The USA/USM/SELU Mini-Conference on Undergraduate Research in Science and Mathematics is a (very) regional one-day meeting, featuring research presentations in the physical and mathematical sciences from students and faculty from universities in the Gulf Coast area. A principal goal of this conference is to involve undergraduate students in research and provide an opportunity for them to present their work. There is no conference fee, and a free lunch will be provided to all participants.
We encourage interested faculty and students, including those who may not want to present, to attend and learn more about research going on in our Gulf area. For more information, please contact one of the local organizers:
When? Thursday,
April 20, 2023
9am - 3pm (CT)
Where? University of South Alabama
Morning: Terrace Room in Student Center (92 in the campus map, or Google Maps: 350 Student Center Circle)
Lunch + Afternoon: Cafeteria (15 in the campus map, or Google Maps: 6351 Tonsmeire Drive)
Parking? Admin Parking Lot (L602 in the campus map)
Park in a red parking spot and use the following digital parking pass.
Registration and abstract submission:
Submit your abstract to straub@southalabama.edu before Friday, April 14.
Please also send an email, including your name and affiliation, if you just wish to attend.
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Christopher Anderson, Yuki Abe, Tomohiro Sasaki and Sanichiro Yoshida
(Southeastern Louisiana University)
(15min) Optical interferometric analysis of fatigue fracture
Abstract.
We perform an experimental investigation of fatigue fracture of metal specimens using an optical interferometric technique (Electronic Speckle-Pattern Interferometry). The ESPI setup monitors the in-plane displacement field continuously under cyclic loading. We analyze the spatial pattern of the resulting interferometric fringe images to infer the fatigue and fatigue-induced fracture mechanism. We will present the recent progress of the research.
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Haley Broadus
(University of South Alabama)
(15min) Encoding with bipartite graphs
Abstract.
In this talk, we present a way of associating a bi-partite graph to a code with characters \( 0, 1, 2, \ldots, p-1 \), where \( p \) is a prime. If the code can be retrieved uniquely from the graph, we say the graph determines the code.
We ask what are the minimum number of vertices and the minimum number of edges of a bi-partite graph that determines a code. We give a complete answer for \( p=2 \) and \( p=3 \). This work was supervised by Dr. Elena Pavelescu.
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Mark O. Byrne
(Spring Hill College)
(30min) GR in the IR and UV
Abstract.
Abstract: I plan to briefly discuss a few topics in classical physics and general relativity I think are interesting—discretization of inertial frames ("boost discretization") and approximate scale-invariant collapse of density fluctuations/perturbations in GR (in expanding FLRW spacetimes). In the former case it's surprisingly possible to construct an infinite set of exact Lorentz invariant discrete boost frames in 1+1 spacetime. In the latter case, it is interesting to ponder whether the generic, isotropic GR collapse of regions of space of enhanced density are related to the observed ~10^(-5) max fluctuation amplitude (at relevant scales) measured from the CMB (z ~ 1100) and the formation of the first "primordial" seed black holes.
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Courtney Francois
(The University of Southern Mississippi)
(15min) Analysis of Sound Signals using Fourier Series
Abstract.
Music is often only expressed in the form of composing or analyzing the music through the eyes of music theorists. However, mathematicians can express music through the sinusoidal waves it creates. This paper seeks to employ Fourier transformations for the analysis of sound signals. The subjects used to complete the research include sinusoidal functions of various frequencies and orthogonal functions that are solutions of differential equations to approximate and recover sound signals. In addition, MATLAB is necessary to graph the functions and transformations.
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Albert Gapud
(University of South Alabama)
(30min) How nuclear magnetic resonance can probe subtle structural changes in single-crystal superconducting V3Si (and new physics!)
Abstract.
This presentation reflects on the amazing ability of nuclear magnetic resonance to sensitively probe into subtle structural transformations in single crystals, especially details that could not be spotted by other methods. In particular, the A15 superconductor, V3Si (Tc = 17 K) undergoes a so-called Martensitic transformation from cubic to tetragonal symmetry. Just why this occurs a few K above the superconducting transition is still an open question, and uncovers other questions besides, as will be described.
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Jacob Gardner
(The University of Southern Mississippi)
(15min) Differential Equation Modeling the Early Stages of the COVID-19 Pandemic
Abstract.
In this paper, we proposed two differential equation models to investigate the Covid-19 pandemic. A simple SIRF (Susceptible-Infectious-Recovery-Fatality) model is used at the beginning of the pandemic when the vaccines are unavailable. A modified model SIRD-V is used to analyze the introduction of the two-dose vaccine during the pandemic. We first perform a theoretical analysis of the disease-free equilibrium's existence and linear stability. We prove that the linear stability is determined by the reproduction number R0. We use MATLAB to numerically solve the system and optimize the model's parameters over the beginning periods of the pandemic in 2020 using total death data and total confirmed cases given by the Centers for Disease Control (CDC). We want to compare and analyze the Covid-19 pandemic among four states in the USA and we chose Mississippi, Arizona, Washington, and Ohio.
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Corey Guagliardo
(Southeastern Louisiana University)
(15min) Solving a Series RLC Circuit with a Homogeneous Solution
Abstract.
After creating a series RLC circuit with a known capacitor and resistor but an unknown inductor, data was collected using the Picoscope 7 software to measure voltage differences across the capacitor over time. Using this data to find the frequency and decay rate, a homogenous solution of an RLC circuit was calculated using Kirchhoff's voltage law and a second-order differential equation and used to find the unknown inductor. This was reconfirmed by changing the resistance and capacitance values and solving for the solution theoretically and then testing with the Picoscope in the lab.
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Abel Gurung
(The University of Southern Mississippi)
(15min) Modeling the Open Probability of Ion Channels on Cell/Organelle's Membranes by Deep Neural Network
Abstract.
Biological processes are often modeled using mathematical equations. However, for many systems, determining the underlying equations analytically is highly challenging due to the complexity and unknown factors involved in the biological processes. The purpose of our research is to use deep neural networks (DNNs) to model the open probability of ion channels, which can be challenging to model using ODEs. The unique contribution of this research is the reduction of the number of unknowns required to model the open probability of ion channels. Previously, the open probability of ion channels required three unknowns. However, using our method, we only need one unknown compared to three. The DNN models can be trained using data generated from known biological models, with proper cost functions and optimization algorithms. The models can be validated and used to conduct predictions of the open probability of ion channels with different input data and time-dependent parameters. When trained using valid data, the same neural network architecture can be used for different ion channels, such as sodium, potassium, and calcium. This research has the potential to generate more accurate predictions of the open probability of ion channels, which are present in every cell and some organelles, leading to an improved understanding of biological processes. The long-term goal of our research is to reduce the number of unknown needs to solve more complicated equations.
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Daniel Johnson and Romulus Godang
(University of South Alabama)
(15min) Measurement of the Branching Fraction of the Upsilon(4S) to B0 and anti-B0 mesons
Abstract.
Based on a data sample of 476 million B-meson pairs collected at the Upsilon(4S) resonance with the BABAR detector, we measure the branching fraction of the Upsilon(4S) decays to B0 and anti-B0 meson pairs. The anti-B0 mesons are partially reconstructed to D*+ lepton anti-neutrino, where the lepton can be either an electron or muon. The D*+ mesons are detected only through the pion daughter of the decay D*+ to D0 pi+.
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Casandra Saxon
(Southeastern Louisiana University)
(15min) Finding the phase delay of an RLC circuit with a particular solution
Abstract.
A RLC circuit with a signal generator voltage is set up with a known resistance, capacitance, and voltage, but an unknown inductance. During the demonstration the voltage at the capacitor and the current across the resistor are measured. Using the particular solutions method of Vo=Acos(Ω-Δ) it can be proven mathematically that the current running through the resistor is a differential of the voltage across the capacitor. This is then demonstrated by a picoscope to show the phase shift.
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Rebecca Scariano
(The University of Southern Mississippi)
(15min) Convergence Analysis and Optimization of a Hybrid Analytical-Numerical Method for Linear, Variable-Coefficient Two-Point Boundary Value Problems
Abstract.
Allen-Manandhar's Method is a hybrid analytical-numerical method for linear, variable-coefficient two-point boundary value problems. Variable-coefficient ordinary differential equations (ODEs) cannot be solved for an exact solution, but ODEs with constant-coefficients can. This method employs the constant-coefficient approach to approximate the variable-coefficient case but creates error. Conducting a convergence analysis will ensure the method converges and reveals which technique best fits in potentially diminishing that error. To affirm the accuracy and displaying the computing time of Allen-Manandhar's Method, a comparison to the finite-difference method will be incorporated to represent its adequacy when solving linear, variable-coefficient ODEs in two-point boundary value problems.
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Franissa Simon
(The University of Southern Mississippi)
(15min) The Use of Radial Basis Function Collocation Methods to approximate Piecewise Functions
Abstract.
Radial basis functions (RBFs) are functions whose values depend on the distance between a certain input point and another fixed point. RBFs can be used to approximate functions using various collocation methods. The collocation method worked well for polynomial smooth functions whose approximations became more accurate as we increased the number of input points. However, when approximating piecewise functions that are not smooth and not continuous, the accuracy of the approximation decreased and the level of error increased. It was also found that this method for approximating piecewise functions cannot be improved by increasing the number of points. In this research project, we focus on improving the RBF collocation method to approximate piecewise functions that are continuous but not smooth, and discontinuous.
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Peter Sherman, Reeshi Ghosal and Martin Frank
(University of South Alabama)
(20min) Fermilab Detectors and Magnetic Monopoles
Abstract.
Fermilab, located in northern Illinois, is home to the NOvA experiment. This scientific endeavor
utilizes two detectors, known as the near and far detectors, to investigate neutrino oscillation. By
transmitting a neutrino beam over a distance of 500 miles through the earth, scientists are able to study
the states and interactions of particles passing through each detector. The detectors use straightforward yet
effective techniques for this purpose. In addition to searching for neutrino oscillations, the NOvA
experiment conducts searches for magnetic monopoles. These are magnetic particles with a singular
magnetic pole, and while they have yet to be observed, their existence has been postulated in numerous
models of the universe. If magnetic monopoles are discovered, it would have significant implications and
potentially lead to new theories. We will be describing and analyzing how the near and far detectors
function and coordinate to conduct neutrino oscillation research, and we will be delving into the history
and significance of magnetic monopoles.
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Morgan Wilson
(The University of Southern Mississippi)
(15min) Using the global dynamics of a SIR model that considers the competition among multiple strains in patchy environments to analyze 2020 COVID strains
Abstract.
COVID-19 is an infectious disease that has been known to quickly adapt, mutating and having multiple different strains infecting groups of people at once. In this study, we introduce a novel high-dimensional SIR model to examine the competition among multiple strains of COVID-19 in patchy environments, specifically focusing on the statistics of the United States and Canada in 2020. The two countries serve as two distinct patchy environments being analyzed and the model will be modified to generalize the results. The ongoing research aims to understand the effect of limiting migration and enforcing isolation measures on the spread of COVID-19, particularly in situations where multiple strains are present simultaneously. The model will observe how policy changes impact the behavior of the different strains and the public, in order to better understand the efficacy of isolation as a solution for controlling the pandemic.
