Applied Mathematics Commons^™

Impact Of Spallation And Internal Radiation On Fibrous Ablative Materials, Raghava Sai Chaitanya Davuluri

Theses and Dissertations--Mechanical and Aerospace Engineering

Space vehicles are equipped with Thermal Protection Systems (TPS) that encounter high heat rates and protect the payload while entering a planetary atmosphere. For most missions that interest NASA, ablative materials are used as TPS. These materials undergo several mass and energy transfer mechanisms to absorb intense heat. The size and construction of the TPS are based on the composition of the planetary atmosphere and the impact of various ablative mechanisms on the flow field and the material. Therefore, it is essential to quantify the rates of different ablative phenomena to model TPS accurately. In this work, the impact of …

Quantifying The Carbon Stored And Sequestered By The Trees On Pomona College’S Campus, Paola A. Giron-Carson

Scripps Senior Theses

We are experiencing a climate crisis that must be confronted with strategic mitigation. Pomona College contributes to the climate crisis through its emissions for which there is a baseline record. However there is no baseline record of the climate mitigation currently performed by the trees on Pomona’s campus through carbon storage. This study seeks to determine a current baseline quantity of carbon stored and sequestrated by Pomona’s trees as well as possible courses of climate mitigation for Pomona College to take. Initial information gathering was conducted through interviews with several stakeholders. This study was conducted using data collected prior to …

A Mathematical Modeling Technique To Understand The Role Of Decoy Receptors In Ligand‑Receptor Interaction, Subrata Dey, Aditi Ghosh, Malay Banerjee

Faculty Publications

The ligand‑receptor interaction is fundamental to many cellular processes in eukaryotic cells such as cell migration, proliferation, adhesion, signaling and so on. Cell migration is a central process in the development of organisms. Receptor induced chemo‑tactic sensitivity plays an important role in cell migration. However, recently some receptors identified as decoy receptors, obstruct some mechanisms of certain regular receptors. DcR3 is one such important decoy receptor, generally found in glioma cell, RCC cell and many various malignant cells which obstruct some mechanism including apoptosis cell‑signaling, cell inflammation, cell migration. The goal of our work is to mathematically formulate ligand‑receptor interaction …

Beginner's Analysis Of Financial Stochastic Process Models, David Garcia

HMC Senior Theses

This thesis explores the use of geometric Brownian motion (GBM) as a financial model for predicting stock prices. The model is first introduced and its assumptions and limitations are discussed. Then, it is shown how to simulate GBM in order to predict stock price values. The performance of the GBM model is then evaluated in two different periods of time to determine whether it's accuracy has changed before and after March 23, 2020.

The Lagrangian Formulation For Wave Motion With A Shear Current And Surface Tension, Conor Curtin, Rossen Ivanov

Articles

The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant vorticity, which arises for example when a shear current is present, the separation of the energy into kinetic and potential is not at all obvious and neither is the Lagrangian formulation of the problem. Nevertheless, we use the known Hamiltonian formulation of the problem in this case to obtain the Lagrangian density function, and utilising the Euler-Lagrange equations we proceed to derive some …

Bifurcation Levels Of The Integral Manifolds Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem, first proposed by Isaac Newton, is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It has significance to many areas of science, including physics and computer science, and is crucial in understanding how the universe works. In fact, it was a primary motivation for Newton's development of calculus. An important application of the N-body problem is within celestial mechanics and involves how planets and other celestial bodies move with mutual gravitational attraction. It is important in developing how satellites behave in space using complicated …

Enhancing Control Room Operator Decision Making: An Application Of Dynamic Influence Diagrams In Formaldehyde Manufacturing, Joseph Mietkiewicz, Anders L. Madsen

Articles

Intoday’s rapidly evolving industrial landscape, control room operators must grapple with an ever-growing array of tasks and respon sibilities. One major challenge facing these operators is the potential for task overload, which can lead to decision fatigue and increased reliance on cognitive biases. To address this issue, we propose the use of dynamic influence diagrams (DID) as the core of our decision support system. By monitoring the process over time and identifying anomalies, DIDs can recommend the most effective course of action based on a probabilistic assessment of future outcomes. Instead of letting the operator choose or search for the …

Evaluating A Temperature-Dependent Mosquito Population Model, Morgan H. Jackson, Elizabet L. Estallo, Cheng Ly, Michael A. Robert

Graduate Research Posters

Dengue Virus causes over 390 million infections and around 40,000 deaths each year. This virus is primarily transmitted by the mosquito Aedes aegypti. The life cycle of these mosquitos is significantly impacted by temperature, however, temperature is often neglected in mechanistic models. Predictive models of mosquito populations thus require the inclusion of temperature and are valuable for helping medical officials plan for the impact of outbreaks. Using mosquito and climate data collected in Córdoba, Argentina from 2010-2013, we developed a non-autonomous ordinary differential equations model that includes temperature dependent parameters associated with mosquito life history. We performed local sensitivity …

Odd Solutions To Systems Of Inequalities Coming From Regular Chain Groups, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Hoffman’s theorem on feasible circulations and Ghouila-Houry’s theorem on feasible tensions are classical results of graph theory. Camion generalized these results to systems of inequalities over regular chain groups. An analogue of Camion’s result is proved in which solutions can be forced to be odd valued. The obtained result also generalizes the results of Pretzel and Youngs as well as Slilaty. It is also shown how Ghouila-Houry’s result can be used to give a new proof of the graph- coloring theorem of Minty and Vitaver.

Using Modflow To Assess Groundwater Storage Enhancement Via A Floodplain Infiltration Basin, Lindsay Henning

All Master's Theses

Delaying groundwater discharge into rivers until it is critically needed during baseflow conditions provides promise for lowering elevated stream temperatures and improving habitat for aquatic species. Increasing groundwater storage may accomplish this in locations where excess spring runoff can be captured and allowed to infiltrate into the subsurface for later beneficial use, a process known as Managed Aquifer Recharge (MAR). Here, MAR via an infiltration basin is considered at a site along the Teanaway River in central Washington State. The effects of simulated ephemeral ponds of sizes varying from 554 m³ to 2430 m³ (0.449 acre-feet to 1.97 …

Clusters, Curves, And Centroids: Stellar Flare Morphology In The Ultraviolet, Vera Berger

Pomona Senior Theses

With a novel sample of 495 high-cadence light curves for stellar flares in the near-ultraviolet, I explore similarity measures, clustering algorithms, averaging methods, and curve fitting techniques for time series. This work seeks to provide insight into whether stellar flares are similar across stars, if we can identify physically meaningful patterns in their light curves, and how to construct a comprehensive model for flares. I construct the first empirical template for flare light curves in the ultraviolet, and compute ``average elements" of flares displaying complex features such as quasi-periodic oscillations and multipeak structures. Developing accurate models for flares in the …

Models For Decision-Making - Second Edition, Steven Cosares, Fred Rispoli

Open Educational Resources

Decision-Making often refers to a multi-stage process that starts with some form of introspection or reflection about a situation in which a person or group of people find themselves. These ruminations usually lead to series of questions that need to be answered, or to a set of data that needs to be collected and analyzed, or to some calculations that need to be performed before someone can be in a position to make informed decisions and take appropriate actions.

We provide some simple examples of Quantitative Models, which are often found in a decision-making situation. We focus on the use …

Addressing The Opioid Crisis In The United States And Modeling Its Proposed Interventions, Liza Eubanks

Honors Program Theses

A novel application of compartmental modeling is used to quantitatively study the impact of call centers on influencing an individual’s mindset as they begin or attempt to recover from opioid addiction. The opioid epidemic in the United States has affected millions of Americans, especially in West Virginia. This project studies the effectiveness of call centers in increasing the rate of recovery from opioid abuse. An active response is characterized by an open mindset and acceptance of help from others, while a passive response is defined by a closed mindset and an unwillingness to believe in the real possibility of recovery. …

Medical Diagnosis Via Refined Neutrosophic Fuzzy Logic: Detection Of Illness Using Neutrosophic Sets, K. Hemabala, B. Srinivasa Kumar, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures in refined neutrosophic fuzzy sets.

Feature Extraction Of Footwear Impression Images For Quality Assessment, Alexandra Hill

Graduate Theses, Dissertations, and Problem Reports (ETD)

Forensic footwear impression analysis is a valuable tool in criminal investigations. Extracting useful features from images of footwear impressions is a critical step in this process. However, the quality of these images can vary widely, making feature extraction challenging. In order to give a quality assessment rating to a footwear impression image, the image should first be analyzed to extract features from the impression. In this paper, we present a method to extract features from a 2D grayscale footwear impression image. A Hierarchical Grid Model implementation has been adapted from use on a 3D dataset to assist in finding features, …

Study Of Bounds For Effective Moduli Of Polycrystals And Composites Using Variational Principle For Probabilistic Measures, Md. Tofiqul Islam

Wayne State University Dissertations

Tensors that are invariant with respect to subgroups of 3D group of rotations were constructed first by Lokhin and Sedov (J. Appl. Math. Mech. (PMM), 1963, 27, 597-629). In this paper we do one more step and derive formulas for the elastic modulus tensors for all symmetry groups from the Lokhin-Sedov results. The tensor basis obtained in this way has an advantage of being built upon the same tensors that are used in construction of nonlinear tensor functions. One consequence of the formulas derived is that the number of types of anisotropic elastic behaviors is ten. There is a long- …

A Hierarchical Approach To Improve The Ant Colony Optimization Algorithm, Bryan J. Fischer

EWU Masters Thesis Collection

The ant colony optimization algorithm (ACO) is a fast heuristic-based method for finding favorable solutions to the traveling salesman problem (TSP). When the data set reaches larger values however, the ACO runtime increases dramatically. As a result, clustering nodes into groups is an effective way to reduce the size of the problem while leveraging the advantages of the ACO algorithm. The method for recombining groups of nodes is explored by treating the graph as a hierarchy of clusters, and modifying the original ACO heuristic to operate on a hypergraph. This method of using hierarchical clustering is significantly faster than the …

Stability Properties Of A System Of Receptors In The Presence Of Attractive Domains, Basim Mohammed Al-Maliki

Graduate Theses, Dissertations, and Problem Reports (ETD)

I use mathematical modeling to understand aspects of molecular processes in living cells. Specifically, we look at the first few steps in cell signaling. Signal initiation requires that receptors located on the cell membrane bind together to form dimers. Microscopic imaging of receptors on the cell membrane revealed that receptors tend to accumulate in small areas (clusters). Studies also show that the membrane has a complex landscape consisting of domains and barriers of various origin.

Here we study the way receptor dimerization is influenced by domains on the cell membrane. Our underlying hypothesis is that the physical and chemical properties …

Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, Andres P. Hyer

Theses and Dissertations

Axisymmetric Drop Shape Analysis (ADSA) is a technique commonly used to determine surface or interfacial tension. Applications of traditional ASDA methods to process analytical technologies are limited by computational speed and image quality. Here, we address these limitations using a novel machine learning approach to analysis. With a convolutional neural network (CNN), we were able to achieve an experimental fit precision of (+/-) 0.122 mN/m in predicting the surface tension of drop images at a rate of 1.5 ms^-1 versus 7.7 s^-1, which is more than 5,000 times faster than the traditional method. The results are validated on real images …

Early Termination In Phase Ii Clinical Trials: Admissible Designs Using Decreasingly Informative Priors, Chen Wang

Theses and Dissertations

In Phase II clinical trials, Thall and Simon’s Bayesian posterior probability design is commonly implemented to allow for an early termination to determine whether a new treatment warrants further investigation in a larger-scale Phase III trial; this in turn requires a pre-selected prior distribution based on known clinical opinion or historical information. Moreover, this Bayesian approach can result in an issue of inflating type I error rate by monitoring interim data to inform early termination decisions. Alternatively, a Bayesian approach with the decreasingly informative prior (DIP), which is an informative yet skeptical prior, can be implemented to overcome the contentious …

Effects Of Slip On Highly Viscous Thin-Film Flows Inside Vertical Tubes (Constant Radius, Constricted And Flexible), Mark S. Schwitzerlett

Theses and Dissertations

Viscous liquid film flows in a tube arise in numerous industrial and biological applications, including the transport of mucus in human airways. Previous modeling studies have typically used no-slip boundary conditions, but in some applications the effects of slip at the boundary may not be negligible. We derive a long-wave model based on lubrication theory which allows for slippage along the boundary. Linear stability analysis verifies the impact of slip-length on the speed, growth rate, and wavelength of the most unstable mode. Nonlinear simulations demonstrate the impact of slip-length on plug formation and wave dynamics. These simulations are conducted for …

Analysis Of Localization Algorithms For Wireless Sensor Networks Using Binary Data, Alexander Joseph Hart

Graduate Research Theses & Dissertations

The detection, localization, and tracking of environmental and physical conditions can be accomplished using wireless sensor networks (WSNs). Recent advancements in sensors, processors, and wireless communications have improved the quality and acquisition speed of data in WSNs. However, the data gathered by a WSN is inherently random due to component and environmental variations. Thus, statistical signal processing algorithms are needed to analyze the random data in a robust way. Though many algorithms for the analysis of random data are established and available, they are problem-specific and must be adapted to the application. This thesis provides an analysis of established localization …

Dynamic Function Learning Through Control Of Ensemble Systems, Wei Zhang, Vignesh Narayanan, Jr-Shin Li

Publications

Learning tasks involving function approximation are preva- lent in numerous domains of science and engineering. The underlying idea is to design a learning algorithm that gener- ates a sequence of functions converging to the desired target function with arbitrary accuracy by using the available data samples. In this paper, we present a novel interpretation of iterative function learning through the lens of ensemble dy- namical systems, with an emphasis on establishing the equiv- alence between convergence of function learning algorithms and asymptotic behavior of ensemble systems. In particular, given a set of observation data in a function learning task, we …

Moment-Based Reinforcement Learning For Ensemble Control, Yao-Chi Yu, Vignesh Narayanan, Jr-Shin Li

Publications

Problems involving controlling the collective behavior of a population of structurally similar dynamical systems, the so-called ensemble control, arise in diverse emerging applications and pose a grand challenge in systems science and control engineering. Owing to the severely under-actuated nature and the difficulty of placing large-scale sensor networks, ensemble systems are limited to being actuated and monitored at the population level. Moreover, mathematical models describing the dynamics of ensemble systems are often elusive. Therefore, it is essential to design broadcast controls that excite the entire population in such a way that the heterogeneity in system dynamics are robustly compensated. In …

Longitudinal Sport Science Implementation In American Collegiate Men’S Basketball, Jason Stone

Graduate Theses, Dissertations, and Problem Reports (ETD)

The expanding opportunities to implement sport science frameworks in elite-level basketball environments coincide with the sport’s increasing global prominence. Concomitant to these opportunities is the continual growth of the sport technology market (e.g., wearables, force plates) and computational power (e.g., data management tools, coding capabilities), which yields solutions and challenges for both athletes and practitioners. Due to the rapid influx of new sport technologies in high performance environments, particularly American Collegiate Men’s Basketball, more formal and ecologically valid research on how to effectively utilize data derived from them, particularly over long periods of time (i.e., multiple seasons) is needed. To …

Application Of The Two-Variable Model To Simulate A Multisensory Reaction-Time Task, Rebecca Brady, John Butler

Academic Posters Collection

To navigate the world in an efficient manner, the brain seamlessly integrates signals received across multiple sensory modalities. Behavioral studies have suggested that multisensory processing is a winner-take-all sensory response mechanism to some optimal combination of sensory signals. In addition, multiple sensory cues are not always beneficial with some studies showing maladaptive multisensory processing as an identifier of older adults prone to falls from age matched healthy controls.

A stalwart of modelling sensory decision-making is the work by (Wong &Wang, 2006) but to date almost all of this research has been focused on unisensory tasks. We extend the reduced two-variable …

Modeling The Spread Of Covid-19 In Spatio-Temporal Context, S.H. Sathish Indika, Norou Diawara, Hueiwang Anna Jeng, Bridget D. Giles, Dilini S.K. Gamage

Mathematics & Statistics Faculty Publications

This study aims to use data provided by the Virginia Department of Public Health to illustrate the changes in trends of the total cases in COVID-19 since they were first recorded in the state. Each of the 93 counties in the state has its COVID-19 dashboard to help inform decision makers and the public of spatial and temporal counts of total cases. Our analysis shows the differences in the relative spread between the counties and compares the evolution in time using Bayesian conditional autoregressive framework. The models are built under the Markov Chain Monte Carlo method and Moran spatial correlations. …

Not Your Typical Tower Of Sauron, John Adam

Mathematics & Statistics Faculty Publications

The picture is of the tapering Chester Shot Tower, located in Chester, England. It was built in 1799 for the manufacture of lead shot for use in the Napoleonic Wars. Molten lead was poured through a sieve at the top of the tower, with the tiny droplets forming perfect spheres during the fall; these were then cooled in a vat of water at the base. This process was less labor intensive than an earlier method using molds. It is the oldest of the three remaining shot towers in the UK.

Question 1: Using the parked van at the base, estimate …

The Lie Algebra Sl2(C) And Krawtchouk Polynomials, Nkosi Alexander

UNF Graduate Theses and Dissertations

The Lie algebra L = sl2(C) consists of the 2 × 2 complex matrices that have trace zero, together with the Lie bracket [y, z] = yz − zy. In this thesis we study a relationship between L and Krawtchouk polynomials. We consider a type of element in L said to be normalized semisimple. Let a, a^∗ be normalized semisimple elements that generate L. We show that a, a^∗ satisfy a pair of relations, called the Askey-Wilson relations. For a positive integer N, we consider an (N + 1)-dimensional irreducible L-module V consisting of the homogeneous polynomials in two variables …

Optimal Agricultural Land Use: An Efficient Neutrosophic Linear Programming Method, Maisam Jdid, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The increase in the size of the problems facing humans, their overlap, the division of labor, the multiplicity of departments, as well as the diversity of products and commodities, led to the complexity of business and the emergence of many administrative and production problems. It was necessary to search for appropriate methods to confront these problems. The science of operations research, with its diverse methods, provided the optimal solutions. It addresses many problems and helps in making scientific and thoughtful decisions to carry out the work in the best way within the available capabilities. Operations research is one of the …