Applied Mathematics Commons^™

Numerical Studies On Bose–Einstein Condensates, Megan Benkendorf

Undergraduate Research Conference at Missouri S&T

Bose-Einstein condensate (BEC) is a state of matter near absolute zero temperature for which all atoms lose their individual properties and condense into a macroscopic coherent "super-wave". The superfluidity of BEC has been the focus of active research since the first experimental realization of BEC in 1995. The recent launch of the Cold Atom Laboratory to the space station on May 21, 2018, has once again drawn spotlights to these fascinating properties of BEC. In this project, we will carry out numerical studies to understand the behavior of exciton-polariton BECs. A modified Gross-Pitaevskii equation is used to model the dynamics …

Gender And The Billboard Top 40 Charts Between 1958 And 2023, Brileigh Cates, Justin W. Pope

Undergraduate Research Conference at Missouri S&T

Is there an inherent bias towards male artists in the music industry? Evidence has been shown in previous studies, the most recent being from 2017, that there may be bias towards male artists appearing in Billboard Magazine s Hot 100 list. This study not only updates previous data to include 2017 through 2023, but also looks at the top 40 charts on a week-by-week bias as opposed to the year-end charts that other studies used for their data. We coded each song so as to indicate the gender of the artist(s) as well as whether or not the artists appeared …

Numerical Studies On Bose-Einstein Condensates, Megan Benkendorf

Undergraduate Research Conference at Missouri S&T

Bose-Einstein condensate (BEC) is a state of matter near absolute zero temperature for which all atoms lose their individual properties and condense into a macroscopic coherent "super-wave". The superfluidity of BEC has been the focus of active research since the first experimental realization of BEC in 1995. The recent launch of the Cold Atom Laboratory to the space station on May 21, 2018, has once again drawn spotlights to these fascinating properties of BEC. In this project, we will carry out numerical studies to understand the behavior of exciton-polariton BECs. A modified Gross-Pitaevskii equation is used to model the dynamics …

Towards Fast, Realistic Gas Plume Simulation For Lwir Hyperspectral Images To Improve Deep Learning Identification Models, Scout Jarman

Student Research Symposium

• Longwave infrared (LWIR) hyperspectral images (HSI) are taken from airborne platforms and can be used to find gas plumes.
• Detection and identification of gas plumes has applications in environmental monitoring, disaster response, and national security
• Deep learning can be used to identify gases from a large library of materials,  but can be difficult to apply in practice

The Conformable Information Filter, Sophia Hungerford, Joseph E. Smith

2024 Student Academic Showcase

In this project, we construct an information filter associated with a linear continuous control system corrupted by some noise. Here, the system is defined in terms of a conformable derivative introduced by Khalil et al. in 2014. This time-weighted derivative shares many of the same properties as the classical derivative but lacks the usual semigroup property associated with the exponential. Mathematically, this conformable information filter is a backward-time counterpart of the recently constructed conformable Kalman filter. Here, the inverse of the error covariance associated with the Kalman filter becomes the information matrix for the information filter. The conformable information filter …

Modeling An Infection Outbreak With Quarantine: The Sibkr Model, Mikenna Dew, Amanda Langosch, Theadora Baker-Wallerstein

Rose-Hulman Undergraduate Mathematics Journal

Influenza is a respiratory infection that places a substantial burden in the world population each year. In this project, we study and interpret a data set from a flu outbreak in a British boarding school in 1978 with mathematical modeling. First, we propose a generalization of the SIR model based on the quarantine measure in place and establish the long-time behavior of the model. By analyzing the model mathematically, we determine the analytic formulas of the basic reproduction number, the long-time limit of solutions, and the maximum number of infection population. Moreover, we estimate the parameters of the model based …

Exploration Of Characteristic Curve In Fox Float 3 Shock Dampers To Expedite Shock Damp Tuning., Joshua R. Moore

Honors College Theses

The shock absorber is an integral part of a vehicle suspension system and has a strong influence on its performance, especially in the case of motorsports. It is important to study the force versus velocity relationship, commonly known as the characteristic curve of the shock absorber both during compression and rebound. Vendor-supplied characteristics often reflect the behavior of the shock absorber in a particular setting. However, during the installation, the settings inside the shock absorber are adjusted to increase the human comfort level and performance of the vehicle. This may change the characteristic curve of the shock. The available data …

Localized Collocation Meshless Method For Modeling Transdermal Pharmacokinetics In Multiphase Skin Structures, Eduardo Divo

Math Department Colloquium Series

The human skin has a complicated structure with many multi-scale, biophysical effects impacting the propagation of skin-injected substances, such as partitioning, metabolic reactions, adsorption and elimination. An extended version of Fick’s second law governing the process of the compound diffusion in various skin layer is employed in the current work by considering the conservation of mass of the substance and the metabolic reaction of the substance in viable skin. Additionally, a model assuming linear coupling between the substance concentrations that are bound and unbound with blood was developed. Using such a model, a set of coupled partial differential equations are …

How Generative Ai Models Such As Chatgpt Can Be (Mis)Used In Spc Practice, Education, And Research? An Exploratory Study, Fadel M. Megahed, Ying-Ju (Tessa) Chen, Joshua A. Ferris, Sven Knoth, L. Allison Jones-Farmer

Mathematics Faculty Publications

Generative Artificial Intelligence (AI) models such as OpenAI's ChatGPT have the potential to revolutionize Statistical Process Control (SPC) practice, learning, and research. However, these tools are in the early stages of development and can be easily misused or misunderstood. In this paper, we give an overview of the development of Generative AI. Specifically, we explore ChatGPT's ability to provide code, explain basic concepts, and create knowledge related to SPC practice, learning, and research. By investigating responses to structured prompts, we highlight the benefits and limitations of the results. Our study indicates that the current version of ChatGPT performs well for …

Enhancing Rotating Machinery Fault Diagnosis: A Dual-Head Attention Mechanism In Deep Learning Neural Networks, Qing Snyder

Dissertations

Rotating machinery is crucial to production efficiency and safety in manufacturing industries for an extended time. Ensuring machinery reliability necessitates effective diagnostic systems, particularly for rotating bearings, the key components of such equipment. Fault diagnosis in rotating machinery is essential to prevent failures and minimize downtime, thereby playing an important role in industrial operations. The application of advanced neural network techniques in industry has risen recently. Among these, attention-based neural networks, especially the Transformer models, are originally noteworthy for their sequential data handling capability. This research delves into attention-based algorithms for rotating machinery fault diagnosis, signifying a substantial advancement in …

Predicting Biomolecular Properties And Interactions Using Numerical, Statistical And Machine Learning Methods, Elyssa Sliheet

Mathematics Theses and Dissertations

We investigate machine learning and electrostatic methods to predict biophysical properties of proteins, such as solvation energy and protein ligand binding affinity, for the purpose of drug discovery/development. We focus on the Poisson-Boltzmann model and various high performance computing considerations such as parallelization schemes.

Tools For Biomolecular Modeling And Simulation, Xin Yang

Mathematics Theses and Dissertations

Electrostatic interactions play a pivotal role in understanding biomolecular systems, influencing their structural stability and functional dynamics. The Poisson-Boltzmann (PB) equation, a prevalent implicit solvent model that treats the solvent as a continuum while describes the mobile ions using the Boltzmann distribution, has become a standard tool for detailed investigations into biomolecular electrostatics. There are two primary methodologies: grid-based finite difference or finite element methods and body-fitted boundary element methods. This dissertation focuses on developing fast and accurate PB solvers, leveraging both methodologies, to meet diverse scientific needs and overcome various obstacles in the field.

Generation, Dynamics, And Interaction Of Quartic Solitary Waves In Nonlinear Laser Systems, Sabrina Hetzel

Mathematics Theses and Dissertations

Solitons are self-reinforcing localized wave packets that have remarkable stability features that arise from the balanced competition of nonlinear and dispersive effects in the medium. Traditionally, the dominant order of dispersion has been the lowest (second), however in recent years, experimental and theoretical research has shown that high, even order dispersion may lead to novel applications. Here, the focus is on investigating the interplay of dominant quartic (fourth-order) dispersion and the self-phase modulation due to the nonlinear Kerr effect in laser systems. One big factor to consider for experimentalists working in laser systems is the effect of noise on the …

Invariance Of Chsh Parameters When Projecting Weakly Signaling Distribution Into A No Signaling Subspace, Aaditya Paudel

LSU New Orleans Theses and Dissertations

The seminal 1935 paper by Einstein, Podolsky, and Rosen (EPR) sparked a fundamental debate in quantum mechanics about the completeness of physical reality through the EPR paradox. They questioned local realism by suggesting that particles could exhibit instantaneous correlations across any distance, challenging classical physics. Bell's theorem (1964) argued that no local hidden variable theory could replicate quantum predictions, introducing Bell's inequalities and their experimental tests. These tests, particularly through violations of Bell's inequalities, confirmed quantum predictions of non-local correlations that local realism could not account for. Quantum theory, while supporting such correlations, adheres to the no-signaling principle to prevent …

Methods, Analyses, And Applications Of Multilayer Temporal Link Prediction In Networks, Xie He

Dartmouth College Ph.D Dissertations

Many applications stem from the possibility of accurately predicting links in various types of networks. In this thesis, we present methods, analyses, and applications for static, temporal, and multilayer networks. The first part of this thesis demonstrates how static network features serve as efficient and accurate predictors for link prediction in temporal networks. It includes an ensemble learning method we developed and presents experimental results on 90 synthetic stochastic block models and 19 real-world datasets. The second part closely follows, showcasing 20 different sampling methods and their effects on nine different link prediction algorithms for 250 real-world networks across 6 …

Modeling And Numerical Analysis Of The Cholesteric Landau-De Gennes Model, Andrew L. Hicks

LSU Doctoral Dissertations

This thesis gives an analysis of modeling and numerical issues in the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We derive various time-step restrictions for a (weighted) $L^2$ gradient flow scheme to be energy decreasing. Furthermore, we prove a mesh size restriction, for finite element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers that is not well-known in the LC literature, particularly when simulating cholesteric LCs that exhibit ``twist''. Furthermore, we perform a computational exploration of the model and present several numerical simulations in 3-D, on both slab geometries and spherical …

Scaled And Graduated Learning In Deep Relu Networks And Reconstructing Depp Inelastic Scattering Kinematics, Abdullah Ayar Farhat

Mathematics & Statistics Theses & Dissertations

To address computational challenges in learning deep neural networks, properties of deep RELU networks were studied to develop a multi-scale learning model. The multi-scale model was compared to the multi-grade learning models. Unlike the deep neural network learned from the standard single-scale, single-grade model, the multi-scale neural networks use low scale information from all hidden layers, and thusly provide a robust approximation method that requires fewer parameters, lower computational time, and is resistant to noise. It is shown that the multiscale method is not subject to issues arising from the vanishing gradient problem. This allows very deep multi-scale networks to …

Analyzing The Influence Of Design And Operating Conditions On Combustion And Emissions In Premixed Turbulent Flames: A Comprehensive Review, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar Alm-Eldin Bastawissi, Ibrahim Ali Mousa Eng., Mohamed M. Abdel-Raouf Ibrahim Dr. Eng.

Journal of Engineering Research

Recently, premixed combustion has dominated the field of combustion research worldwide. The current work is a review that addresses the effects of design and operating regimes on the combustion and emission characteristics of premixed turbulent flames. The study accounts for recent developments aimed at overcoming combustor operability issues that influence emissions and flame stability. Various experimental setups have been utilized in investigations, with results pertaining to performance and emissions concerning premixed turbulent flames. Thus, the objective of this paper is to provide a comprehensive review of the effects of swirl vane angles and equivalence fuel-air ratios for tests conducted both …

Building For Safety: Design Considerations For Refuge Areas In Tall Buildings From Quality Management Perspective, Enass. A. Salama, Heba. M. Gaber, Ahmed. M. Selim

Journal of Engineering Research

New El Alamein City is one of the largest urban projects in Egypt, and the largest project on the north coast. Tall buildings (super high-rise buildings) are considered the prevailing trend by architectural designers to obtain the maximum view of the Mediterranean Sea. The provision of safety evacuation in emergencies for these buildings’ occupants is a crucial challenge from the Quality management point of view. In contrast, there are no sufficient architectural design guidelines for the tall buildings provided by the Egyptian code for protecting buildings from fire, especially the design of the refuge areas. This study aims to investigate …

Effect Of Organic Compounds Additives For Biodiesel Fuel Blends On Diesel Engine Vibrations And Noise Characteristics, Medhat Elkelawy Prof. Dr, Eng., Hagar Alm-Eldin Bastawissi Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Mahmoud Soliman Eng.

Journal of Engineering Research

The extensive consumption of petroleum fuel directly correlates with both hazardous exhaust emissions affecting human health and contributing to global warming. Initially, biodiesel fuels were proposed as a viable alternative to address these issues. This perspective finds support in numerous published studies that highlight how the significant catalytic effect of nanoparticles allows for their integration into biodiesel blends, resulting in improved combustion characteristics, reduced exhaust emissions, and enhanced performance. This study investigates the impact of additives on biodiesel fuel properties and its effects on engine performance metrics such as brake power, brake thermal efficiency, exhaust gas concentration, engine vibration, and …