margaret Mars Brisbin
School of Earth, Environmental, & Marine Sciences Faculty Publications
Metaproteomics is an increasingly popular methodology that provides information regarding the metabolic functions of specific microbial taxa and has potential for contributing to ocean ecology and biogeochemical studies. A blinded multi-laboratory intercomparison was conducted to assess comparability and reproducibility of taxonomic and functional results and their sensitivity to methodological variables. Euphotic zone samples from the Bermuda Atlantic Time-series Study (BATS) in the North Atlantic Ocean collected by in situ pumps and the autonomous underwater vehicle (AUV) Clio were distributed with a paired metagenome, and one-dimensional (1D) liquid chromatographic data-dependent acquisition mass spectrometry analysis was stipulated. Analysis of mass spectra from …
Quantization Dimensions For The Bi-Lipschitz Recurrent Iterated Function Systems, Amit Priyadarshi, Mrinal Kanti Roychowdhury, Manuj Verma
Quantization Dimensions For The Bi-Lipschitz Recurrent Iterated Function Systems, Amit Priyadarshi, Mrinal Kanti Roychowdhury, Manuj Verma
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, the quantization dimensions of the Borel probability measures supported on the limit sets of the bi-Lipschitz recurrent iterated function systems under the strong open set condition in terms of the spectral radius have been estimated.
Non-Vanishing Modulo P Of Hecke L-Values Over Imaginary Quadratic Fields, Debanjana Kundu, Antonio Lei
Non-Vanishing Modulo P Of Hecke L-Values Over Imaginary Quadratic Fields, Debanjana Kundu, Antonio Lei
School of Mathematical & Statistical Sciences Faculty Publications
Let p and q be two distinct odd primes. Let K be an imaginary quadratic field over which p and q are both split. Let Ψ be a Hecke character over K of infinity type (k, j) with 0 ≤ − j < k. Under certain technical hypotheses, we show that for a Zariski dense set of finite-order characters κ over K which factor through the Z2q -extension of K, the p-adic valuation of the algebraic part of the L-value L(κΨ¯¯¯¯¯¯¯,k+j) is a constant independent of κ. In addition, when j = 0 and certain technical hypothesis holds, this constant is zero.
A Decade Of Monitoring Reveals A Dynamic Fish Assemblage On A Substantial Artificial Reef In The Texas Gulf Of Mexico, David Hicks, Ethan T. Getz, Richard Kline, Carlos E. Cintra-Buenrostro
A Decade Of Monitoring Reveals A Dynamic Fish Assemblage On A Substantial Artificial Reef In The Texas Gulf Of Mexico, David Hicks, Ethan T. Getz, Richard Kline, Carlos E. Cintra-Buenrostro
School of Earth, Environmental, & Marine Sciences Faculty Publications
Fish communities on artificial reefs have rarely been monitored over long periods to evaluate success of reef deployment. Here, we used roving diver surveys to assess changes in fish assemblages on a large, reefed vessel during 2008–2017. Multivariate analyses revealed a dynamic community that stabilized after 5 years. Species richness increased and species dominance decreased during 2008–2017. The fish community shifted toward reef-associated species such as hogfish and pufferfish. Species composition shifted, but trophic structure was relatively stable, which suggested that functional groups may not reflect larger community shifts. Our results indicate that fish communities on artificial reefs are temporally …
Algebraic Structures On Parallelizable Manifolds, Sergey Grigorian
Algebraic Structures On Parallelizable Manifolds, Sergey Grigorian
School of Mathematical & Statistical Sciences Faculty Publications
In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold L , there exists a global trivialization of the tangent bundle, which defines a map ρ p : l ⟶ T p L for each point p ∈ L , where l is some vector space. This allows us to define a particular class of vector fields, known as fundamental vector fields, that correspond to each element of l . Furthermore, flows of these vector fields give rise to a product between elements of l and L , which in turn induces …
Topology And The Quantum Hall Effects, Paul Bracken
Topology And The Quantum Hall Effects, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
The quantum Hall effects are an excellent example of physical systems where topology plays a major role in accounting for the physical observations. It is shown that the conductivity that appears in the quantum Hall effect is a topological invariant. It is illustrated how a fiber bundle over a torus can be constructed producing a geometry in which the system can be referred. The fractional effect can be studied by introducing homotopy and associated braid groups. Filling fractions can be obtained as a consequence of commensurability relations.