The UMKC Math and Stat Research Day is part of the Research-A-Thon Day organized by Division of Computing, Analytics and Mathematics. It is an annual one-day event celebrating student and faculty research and creative and scholarly activities. The event promotes research in computer science, mathematics, statistics, and applications in various fields, and is open to the public. For this year, graduate students will present their research in a poster session. This is an excellent opportunity for the graduate students to present their research and network with the others.
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The 11th Annual UMKC Math and Stat Research Day
Pease submit your abstract and title to Dr. Majid Bani baniyaghoubm@umkc.edu
Abstract and Title Submission: March 20
Notification of Acceptance: March 25
Time: 10:00 AM - 1:00 PM
Day: April 4, 2025
Location: Atterbury Student Success Center, Pierson Auditorium
Abstracts and Titles
Abstracts and Titles
NCBI Genomic Data Downloading and Formatting
Bryan Harris, UMKC PhD Mathematics Student
Abstract: The National Center for Biotechnology Information (NCBI) houses a massive database of biosample data obtained around the world for various genomes, viruses, and proteins. Among the uses for the data, researchers can tackle questions related to outbreaks of dangerous pathogens such as E. coli and Salmonella. Due to the massive size of the database, simplifying the obtaining and cleaning of specific biosample data for analysis can be an obstacle, especially with a lack of targeted tutorials for researchers inexperienced with programming. To remedy this, we introduce a Python script that can extend the functionality of the tools offered by NCBI to transform a compact .jsonl file, to a typical .csv file used for data analysis and visualization.
Temporal Trends and Unit-Specific Patterns of MRSA Transmission in a Safety- Net Hosopital: A Bayesian Compartmental Modeling Study with Applications to Substance-Using Populations
Kiel Corkran, UMKC PhD Statistics Student
Abstract: Methicillin-resistant Staphylococcus aureus (MRSA) is a leading driver of healthcare-acquired infections (HAI) within urban anchor hospitals. These infections often result in increases to patient morbidity rates, patient mortality rates, and additional burdens on the hospital ability to provide quality care to patients. Our study’s objective is to first identity statistically significant predictors of MRSA infection in the urban anchor hospital hospitalized patient population through use of a logistic regression model. Once done, our study will then transfer these predictors into a secondary logistic regression model focused on the subpopulation of patients that have admitted to some type of drug use prior or during hospitalization.
We conducted a retrospective analysis of electronic healthcare records (EHRs) for 998 patients that had hospital stays of 2 days or more and also took antibiotics within 6 months. Predictors included in our model focus on key demographic factors (age, sex, weight, etc.), comorbidities, hospitalization and surgical history, insurance status, primary drug use, and alcohol serum levels. Predictor selection was based on multilinear regression with statistical significance for each predictor based off p-values. Model assumptions, such as linearity of the logit or multicollinearity of predictors, were evaluated by VIF based metrics .
Final model statistics for fitness included a AUC score of 0.87, a classification table of 81% for sensitivity and 78% for its specificity. Predictors to be found statistical significant (p <0.05) include demographic factors, surgical history, insurance status, primary drug use, and alcohol serum levels. These predictors will be used to create to create more complex predictive models that employ mathematical techniques , such as univariate logistic regression, multivariate logistic regression, stepwise logistic regression, and even Hierarchical logistic regression. In summary, this study highlight the use of logistic regression to build robust and accurate models for MRSA infection in a healthcare setting while also establishing a foundation on which build a model for targeted studies of MRSA infections within high risk subpopulations, such as drug users.
Stable Periodic Solutions of A Delayed Reaction-Diffusion Model of Hes1-mRNA Interactions
Mohammed Alanazi, UMKC PhD Mathematics Student
Abstract: Hes1 (Hairy and Enhancer of Split 1) is a gene that plays a vital role in embryonic development and cellular differentiation. The interaction between Hes1 and mRNA is critical in the regulation of gene expression, influencing the determination of cell fate during development. Empirical studies have demonstrated that Hes1-mRNA exhibits sustained oscillations in certain cell types. However, several mathematical models of the Hes1-mRNA interaction fail to exhibit stable periodic solutions. In this research, we propose a delayed reaction-diffusion model with stable periodic solutions. Specifically, we establish conditions under which the system undergoes a delay-induced bifurcation. We numerically verify these results.
Enhancing Competitive Lotka-Volterra Models to Assess Extreme Weather Effects: A Zeeman Classification Approach
Barsha Saha, , UMKC PhD Mathematics Student
Abstract: Extreme weather events can disrupt species interactions, altering competitive stability, extinction risk, and coexistence patterns. While traditional Competitive Lotka-Volterra (CLV) models have been widely used to study species dynamics, they often overlook how climate-driven disturbances influence long-term ecological outcomes. This study incorporates extreme weather effects into the three-dimensional CLV framework using Zeeman’s classification, focusing on Class 27, which exhibits complex dynamics including multiple limit cycles and heteroclinic cycles. By selectively modifying interaction inequalities to simulate environmental stress, we examine how transitions in class structure affect species dominance, extinction, and persistence. Our results identify ecological regime shifts—such as transitions to long-term dominance by a single species (competitive exclusion) or partial coexistence where one species goes extinct, and the others persist. This framework provides a systematic approach to predict biodiversity responses under extreme climate variability, offering insights into ecosystem resilience and the stability of competitive systems.
Modelling Football Rushing Yardage Using Proportional Hazards Regression
Rahul Daniel, UMKC MS Mathematics Student
Abstract: Points in American football are gained by advancing the ball the greatest number of yards past the line of scrimmage before the play is ended, usually by being tackled by an opposing defender. Using FBS college football rushing play data, a proportional hazards regression model was tested to measure the quality of teams’ rushing offenses and defenses. Stratifications of the baseline hazard function were made by down and distance to the first down marker. Using the proportional hazard coefficients corresponding to each team as analogues for team quality explains a noticeable proportion of the variance in the winning margin of future games. This is done without considering play types other than rushing (passes, punts, field goals, penalties, etc.), without assuming any prior knowledge about the quality of the teams, and without considering the frequency at which teams choose to do rushing plays. Therefore, further exploration and optimization of this rushing model along with incorporation of non-rushing plays could yield an accurate predictive model for college football games.
A Reaction-Diffusion Model of Vascular Tumor Growth: Bifurcation, Stability and Relapse
Priscilla Owusu Sekyere , UMKC PhD Mathematics Student
Abstract: The model proposed by Pinho et al. has gained attention in studying the effect of anti-angiogenic therapy. In the present work, we extend the model to account for different growth behaviors of the cancer cells and their dispersal. Analysis of the model indicates the presence of several bifurcations. We also established conditions for the stability of the cancer-free steady state in the presence of the diffusion. Moreover, using the Hopf bifurcation theorem, we showed that the model can exhibit periodic solutions. This paper also delved into the various stages of cancer and the effective therapies that eliminate or keep the cancer cells at an optimal level. These results have been numerically verified.
Archive of Math & Stat Research Day
Archive of Math & Stat Research Day
Friday April 12, 2024, 9:00 AM-4:00 PM
Titles and Abstracts
10th Annual UMKC Math and Stat Research Day
Division of Computing, Analytics & Mathematics,
School of Science and Engineering
University of Missouri - Kansas City
A Decoupled Scheme for a Single-Phase Model in Ferrohydrodynamics
Lucas Delibas
Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
In this research, we study a numerical approximation of a simplified PDE model for single phase ferrofluid flow, which consists of the Navier–Stokes equations coupled with the Poisson equation. Using existing spatial and temporal discretization techniques for the weak formulation, we construct a fully discretized coupled and decoupled finite element schemes with Newton linearization to solve the nonlinear and coupled multi-physics PDE system in Ferrohydrodynamics (FHD). Using MATLAB code packages, we perform numerical simulations for both coupled and decoupled schemes to verify convergence of the numerical solutions. Ferrofluids are colloidal solutions made of ferromagnetic nanoparticles suspended in a liquid, also known magnetic liquid. Such fluid can be controlled directly by the application of a magnetic field, its magnetization properties vanish entirely when the applied magnetic field is removed. This magnetizing property of ferrofluids widely utilized in many scientific and engineering fields requiring precise control, including drug delivery, electronic, biomedical engineering, nanotechnologies, assembly of nanoparticles, fluid transport and control, in optics, electronic and devices, etc.
Analyzing Biosecurity Adherence and Antibiotic Resistance Dynamics in Animals and Humans through Mathematical Modeling
Arash Arjmand1,
Joint work with Majid Bani-Yaghoub1, Kiel Corkran1, Pranav S. Pandit2, and Sharif Aly2
1Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
2Department of Population Health and Reproduction, University of California, Davis School of Veterinary Medicine, Davis, California, United States of America
In addressing the growing challenge of antimicrobial resistance, our study investigates the impact of biosecurity measures on Salmonella transmission among dairy cattle. Through a framework of ODE, we examine how different levels of biosecurity compliance (Excellent, Good, Marginal and Low) affect the spread of pathogens within animal populations. Our findings highlight that while individual biosecurity actions are important, no single method completely stops outbreaks. Instead, combining measures, especially those reducing direct animal-to-animal transmission, significantly lowers infection rates. Our study underscores the need for comprehensive biosecurity to safeguard livestock and community health.
Approximating the periodic solutions of an Hes1-mRNA model
Mohammed Alanazi
Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
Hes1 (Hairy and Enhancer of Split 1) is a gene that plays a crucial role in embryonic development and cellular differentiation. mRNA plays a crucial role in the process of gene expression. The importance of Hes1 mRNA interaction lies in its role as a regulator of cell fate determination and differentiation during development. This research outlines the preliminary steps towards approximating periodic solutions for a model governing the dynamics of Hes1 mRNA interactions. By linearizing this model, we have identified a critical value (i.e., a bifurcation point) resulting in loss of linear stability. This bifurcation gives rise to periodic solutions as verified via numerical simulations. The subsequent phase of this research will apply the Poincare method to drive an approximation of the periodic solutions
An Extended Model to Study the Effects of Healthy Cell Growth Behaviors on the Dynamics of Vascular Cancer
Priscilla Owusu Sekyere
Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
This study investigates the effectiveness of chemotherapy and anti-angiogenic therapy in controlling the growth of cancer cells within the context of an extended cancer model. We extend a cancer model consisting of a system of five ordinary differential equations that simulates the interactions between normal cells, cancer cells, endothelial cells, chemotherapy agent and anti-angiogenic agent in tumor growth. Numerical simulations with varying initial conditions and combinations are used to assess the impact of healthy cell growth behaviors on the dynamics of vascular cancer. The numerical method used is the Runge-Kutta method. It was used through Matlab ODE 45. These findings help guide the development of targeted treatments for vascular cancer.
Comparative Analysis of FTCS and FECD for Numerical Simulation of SIR RD Model
Adriana Martínez Cappello
Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
This study aims to compare the computational speed of two explicit numerical methods, Forward Time Centered Scheme (FTCS) and Forward Euler Centered Difference (FECD), for simulating the Susceptible-Infectious-Removed (SIR) Reaction-Diffusion (RD) model. The SIR model is a classical tool in epidemiology used to understand disease spread within a population. Both methods utilize finite difference schemes to approximate spatial derivatives by discretizing space and time. We evaluate the efficiency of FTCS and FECD by comparing their computational speed and scalability performance. Results demonstrate that FECD exhibits greater computational efficiency than FTCS using the above metrics. Further, increasing the disease transmission rate (β) leads to a rise in the infected population concentration, which spreads to the susceptible population, regardless of the chosen method.
Probabilistic Learning on Manifold for Unsteady Fluid Dynamics Simulations under Uncertainties
Long Dang
Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
In the field of computational fluid dynamics (CFD), simulating unsteady fluid flows, particularly those governed by the Navier-Stokes equations, presents significant challenges due to the complexity of nonlinear convection, diffusion, and pressure velocity coupling.
We solve the unsteady 2D Navier Stokes equations for incompressible fluid started with fixing Reynold's number using Chorin’s Splitting Method. This method separates the pressure-velocity coupling problem into distinct, more manageable sub-problems. The stability, consistency, and convergence conditions will be used to analyze this method.
This research aims to employ Probabilistic Learning on Manifold(PLoM) to explore the fluid dynamics under uncertainty, where the Reynold number is treated as the random control parameter. The Karhunen-Loeve (KL) expansion is implemented to reduce the dimensionality of the obtained velocity to capture essential features. Then PLoM is used to generate additional realization (sample) to robust model predictions and uncertainty quantification
Investigation of a numerical approach replacement for domain discretizing in wall bounded laminar flows
Milad Mohammadi
Division of Energy, Matter and Systems, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
Laminar flows carry on simple physical features compared to turbulent flows. One of the major applications of these flows is in medical fields (Cerebral spinal fluid and vessel diseases). Since the
governing equations of the laminar flow is much simpler than turbulent flows, maybe the reasonable approach to discretize the equations would be a method with computational costs and numerical challenges less than original finite volume method (FVM). In this study, we are investigating a possible replacement of FVM with FDM to get the desirable results with less computational cost and less
numerical challenges. We simulated 18 cases of channel flow with different step height. For grid generation, the number of grid points for both approaches considered to be the same in order to make a reasonable comparison. Simulations carried out using Ansys Fluent software and MATLAB software for the FVM and FDM methods, respectively. The velocity fields from the FDM and FVM methods for
18 cases were compared. The results show that with FDM approach, the computational costs and simulation challenges (such as using different software for geometry and grid generation) reduces,
compared to FVM method. Although, there is still the weakness of FDM method regarding complex geometries to deal with, which diminishes its range of applicability.
Evaluating PDE-Refiner: Comparing a Neural PDE Solver Against Traditional Numeric Methods for
Long Rollout of the 1D Kuramoto-Sivashinsky Equation
David Wagner
Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
In this paper we aim to reproduce and further quantify the results comparing the PDE-Refiner neural PDE solver to the traditional finite difference method. First a comparison with the results of the original paper will be made to quantify the reproduction of the experiment. The rollouts between the two methods will be compared visually with their outputs alongside a diff of the outputs. Then the compute tradeoffs between the methods, the stability and consistency of
rollouts, as well as long term accuracy of rollouts will be assessed. In evaluating the strengths and weaknesses of the neural PDE solver we will identify areas for future research in improving performance of neural PDE solvers for long rollouts.
Social and Economic Contributions to COVID-19 Prevalence in Nursing Homes
Julia Pluta
Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
The COVID-19 pandemic struck long-term care facilities hard in the first year of the pandemic, prior to the widespread availability of vaccines. In the general population, COVID-19 generally hit poorer communities and communities of color harder than affluent communities or communities with a higher percentage of white residents. The Regional Planning Association and American Planning Association use a concept of “Megaregions” to describe large, multicity areas connected through common transportation and commercial hubs. The placement of Kansas City in those Megaregions is inconsistent.
In prior work, clusters of COVID risk roughly followed Megaregion patterns in the early phases of the pandemic. However, national-scale analysis proved unwieldy. This study was meant to serve as a proof-of-concept for analyzing the pandemic based on Megaregion grouping, while trying to use Kansas City to determine which Megaregion model worked best. At the same time, this was also serving as a small-scale test to determine whether Social Determinants of Health could be combined with factors unique to a given nursing home to determine whether they could be a suitable basis for predicting pandemic risk.
Numerical Explorations of the Competitive Reaction-Diffusion Lotka-Volterra Model with Seasonal Growth Rates
Most Shewly Aktar
Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
This research explores the spatio-temporal dynamics of competing species within the framework of the Lotka-Volterra model. In the absence of diffusion, the parameter space for the classical model is divided into four regions of coexistence, competitive exclusion or founder control. The main objective of this research is to determine whether the presence of diffusion can alter any of these regions. We use Matlab pdepe to numerically explore the solutions of the PDE model with Neuman boundary conditions. The numerical simulations suggest that diffusion has stabilizing effects and the outcomes of the PDE model are consistent with the corresponding ODE model. Also, the seasonal growth rates did not have any effect on the convergence of the PDE solution to the equilibria
Comparative analysis of ODE solutions by using Fast and well-conditioned Spectral and Numerical methods
Farzana Sultana Rafi
Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
Spectral methods are numerical techniques utilized for solving differential equations with high accuracy and efficiency. Fast and well-conditioned spectral methods are particularly notable for their ability to swiftly converge to accurate solutions.
In this research, I apply fast and well-conditioned spectral methods to solve ordinary differential equation (ODE) problems. Specifically, here I employ spectral methods with increasing Chebyshev nodes to approximate the solutions. The accuracy of these approximations is compared with both exact solutions and solutions obtained using the ODE45.
My research observes how spectral methods perform when increasing the number of Chebyshev nodes. For 1st example as the number of Chebyshev nodes increases from N=1 to N=3, the solutions provided by the spectral method gradually converge towards the exact solution. However, at N=4 and N=5, differences arise between the spectral method's solution and the exact one, indicating potential limitations of the approach for higher node counts. Nevertheless, for the 2nd ODE problem, it observes that increasing the number of Chebyshev nodes to N=10, N=20, and N=30 leads to significantly improved solutions compared to lower node counts.
For one ODE, the results vary at N=4 and 5, while for another, the spectral method improves as Chebyshev node count increases. Further research is needed to confirm if this trend extends to other ODEs.
Converging of PDE Solutions to Travelling Wave Trains of Competitive Lotka-Volterra Model
Barsha Saha
Division of Computing, Analytics & Mathematics, School of Science and Engineering, University of Missouri - Kansas City, MO, USA
Lotka-Volterra (LV) Models have been used to study population dynamics of interacting species. The ODE version of Competitive Lotka-Volterra (CLV) models exhibits several periodic solutions. Three stable periodic limit cycles have been identified within Zeeman class of 29. The main focus of this study is to numerically explore how the solutions of the corresponding PDE CLV model behave with Neumann boundary conditions near the identified limit cycles. The numerical simulations suggest that the PDE solutions converge to the traveling wave trains of the model. This study confirms the previous theoretical results.
Friday April 14, 2023, 9:00 AM-4:00 PM
Titles and Abstracts
9th Annual UMKC Math and Stat Research Day
Division of Computing, Analytics & Mathematics,
School of Science and Engineering
University of Missouri - Kansas City
Morning Session: Modeling and Analysis of Infectious Diseases
Chair of the Session: Dr. Noah Rhee
Agent-Based Simulation of Infectious Disease Spread Using MESA Framework
Sarawat Murtaza Sara smtn8@umkc.edu
Division of Computing, Analytics & Mathematics,
School of Science and Engineering,
University of Missouri - Kansas City
Infectious disease outbreaks in hospitals can severely impact both patient health and the efficiency of the healthcare system as a whole. Agent-based simulations offer researchers and decision-makers a useful tool for studying the transmission of these outbreaks. In this study, we use the MESA framework to present a simple agent-based simulation of the spread of infectious diseases in a hospital setting. For this, we leverage MESA, an agent-based modeling (ABM) framework in Python. MESA is particularly useful for simulating complicated systems such as those involved in hospital-based disease spreading. In MESA, participating entities, called "agents" in ABM's parlance, are separately modeled and interact to produce system-level behavior. By this, ABMs capture individual agents' behavior in a given environment, impacting the whole patterns of disease transmission. In our (over) simplified agent-based simulation of the classical SIR (susceptible, infected, and recovered) Epidemic modeling, we deploy one type of agent, nurses, and let them move and interact on a fictional hospital floor (a 2D grid space) thus spreading diseases among themselves. In our presentation, we will describe how the architecture and design of MESA's framework support this simulation. We will also show some preliminary results regarding the disease spread in the hospital area and show the visualization of the simulation progress in MESA.
Multi-state modeling of methicillin-resistant Staphylococcus aureus infection in a hospital environment
Kathryn Menta, mentak@mail.umkc.edu
Division of Computing, Analytics & Mathematics,
School of Science and Engineering,
University of Missouri - Kansas City
The development of antibiotic-resistant strains of bacteria commonly found in healthcare environments is a major public health concern. One such type of bacteria of focus is Methicillin-resistant Staphylococcus aureus, or MRSA, which can cause staph, bloodstream, and other infections and can be lethal. MRSA is also difficult to eradicate, as it has evolved to be resistant to several types of antibiotics. There is an increased emphasis on enhancing statistical modeling methods to gain perspective and knowledge of how these antibiotic-resistant bacteria strains develop and are transmitted in healthcare settings. We develop parallel multi-state MRSA models for hospital patients and healthcare workers. Using the simulated panel data, we aim to unpack the MRSA transmission dynamics within and between patients and hospital workers.
When Care is Shared: Using Agent-Based Models to Analyze Covid-19 Transmission Between Nursing Homes That Share Staff
Kiel Corkran, kcbch@umkc.edu
Division of Computing, Analytics & Mathematics,
School of Science and Engineering,
University of Missouri - Kansas City
The spread of infectious diseases within nursing home facilities has been a concern for epidemiologists, due to the ongoing Covid-19 pandemic and its deadly effects on this specific population. The need for a more detailed understanding of precise structures that govern disease transmission in a nursing home has become increasingly apparent. Current agent-based models focus on understanding disease spread without considering that caregivers may work in multiple nursing homes. These models don’t give detailed information on the dynamics of Covid-19 when caregivers work in multiple homes. To fill this gap, we developed an agent-based model structure to simulate the Covid-19 outbreak in two different nursing homes under a variety of different scenarios. Using the model simulations and the observed Covid-19 outbreaks, we measure the effects of shared caregivers on Covid-19 transmission in multiple facilities.
What can Nursing Home Quality Measures tell us about pandemic preparedness?
Julia Pluta, plutaj@umkc.edu
Division of Computing, Analytics & Mathematics,
School of Science and Engineering,
University of Missouri - Kansas City
The Center for Medicare and Medicaid Services (CMS) tracks several measures to rate the quality of care at nursing homes throughout the United States. These measures produce rating systems, compiled into three domains: Health Inspection Rating, Staffing Rating, and Quality Measure (QM) Rating, which are used to create an overall rating in the Five-Star Quality Rating (FSQR) system. By combining the weekly reported COVID-19 morbidity and mortality data collected by CMS with the FSQR data, I conducted correlation, principal component, and boxplot analyses to determine whether any of the rating systems and their components predicted or reflected the progression of COVID-19 in each of 113 KC Metro Nursing Homes through the end of the first year of the pandemic. I determined that none of the major quality ratings or the FSQR overall rating had any statistically significant correlation with COVID-19-related outcomes during the first year of the pandemic, which raises two new questions: 1) What is the FSQR measuring and why doesn’t that translate to better COVID-19 outcomes?; and 2) What components of a rating system might be better used to generate a rating that would be more predictive of outcomes for a future pandemic?
Afternoon Session: Theory and Applications of Ordinary Differential Equations, Advanced Numerical Methods
Chair of the Session: Dr. Shuhao Cao
Using the Stable Manifold Theorem: Connection between Solutions to Linear and Non-linear Systems
Makayla Devening, mtdg84@umsystem.edu
Division of Computing, Analytics & Mathematics,
School of Science and Engineering,
University of Missouri - Kansas City
In differential equations, mathematicians have figured out ways to solve linear differential equations with relative ease, but non-linear equations have proven to be more difficult. The Stable Manifold Theorem states that the stable manifold of a stable equilibrium point is tangent to the eigenspace associated with the stable eigenvalues of the linearized system at the equilibrium point. This theorem is a tool that helps to predict the behavior of non-linear systems. I will present a sketch of the proof through an example and give a real-world application of the theorem.
Establishing Topological Conjugacy of Local Solutions Using Hartman-Grobman
Theorem, Steven Giangreco, smgrmd@umsystem.edu
Division of Computing, Analytics & Mathematics,
School of Science and Engineering,
University of Missouri - Kansas City
A real-world example of a system of non-linear differential equations is presented to introduce the practical utility of the Hartman-Grobman theorem. First, pre-requisite concepts such as homeomorphisms, trajectories, and flows are reviewed. Then the Hartman-Grobman theorem is stated and explained. Numerical simulations are conducted to demonstrate the implementations of homeomorphisms to map between topologically conjugate systems within the neighborhood of a given solution. Limitations regarding the applicability and scope of the Hartman-Grobman theorem are discussed.
Implications and Applicability of Hartman-Grobman Theorem for Analyzing Nonlinear Dynamical System
Jodi Donald donaldjo@umkc.edu
Division of Computing, Analytics & Mathematics,
School of Science and Engineering,
University of Missouri - Kansas City
In this presentation, we will learn when it is appropriate to use the Hartman-Grobman Theorem. Once established, it will accurately depict what is happening around a hyperbolic equilibrium point, allowing us to determine a nonlinear system's qualitative behavior. Additionally, the stability of the solutions of the system can be determined. The example of a competing species model will be utilized to demonstrate the Theorem.
Finite Element Methods for Phase Field Models of Two-Phase Ferro-Fluid Flows
Mahdi Gharehbaygloo, mgharehbaygloo@mst.edu
Department of Mathematics and Statistics,
Missouri University of Science and Technology,
Rolla, Missouri
In this research a modified mathematical model for Ferro-Fluids will be developed. The model is being developed using the existing PDE models for ferrofluids, namely Rosensweig and Shliomis models. This resultant model will be investigated for the existence of the solution (convergence), uniqueness of the solution, and stability.
Then, DEAL.ii software will be used to numerically solve this model by applying Finite Element Methods. Due to the existence of different phases, a phase-field approach will be imposed for both the development and simulation of the model. The results are expected to be studied in contrast with the available results from lab experiments.
Decoupled finite element method for a phase field model of two-phase ferrofluid flows
Youxin Yuan yyuan@mst.edu
Department of Mathematics and Statistics,
Missouri University of Science and Technology
Ferrofluid is a liquid that is attracted to the poles of a magnet and usually does not retain magnetization in the absence of an externally applied magnetic field. In this talk, the decoupled finite element method for the two-dimensional ferrohydrodynamics model and the numerical validation of the method, which consists of the Navier-Stokes equation, the Cahn-Hilliard equation, and the magnetic field equation, will be discussed.
Understanding the Concept of Lyapunov Stability and Applications of Lyapunov Functions
Cole Flackmiller, cjfhmr@umsystem.edu
Division of Computing, Analytics & Mathematics,
School of Science and Engineering,
University of Missouri - Kansas City
Linear stability analysis is a powerful tool in dynamical systems theory to analyze the behavior of local solutions near a hyperbolic equilibrium solution. Nonetheless, it cannot be applied to systems with nonhyperbolic equilibrium solutions. In this talk, I introduce the concept of Lyapunov stability and the method of Lyapunov function to study the global behavior of solutions. The method of Lyapunov function has important applications in various fields, including control engineering, robotics, and economics. I will provide a few examples to demonstrate its applications to stabilize the behavior of complex systems and predict the long-term behavior of nonlinear systems.
On the fundamental theorem of existence and uniqueness
Dustin Fluderer dwfw4f@umsystem.edu
Division of Computing, Analytics & Mathematics,
School of Science and Engineering,
University of Missouri - Kansas City
The fundamental theorem of existence and uniqueness (FTUE) is a central theorem in differential equations that provides conditions for the existence and uniqueness of solutions to initial value problems. In this talk, I will explain how FTUE can be proved and discuss the application of this theorem. An important application of the FTUE is in the analysis of control systems. Control systems are designed to regulate the behavior of complex systems, such as robots, aircraft, and chemical processes. The FTUE provides a way to ensure that the control algorithms are well-defined and have unique solutions. This is important for designing stable control systems that can reliably regulate the behavior of the complex system.
Friday, April 8, and Saturday, April 9, 2022, 9:00 am - 4:00 pm Joint meeting with Missouri Section Meeting of the Mathematical Association of America
Friday, April 23, 2021, 9:00 am – 4:00 pm
Friday, April 17, 2020, 10:00 am – 3:00 pm
Friday, April 19, 2019, 10:00 am – 3:00 pm
Friday, April 20, 2018, 10:00 am – 3:00 pm
Friday, April 14, 2017, 10:00 am – 3:00 pm
Friday, April 15, 2016, 10:00 am – 3:00 pm
Friday, April 24, 2015, 10:00 am – 3:00 pm
Friday, April 23, 2021, 9:00 am – 4:00 pm
Friday, April 17, 2020, 10:00 am – 3:00 pm
Friday, April 19, 2019, 10:00 am – 3:00 pm
Friday, April 20, 2018, 10:00 am – 3:00 pm
Friday, April 14, 2017, 10:00 am – 3:00 pm
Friday, April 15, 2016, 10:00 am – 3:00 pm
Friday, April 24, 2015, 10:00 am – 3:00 pm
Organizers
Dr. Majid Bani baniyaghoubm@umkc.edu
Dr. Noah Rhee RheeN@umkc.edu
Dr. Shuhao Cao scao@umkc.edu
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