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Old Dominion University

Applied Mathematics

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Full-Text Articles in Physical Sciences and Mathematics

Quantification Of Antiviral Drug Tenofovir (Tfv) By Surface-Enhanced Raman Spectroscopy (Sers) Using Cumulative Distribution Functions (Cdfs), Marguerite R. Butler, Jana Hrncirova, Meredith Clark, Sucharita Dutta, John B. Cooper Jan 2024

Quantification Of Antiviral Drug Tenofovir (Tfv) By Surface-Enhanced Raman Spectroscopy (Sers) Using Cumulative Distribution Functions (Cdfs), Marguerite R. Butler, Jana Hrncirova, Meredith Clark, Sucharita Dutta, John B. Cooper

Chemistry & Biochemistry Faculty Publications

Surface-enhanced Raman spectroscopy (SERS) is an ultrasensitive spectroscopic technique that generates signal-enhanced fingerprint vibrational spectra of small molecules. However, without rigorous control of SERS substrate active sites, geometry, surface area, or surface functionality, SERS is notoriously irreproducible, complicating the consistent quantitative analysis of small molecules. While evaporatively prepared samples yield significant SERS enhancement resulting in lower detection limits, the distribution of these enhancements along the SERS surface is inherently stochastic. Acquiring spatially resolved SERS spectra of these dried surfaces, we have shown that this enhancement is governed by a power law as a function of analyte concentration. Consequently, by definition, …

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A Unit-Load Approach For Reliability-Based Design Optimization Of Linear Structures Under Random Loads And Boundary Conditions, Robert James Haupin, Gene Jean-Win Hou Aug 2023

A Unit-Load Approach For Reliability-Based Design Optimization Of Linear Structures Under Random Loads And Boundary Conditions, Robert James Haupin, Gene Jean-Win Hou

Mechanical & Aerospace Engineering Faculty Publications

The low order Taylor’s series expansion was employed in this study to estimate the reliability indices of the failure criteria for reliability-based design optimization of a linear static structure subjected to random loads and boundary conditions. By taking the advantage of the linear superposition principle, only a few analyses of the structure subjected to unit-loads are needed through the entire optimization process to produce acceptable results. Two structural examples are presented in this study to illustrate the effectiveness of the proposed approach for reliability-based design optimization: one deals with a truss structure subjected to random multiple point constraints, and the …

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Deep Virtual Pion Pair Production, Dilini Lakshani Bulumulla Aug 2023

Deep Virtual Pion Pair Production, Dilini Lakshani Bulumulla

Physics Theses & Dissertations

This experiment investigates the deep virtual production of both σ− and ρ− mesons, with a particular focus on the microscopic structure of the σ mesons. While the ρ meson is an ordinary qq¯ pair, the σ meson is composed of not only the typical qq¯ pair, making it a topic of controversy for nearly six decades. Although the existence of the σ− meson is now well established, its microscopic structure remains poorly understood. The primary objective of this thesis is to contribute to the understanding of the σ meson by analyzing its deep virtual production. The main focus of this …

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Gradient-Based Trade-Off Design For Engineering Applications, Lena A. Royster, Gene Hou Jun 2023

Gradient-Based Trade-Off Design For Engineering Applications, Lena A. Royster, Gene Hou

Mechanical & Aerospace Engineering Faculty Publications

The goal of the trade-off design method presented in this study is to achieve newly targeted performance requirements by modifying the current values of the design variables. The trade-off design problem is formulated in the framework of Sequential Quadratic Programming. The method is computationally efficient as it is gradient-based, which, however, requires the performance functions to be differentiable. A new equation to calculate the scale factor to control the size of the design variables is introduced in this study, which can ensure the new design achieves the targeted performance objective. Three formal approaches are developed in this study for trade-off …

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Quantum Computing And Its Applications In Healthcare, Vu Giang Jan 2023

Quantum Computing And Its Applications In Healthcare, Vu Giang

OUR Journal: ODU Undergraduate Research Journal

This paper serves as a review of the state of quantum computing and its application in healthcare. The various avenues for how quantum computing can be applied to healthcare is discussed here along with the conversation about the limitations of the technology. With more and more efforts put into the development of these computers, its future is promising with the endeavors of furthering healthcare and various other industries.

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Multipatch Stochastic Epidemic Model For The Dynamics Of A Tick-Borne Disease, Milliward Maliyoni, Holly D. Gaff, Keshlan S. Govinder, Faraimunashe Chirove Jan 2023

Multipatch Stochastic Epidemic Model For The Dynamics Of A Tick-Borne Disease, Milliward Maliyoni, Holly D. Gaff, Keshlan S. Govinder, Faraimunashe Chirove

Biological Sciences Faculty Publications

Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the …

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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 Jan 2023

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. …

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An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu Jan 2023

An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu

OUR Journal: ODU Undergraduate Research Journal

This paper presents an alternate proof of the divergence of the unique maximizer sequence {𝑥∗ 𝑛} of a function sequence {𝐹𝑛(𝑥)} that is derived from an adaptive algorithm based on the now classic optimal stopping problem, known by many names but here ‘the secretary problem’. The alternate proof uses a result established by Nguyen, Xu, and Zhao (n.d.) regarding the uniqueness of maximizer points of a generalized function sequence {𝑆𝜇,𝜎 𝑛 } and relies on the strict monotonicity of 𝐹𝑛(𝑥) as 𝑛 increases in order to show divergence of {𝑥∗ 𝑛}. Towards this, limits of the exponentiated Gaussian CDF are …

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Statistical Methods For Meta-Analysis In Large-Scale Genomic Experiments, Wimarsha Thathsarani Jayanetti Dec 2022

Statistical Methods For Meta-Analysis In Large-Scale Genomic Experiments, Wimarsha Thathsarani Jayanetti

Mathematics & Statistics Theses & Dissertations

Recent developments in high throughput genomic assays have opened up the possibility of testing hundreds and thousands of genes simultaneously. With the availability of vast amounts of public databases, researchers tend to combine genomic analysis results from multiple studies in the form of a meta-analysis. Meta-analysis methods can be broadly classified into two main categories. The first approach is to combine the statistical significance (pvalues) of the genes from each individual study, and the second approach is to combine the statistical estimates (effect sizes) from the individual studies. In this dissertation, we will discuss how adherence to the standard null …

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Atlantic Surfclam (Spisula Solidissima) Population Demographics And Distribution Along The Middle Atlantic Bight, Mauricio González Díaz Dec 2022

Atlantic Surfclam (Spisula Solidissima) Population Demographics And Distribution Along The Middle Atlantic Bight, Mauricio González Díaz

OES Theses and Dissertations

The Atlantic surfclam (Spisula solidissima) is a long-lived benthic biomass dominant organism that occurs on the Middle Atlantic Bight (MAB) continental shelf between 10 m and 50 m. Trends in Atlantic surfclam population specific growth and mortality rates were analyzed using four decades of age and length observations obtained from NOAA stock surveys from the 1980s to 2010s in six regions distributed along the MAB. Atlantic surfclam specific growth rates and asymptotic lengths were estimated from the age and length observations using the von Bertalanffy growth model. The analysis showed that the Atlantic surfclam median asymptotic length in …

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Kinetic Simulations Of Active Nematic Polymers In Channel Flow, Lacey Savoie Schenk Dec 2022

Kinetic Simulations Of Active Nematic Polymers In Channel Flow, Lacey Savoie Schenk

Mathematics & Statistics Theses & Dissertations

Suspensions of active nematic liquid crystalline polymers exhibit complex phenomena such as spontaneous flows, pattern formations, and defects. They have many applications in industry, commercial settings, and our daily lives. We employ the Kinetic Model for our research, an extensive model that couples the Smoluchowski Equation and the incompressible Navier-Stokes Equations to solve for the active nanorod number density function–a function dependent on the polymer’s physical orientation and space at a given time. Using this function, we can derive the polymer’s polarity and nematic orientations as well as other rheological properties. In this research, we conduct numerical simulations of active, …

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Utilization Of Finite Element Analysis Techniques For Adolescent Idiopathic Scoliosis Surgical Planning, Michael A. Polanco Aug 2022

Utilization Of Finite Element Analysis Techniques For Adolescent Idiopathic Scoliosis Surgical Planning, Michael A. Polanco

Mechanical & Aerospace Engineering Theses & Dissertations

Adolescent Idiopathic Scoliosis, a three-dimensional deformity of the thoracolumbar spine, affects approximately 1-3% of patients ages 10-18. Surgical correction and treatment of the spinal column is a costly and high-risk task that is consistently complicated by factors such as patient-specific spinal deformities, curve flexibility, and surgeon experience. The following dissertation utilizes finite element analysis to develop a cost-effective, building-block approach by which surgical procedures and kinematic evaluations may be investigated. All studies conducted are based off a volumetric, thoracolumbar finite element (FE) model developed from computer-aided design (CAD) anatomy whose components are kinematically validated with in-vitro data. Spinal ligament stiffness …

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Evaluation Of Generative Models For Predicting Microstructure Geometries In Laser Powder Bed Fusion Additive Manufacturing, Andy Ramlatchan Aug 2022

Evaluation Of Generative Models For Predicting Microstructure Geometries In Laser Powder Bed Fusion Additive Manufacturing, Andy Ramlatchan

Computer Science Theses & Dissertations

In-situ process monitoring for metals additive manufacturing is paramount to the successful build of an object for application in extreme or high stress environments. In selective laser melting additive manufacturing, the process by which a laser melts metal powder during the build will dictate the internal microstructure of that object once the metal cools and solidifies. The difficulty lies in that obtaining enough variety of data to quantify the internal microstructures for the evaluation of its physical properties is problematic, as the laser passes at high speeds over powder grains at a micrometer scale. Imaging the process in-situ is complex …

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Inexact Fixed-Point Proximity Algorithms For Nonsmooth Convex Optimization, Jin Ren Aug 2022

Inexact Fixed-Point Proximity Algorithms For Nonsmooth Convex Optimization, Jin Ren

Mathematics & Statistics Theses & Dissertations

The aim of this dissertation is to develop efficient inexact fixed-point proximity algorithms with convergence guaranteed for nonsmooth convex optimization problems encountered in data science. Nonsmooth convex optimization is one of the core methodologies in data science to acquire knowledge from real-world data and has wide applications in various fields, including signal/image processing, machine learning and distributed computing. In particular, in the context of image reconstruction, compressed sensing and sparse machine learning, either the objective functions or the constraints of the modeling optimization problems are nondifferentiable. Hence, traditional methods such as the gradient descent method and the Newton method are …

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A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Janani Gamage May 2022

A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Janani Gamage

Mathematics & Statistics Theses & Dissertations

Interface problems have many applications in physics. In this dissertation, we develop a direct method for solving three-dimensional elliptic interface problems and study their application in solving parabolic interface problems. As many of the physical applications of interface problems can be approximated with partial differential equations (PDE) with piecewise constant coefficients, our derivation of the model is focused on interface problems with piecewise constant coefficients but have a finite jump across the interface. The critical characteristic of the method is that our computational framework is based on a finite difference scheme on a uniform Cartesian grid system and does not …

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Electromagnetic Modeling Of A Wind Tunnel Magnetic Suspension And Balance System, Desiree Driver May 2022

Electromagnetic Modeling Of A Wind Tunnel Magnetic Suspension And Balance System, Desiree Driver

Mechanical & Aerospace Engineering Theses & Dissertations

Wind tunnels are used to study forces and moments acting on an aerodynamic body. While most results involve some interference from the mechanical supports used to hold the model, a Magnetic Suspension and Balance System (MSBS) is void of these interferences and presents an ideal test scenario. To further investigate the feasibility of dynamic stability testing at supersonic speeds using a MSBS, a preliminary design idea is currently being developed using an existing MSBS in a subsonic wind tunnel. This review focuses on the development of a mathematical model to more accurately portray the capabilities of the 6 inch Massachusetts …

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Active Polar Liquid Crystal Channel Flows: Analyzing The Roles Of Nematic Strength And Activation Parameter, Lacey Schenk, Ruhai Zhou Apr 2022

Active Polar Liquid Crystal Channel Flows: Analyzing The Roles Of Nematic Strength And Activation Parameter, Lacey Schenk, Ruhai Zhou

College of Sciences Posters

Suspensions of active polar liquid crystalline polymers (APLC) exhibit complex phenomena such as spontaneous flows, pattern formations and defects. Using the Kinetic Model, which couples the Smoluchowski Equation and the Navier-Stokes Equations, we conduct numerical simulations of APLC in a microfluidic channel to investigate the competitive effect among different material constants, such as the nematic concentration (the strength of the potential for nematic order) and active strength (the individual nano-rods strength of their individual movement) with and without a pressure gradient. Both Dirichlet and Neumann boundary conditions on the mathematical model are employed. Steady states, including isotropic and nematic states, …

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A Spatially And Temporally Second Order Method For Solving Parabolic Interface Problems, Kumudu Gamage, Yan Peng Apr 2022

A Spatially And Temporally Second Order Method For Solving Parabolic Interface Problems, Kumudu Gamage, Yan Peng

College of Sciences Posters

Parabolic interface problems have many applications in physics and biology, such as hyperthermia treatment of cancer, underground water flow, and food engineering. Here we present an algorithm for solving two-dimensional parabolic interface problems where the coefficient and the forcing term have a discontinuity across the interface. The Crank-Nicolson scheme is used for time discretization, and the direct immersed interface method is used for spatial discretization. The proposed method is second order in both space and time for both solution and gradients in maximum norm.

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Real-Time Cavity Fault Prediction In Cebaf Using Deep Learning, Md. M. Rahman, K. Iftekharuddin, A. Carptenter, T. Mcguckin, C. Tennant, L. Vidyaratne, Sandra Biedron (Ed.), Evgenya Simakov (Ed.), Stephen Milton (Ed.), Petr M. Anisimov (Ed.), Volker R.W. Schaa (Ed.) Jan 2022

Real-Time Cavity Fault Prediction In Cebaf Using Deep Learning, Md. M. Rahman, K. Iftekharuddin, A. Carptenter, T. Mcguckin, C. Tennant, L. Vidyaratne, Sandra Biedron (Ed.), Evgenya Simakov (Ed.), Stephen Milton (Ed.), Petr M. Anisimov (Ed.), Volker R.W. Schaa (Ed.)

Electrical & Computer Engineering Faculty Publications

Data-driven prediction of future faults is a major research area for many industrial applications. In this work, we present a new procedure of real-time fault prediction for superconducting radio-frequency (SRF) cavities at the Continuous Electron Beam Accelerator Facility (CEBAF) using deep learning. CEBAF has been afflicted by frequent downtime caused by SRF cavity faults. We perform fault prediction using pre-fault RF signals from C100-type cryomodules. Using the pre-fault signal information, the new algorithm predicts the type of cavity fault before the actual onset. The early prediction may enable potential mitigation strategies to prevent the fault. In our work, we apply …

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A Literature Review On Combining Heuristics And Exact Algorithms In Combinatorial Optimization, Hesamoddin Tahami, Hengameh Fakhravar Jan 2022

A Literature Review On Combining Heuristics And Exact Algorithms In Combinatorial Optimization, Hesamoddin Tahami, Hengameh Fakhravar

Engineering Management & Systems Engineering Faculty Publications

There are several approaches for solving hard optimization problems. Mathematical programming techniques such as (integer) linear programming-based methods and metaheuristic approaches are two extremely effective streams for combinatorial problems. Different research streams, more or less in isolation from one another, created these two. Only several years ago, many scholars noticed the advantages and enormous potential of building hybrids of combining mathematical programming methodologies and metaheuristics. In reality, many problems can be solved much better by exploiting synergies between these approaches than by “pure” classical algorithms. The key question is how to integrate mathematical programming methods and metaheuristics to achieve such …

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Horizontal Air Mass: Solutions For Fermi Questions, November 2022, John Adam Jan 2022

Horizontal Air Mass: Solutions For Fermi Questions, November 2022, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

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Drop In The Bucket?, John Adam Jan 2022

Drop In The Bucket?, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

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Camouflaged Poisoning Attack On Graph Neural Networks, Chao Jiang, Yi He, Richard Chapman, Hongyi Wu Jan 2022

Camouflaged Poisoning Attack On Graph Neural Networks, Chao Jiang, Yi He, Richard Chapman, Hongyi Wu

Computer Science Faculty Publications

Graph neural networks (GNNs) have enabled the automation of many web applications that entail node classification on graphs, such as scam detection in social media and event prediction in service networks. Nevertheless, recent studies revealed that the GNNs are vulnerable to adversarial attacks, where feeding GNNs with poisoned data at training time can lead them to yield catastrophically devastative test accuracy. This finding heats up the frontier of attacks and defenses against GNNs. However, the prior studies mainly posit that the adversaries can enjoy free access to manipulate the original graph, while obtaining such access could be too costly in …

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On The P-Inner Functions Of ℓPA, James G. Dragas Dec 2021

On The P-Inner Functions Of ℓPA, James G. Dragas

Mathematics & Statistics Theses & Dissertations

Define ℓpA as the space of all functions holomorphic over the unit disk whose Taylor coefficients are p-summable. Despite their classical origins and simple definition, these spaces are not as well understood as one might expect. This is particularly true when compared with the Hardy spaces, which provide a useful road map for the types of questions we might consider reasonable. In this work we examine the zero sets of ℓpA, p ∈ (1;∞), as well as a notion of inner function that is consistent with the approach taken on numerous other function spaces. …

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High-Order Positivity-Preserving L2-Stable Spectral Collocation Schemes For The 3-D Compressible Navier-Stokes Equations, Johnathon Keith Upperman Jul 2021

High-Order Positivity-Preserving L2-Stable Spectral Collocation Schemes For The 3-D Compressible Navier-Stokes Equations, Johnathon Keith Upperman

Mathematics & Statistics Theses & Dissertations

High-order entropy stable schemes are a popular method used in simulations with the compressible Euler and Navier-Stokes equations. The strength of these methods is that they formally satisfy a discrete entropy inequality which can be used to guarantee L2 stability of the numerical solution. However, a fundamental assumption that is explicitly or implicitly used in all entropy stability proofs available in the literature for the compressible Euler and Navier-Stokes equations is that the thermodynamic variables (e.g., density and temperature) are strictly positive in the entire space{time domain considered. Without this assumption, any entropy stability proof for a numerical scheme …

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Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis Jul 2021

Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis

Mathematics & Statistics Theses & Dissertations

Volterra integral equations arise in a variety of applications in modern physics and engineering, namely in interactions that contain a memory term. Classical formulations of these problems are largely inflexible when considering non-homogeneous media, which can be problematic when considering long term interactions of real-world applications. The use of fractional derivative and integral terms naturally relax these restrictions in a natural way to consider these problems in a more general setting. One major drawback to the use of fractional derivatives and integrals in modeling is the regularity requirement for functions, where we can no longer assume that functions are as …

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Electrohydrodynamic Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Scheme, Charles Leland Armstrong Jul 2021

Electrohydrodynamic Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Scheme, Charles Leland Armstrong

Mathematics & Statistics Theses & Dissertations

Capsules are fluid-filled, elastic membranes that serve as a useful model for synthetic and biological membranes. One prominent application of capsules is their use in modeling the response of red blood cells to external forces. These models can be used to study the cell’s material properties and can also assist in the development of diagnostic equipment. In this work we develop a three dimensional model for numerical simulations of red blood cells under the combined influence of hydrodynamic and electrical forces. The red blood cell is modeled as a biconcave-shaped capsule suspended in an ambient fluid domain. Cell deformation occurs …

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A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Gamage, Yan Peng Apr 2021

A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Gamage, Yan Peng

College of Sciences Posters

Interface problems have many applications in fluid dynamics, molecular biology, electromagnetism, material science, heat distribution in engines, and hyperthermia treatment of cancer. Mathematically, interface problems commonly lead to partial differential equations (PDE) whose in- put data are discontinuous or singular across the interfaces in the solution domain. Many standard numerical methods designed for smooth solutions poorly work for interface problems as solutions of the interface problems are mostly non-smoothness or discontinuous. Moving interface problems depends on the accuracy of the gradient of the solution at the interface. Therefore, it became essential to derive a method for interface problems that gives …

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End-To-End Physics Event Generator, Yasir Alanazi, N. Sato, Tianbo Liu, W. Melnitchouk, Michelle P. Kuchera, Evan Pritchard, Michael Robertson, Ryan Strauss, Luisa Velasco, Yaohang Li Apr 2021

End-To-End Physics Event Generator, Yasir Alanazi, N. Sato, Tianbo Liu, W. Melnitchouk, Michelle P. Kuchera, Evan Pritchard, Michael Robertson, Ryan Strauss, Luisa Velasco, Yaohang Li

College of Sciences Posters

We apply generative adversarial network (GAN) technology to build an event generator that simulates particle production in electron-proton scattering that is free of theoretical assumptions about underlying particle dynamics. The difficulty of efficiently training a GAN event simulator lies in learning the complicated pat- terns of the distributions of the particles physical properties. We develop a GAN that selects a set of transformed features from particle momenta that can be generated easily by the generator, and uses these to produce a set of augmented features that improve the sensitivity of the discriminator. The new Feature-Augmented and Transformed GAN (FAT-GAN) is …

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Undetermined Coefficients: A Fully Generalized Approach, Taylor Powell Mar 2021

Undetermined Coefficients: A Fully Generalized Approach, Taylor Powell

Undergraduate Research Symposium

In this presentation, I outline the development of a fully-generalized solution of linear, non-homogeneous differential equations with constant coefficients and whose non-homogeneous function is any product of sinusoidal, exponential, and polynomial functions. This particular method does not require the reader to work with annihilator operators or additional related ODEs, and only requires an understanding of summation notation, matrix multiplication, and calculus. Additionally, this method provides a straightforward way to develop a program to implement the technique, and potentially reduces the time-complexity for solutions with comparisons to other methods.

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