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Numerical Analysis and Computation Commons™
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Articles 1 - 13 of 13
Full-Text Articles in Numerical Analysis and Computation
Human-Centered Modeling Of Traffic As A Complex System, Poorendra P. Ramlall
Human-Centered Modeling Of Traffic As A Complex System, Poorendra P. Ramlall
Discovery Day - Daytona Beach
Traffic systems are driven not only by motion, but by interaction: vehicles influence one another, drivers continuously adapt to surrounding behaviour, and cognitive processes shape decisions that can propagate through the flow of traffic. Understanding these layered interactions is essential for improving traffic safety and for designing the next generation of intelligent, connected, and automated transportation systems. This PhD research develops a multiscale, data-driven framework for identifying, modelling, and ultimately interpreting interaction structure in traffic systems. The work first established an information-theoretic basis for this problem, demonstrating how information flow can uncover directional relationships in traffic dynamics and help infer …
Analyzing Fungal Growth Dynamics Under Different Environmental Conditions Using A Lotka–Volterra Competition System, Maria Ordonez, Fabrio Araujo
Analyzing Fungal Growth Dynamics Under Different Environmental Conditions Using A Lotka–Volterra Competition System, Maria Ordonez, Fabrio Araujo
Discovery Day - Daytona Beach
Fungi play a critical role in ecosystems as decomposers that recycle nutrients and maintain environmental balance. Their populations are influenced by multiple environmental factors such as temperature, humidity, nutrient availability, and interactions with other organisms. In this project, the Lotka–Volterra model is used to analyze how competing fungal species interact and how these interactions influence population dynamics over time. By modeling two fungal populations competing for the same limited resources, the equations illustrate how environmental conditions and competition coefficients determine whether one species dominates; both species coexist, or one species becomes extinct. The model provides insight into how changes in …
Modeling Stellar Structure: Comparing Numerical Solutions Of The Lane-Emden Equation, Jasman Jasmanjot, Bailey Dale, Ryan Dickey
Modeling Stellar Structure: Comparing Numerical Solutions Of The Lane-Emden Equation, Jasman Jasmanjot, Bailey Dale, Ryan Dickey
Discovery Day - Daytona Beach
The Lane-Emden equation is a differential equation that is often used in astrophysics to describe the distribution of the density inside a star, and by extension, its pressure distribution. Analytic solutions of the Lane-Emden equation can only be found at polytropic indices n = 0,1,5, matching certain physical conditions. For all other polytropic values, a numerical solution is needed. In this work, a comparison between two numerical schemes for solving the Lane-Emden equation is presented, namely the Euler method and the classical 4th order Runge-Kutta method. The accuracy of these models is first compared to the cases with known analytical …
Numerical Modeling Of Thermo-Poroelasticity Using Finite Element Method, Maya Mckean
Numerical Modeling Of Thermo-Poroelasticity Using Finite Element Method, Maya Mckean
Discovery Day - Daytona Beach
We propose a numerical method for solving and modeling thermo-poroelasticity problems using a finite element formulation. Thermo-poroelasticity models describe the coupled interaction between mechanical deformation, fluid flow, and heat transfer in specific materials or environments over time. These models demonstrate the evolution of displacement, pressure, and temperature; we compute these fields in this work using backward Euler time discretization and Enriched Galerkin finite element spatial discretization. For these computations we used FreeFEM, a partial differential equation solver that uses the finite element method, which produced our numerical results. We then compared these values with the expected analytical solution. This was …
Numerical Methods For Nonlinear Problems Using The Finite Element Method, Logan Price
Numerical Methods For Nonlinear Problems Using The Finite Element Method, Logan Price
Discovery Day - Daytona Beach
Numerical Methods for Nonlinear Problems Using the Finite Element Method is a computational mathematics capstone that builds and tests finite element method (FEM) workflows for nonlinear partial differential equations in FreeFEM++, with ParaView used for visualization. Two nonlinear model problems are used to demonstrate the approach. The first is a semilinear reaction-diffusion equation with a cubic nonlinearity. A manufactured solution is used so accuracy can be checked at a fixed final time, and refinement studies in both time step and mesh size are run while nonlinear iteration counts are tracked to show solver effort. The second problem is the steady …
Classification Of Sequential Factors In Aviation Accident Cause Prediction, Sophia Nasca, Addyson Wolfe
Classification Of Sequential Factors In Aviation Accident Cause Prediction, Sophia Nasca, Addyson Wolfe
Discovery Day - Daytona Beach
Uncovering the root causes of aviation accidents is a critical component of improving aviation safety. Traditional approaches are largely reactive, relying on post-incident analysis rather than proactively identifying risk factors. This project addresses the need for proactive safety by using a multi-source dataset that integrates aviation accident records, weather conditions, and maintenance data extracted from investigative reports. The objective of this work is to move beyond predicting broad probable causes and instead model the sequence of contributing factors that lead to aviation incidents. Using the Swiss Cheese Model, the study will capture layered failures across operational, environmental, and maintenance domains. …
Quantifying The Effect Of Metallicity On Stellar Properties And Evolutionary Timescales, Jacob Becker
Quantifying The Effect Of Metallicity On Stellar Properties And Evolutionary Timescales, Jacob Becker
Discovery Day - Daytona Beach
Stellar age estimations derived from asteroseismology depend on stellar models that are sensitive to metallicity (Z). Variations in this parameter could alter the agreement between gyrochronological and asteroseismic ages, as well as main sequence lifetimes and observational properties such as effective temperature and luminosity. We test how much typical metallicity differences (±0.2 dex) affect main-sequence models of solar-type stars. Using MESA, evolutionary tracks are created for 1 M☉ stars at three metallicities (Z = 0.009, 0.014, 0.022), and it is measured how these changes shift the positions of the zero-age main sequence and the corresponding main sequence lifetimes. This work …
Analytical And Numerical Solutions For The Hydrogen Atom, Kassidy Myers
Analytical And Numerical Solutions For The Hydrogen Atom, Kassidy Myers
Discovery Day - Daytona Beach
The Schrödinger equation is the foundational equation of non-relativistic quantum mechanics. The hydrogen atom is the simplest system for solving this equation, as it consists of only one proton and one electron. In this project, we work on the Schrödinger equation that models the spherically symmetric states of the hydrogen atom that depend only on the radial coordinate. We simplified and nondimensionalized the radial equation and solved the resulting equation using a power series (Frobenius) method. This approach revealed the physically meaningful solutions and led to quantized energy levels. In addition to finding the analytical solution, we numerically solve the …
Optimization Of Engine, Jordan Reed, Dev Shah
Optimization Of Engine, Jordan Reed, Dev Shah
Discovery Day - Daytona Beach
A matrix-based framework for modeling and optimizing fluid and gas in feed systems to pressurize for propulsion applications using advanced linear algebra techniques will be used in this project. The governing equations are derived from conservation of mass, momentum, and energy and are formulated in state space form. This enables the system to be expressed as a set of coupled linear differential equations. These equations are assembled into structured system matrices that show the interactions between pressure, flow rate, and component dynamics. This representation allows for numerical implementation and scalability to complex systems with multiple components. System behavior is analyzed …
Bridging Discrete And Continuous Systems: Fibonacci Sequences And Exponential Growth From Odes, Martyna Wojcik
Bridging Discrete And Continuous Systems: Fibonacci Sequences And Exponential Growth From Odes, Martyna Wojcik
Discovery Day - Daytona Beach
Bridging Discrete and Continuous Systems: Fibonacci Sequences and Exponential Growth from Ordinary Differential Equations It has been observed that nature often exhibits specific patterns of growth and structure in biological systems and spiral formations. The Fibonacci sequence, defined as a discrete recursive sequence where each term is generated as the sum of the two preceding terms, “has been applied extensively to understand some natural phenomena” (Pakdemirli, 2023). In contrast, exponential growth describes a continuous process in which the rate of change of a quantity is proportional to its current value. Such behavior is modeled using differential equations that “produce solutions …
Numerical Modeling Of Badminton Shuttlecock Trajectories, Lola G. Torres, Cassandra Pumphrey, Jadyn Peterson, Domenic Barsotti
Numerical Modeling Of Badminton Shuttlecock Trajectories, Lola G. Torres, Cassandra Pumphrey, Jadyn Peterson, Domenic Barsotti
Discovery Day - Daytona Beach
The Trajectory of a badminton Shuttlecock can vary significantly when compared to a classic projectile motion, primarily due to aerodynamic drag. This project aims to model the flight of the shuttlecock using Newton's second law for gravitational and drag related forces, resulting in a nonlinear system of a first order differential equation. The given parameters include the shuttlecock mass, cross-sectional area, air density, as well as the drag coefficient, determining the overall magnitude of the drag force. The resulting initial value problem is solved numerically using a multitude of Runge_Kutta methods to compare the accuracy and stability across different computational …
Numerical Analysis Of The Sir Model For Predicting Disease Spread, Victoria Gaibor, Isabel Tejada, Kate Moore
Numerical Analysis Of The Sir Model For Predicting Disease Spread, Victoria Gaibor, Isabel Tejada, Kate Moore
Discovery Day - Daytona Beach
This project, Numerical Solutions of the SIR Model for Predicting Disease Spread, investigates the application of numerical methods to analyze the dynamics of infectious diseases using the classical Susceptible–Infected–Recovered (SIR) model. The SIR model, a system of nonlinear ordinary differential equations, is widely used to describe how diseases such as COVID-19 propagate through a population. The primary objective of this study is to solve the SIR initial value problem using multiple numerical techniques, including Euler’s method, Runge–Kutta methods, and multistep methods, and to compare their accuracy and efficiency. The model is implemented using given initial conditions and parameters, and additional …
Numerical Investigation Of The Nonlinear Simple Pendulum And The Dependence Of Oscillation Period On Initial Angle, Kelly Wold, Aidan Hart, Patrick Gilliam
Numerical Investigation Of The Nonlinear Simple Pendulum And The Dependence Of Oscillation Period On Initial Angle, Kelly Wold, Aidan Hart, Patrick Gilliam
Discovery Day - Daytona Beach
Numerical Investigation of the Nonlinear Simple Pendulum and the Dependence of Oscillation Period on Initial Angle examines how the oscillation period of a simple pendulum varies with initial angular displacement and evaluates the accuracy of numerical methods in capturing this behavior. In classical treatments, the small-angle approximation simplifies the governing differential equation and predicts a constant period independent of amplitude; however, this assumption breaks down for larger angles, where the system exhibits nonlinear dynamics. The objective of this project is to model the full nonlinear equation of motion and quantify how the period depends on initial conditions. To achieve this, …