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Articles 541 - 570 of 291657

Full-Text Articles in Physical Sciences and Mathematics

The General Solution Analysis Of Homogeneous Linear Equations, Jacob Schwamb, Edward Whipple Aug 2026

The General Solution Analysis Of Homogeneous Linear Equations, Jacob Schwamb, Edward Whipple

Discovery Day - Daytona Beach

The general solution analysis of homogeneous linear equations are any systems of equations in which all constant terms are equal to zero is classified as a homogeneous linear equation. Some key characteristics of homogeneous linear equations are that there are “zero” solutions, where every system has at least a single solution where all variables are zero, also all solutions to any homogenous linear equation is linearly independent, along with having preserved homogeneity, where if any variable (x) may be added to the system, then any scalar multiple of the variable is also a solution. The General solution of any homogeneous …

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A Compact Representation Of Oscillatory Limits Via Asymptotic Value Distributions, Ibrahim Arnous, Eric M. Rodarte, Chirag Kumar Aug 2026

A Compact Representation Of Oscillatory Limits Via Asymptotic Value Distributions, Ibrahim Arnous, Eric M. Rodarte, Chirag Kumar

Discovery Day - Daytona Beach

Classical limits describe asymptotic behavior through convergence to a single value, but many important oscillatory functions do not converge in this sense. Standard examples such as sin(𝑥) as 𝑥→∞ and sin(1/x) as x→0 instead display stable distributions of values over time. This project examines how such behavior can be described using a measure-theoretic framework, particularly through occupation measures and, in sequence-based settings, Young measures. The objective is to present this perspective in a clear and accessible way while introducing the Ansatz representation, a compact notation for recording the support and density of an asymptotic value distribution when the limiting measure …

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Differentiating The Impossible: Feynman's Trick In Applications Of Modern Physics, Yaohua Zhao Aug 2026

Differentiating The Impossible: Feynman's Trick In Applications Of Modern Physics, Yaohua Zhao

Discovery Day - Daytona Beach

We discuss Feynman’s method of differentiating with respect to a parameter inside an integral and explore its significance on selective topics of modern physics. This powerful technique allows us to integrate functions that may seem impossible. Depending on the underlying parameters, the Feynman method becomes a unifying framework that connects mathematical concepts to many parameter-dependent equations in modern physics. In statistical mechanics, this appears directly in the partition function, where derivatives with respect to temperature-related parameters yield thermodynamic quantities such as internal energy and heat capacity; this demonstrates how parameter dependence gives rise to macroscopic behaviors observable at a larger …

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Reimagining Wind Based Sea Travel With Vertical Axis Wind Turbines, Julian Goins Aug 2026

Reimagining Wind Based Sea Travel With Vertical Axis Wind Turbines, Julian Goins

Discovery Day - Daytona Beach

In the realm of Nautical vehicles, aside from the occasional outliers like rarely used coal steamboats, experimental solar powered ships, or the military grade nuclear vessels, the vast majority of ships run off diesel-powered engines. The unsustainability of such methods will need to be addressed for the security of our planet’s future due to the limited and destructive nature of fossil fuels, much like it already is in many other fields. To that end, this project gains inspiration from the past and looks toward harnessing the power of the wind. In recent times, most sail boats are equipped with some …

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Modeling Doppler-Shifted Solar Spectra From Simulated Asteroidal Dust Populations Using Orbital Evolution Codes, Skylar G. Butler, Jarrett Dieterle Aug 2026

Modeling Doppler-Shifted Solar Spectra From Simulated Asteroidal Dust Populations Using Orbital Evolution Codes, Skylar G. Butler, Jarrett Dieterle

Discovery Day - Daytona Beach

We investigate how orbital properties of interplanetary dust particles produce Doppler-shifted solar absorption lines using synthetic spectra generated from particle outputs of a numerical orbital evolution code. The code is based on the Ipatov dynamical model, written in Fortran and using the SWIFT integration package to track the evolution of dust particles originating from asteroid and comet populations. The program reads input files containing particle orbital elements and heliocentric positions, along with planetary parameters and integration settings, and computes the time evolution of particle trajectories under gravitational perturbations. The resulting particle states are then used to generate synthetic spectra by …

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Dcat - Distributed Computing And Analysis Tool, Asher Zwickel, Jacob Burdge Aug 2026

Dcat - Distributed Computing And Analysis Tool, Asher Zwickel, Jacob Burdge

Discovery Day - Daytona Beach

This project uses distributed computing to process and analyze large datasets related to cyber breaches and attacks. Its main goal is to find patterns between initial cyber incidents and what happens next. It looks at whether responses tend to escalate, calm down, or stay about the same over time. Understanding this helps explain how digital conflicts develop and whether they follow predictable paths. The project was built as part of university research and runs on custom software across a cluster of 17 Chromebooks. While the system can study many topics, it is currently focused on cyber activity. The software uses …

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Ngc 4374 With Jwst/Nircam: A Central Structural Analysis Revealing A Depleted Core And Agn, Elizabeth Crevinston Aug 2026

Ngc 4374 With Jwst/Nircam: A Central Structural Analysis Revealing A Depleted Core And Agn, Elizabeth Crevinston

Discovery Day - Daytona Beach

We use James Webb Space Telescope’s (JWST) Near Infrared Camera (NIRCam) F150W imaging to study the central regions of massive elliptical galaxies, focusing on their partially depleted cores. These cores are thought to form when a binary supermassive black hole (SMBH) ejects stars from the central regions through dynamical three-body interactions. After the binary coalesces, gas accretion onto the newly formed SMBH can trigger a compact active galactic nucleus (AGN), which plays a key role in regulating star formation and shaping galaxy structure. With JWST NIRCam, we extracted the surface brightness profile of NGC 4374, a giant elliptical galaxy in …

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Investigating The Spatial Scales Of Ionospheric Irregularities Using Wavelet Analysis, Nash Mcleod Aug 2026

Investigating The Spatial Scales Of Ionospheric Irregularities Using Wavelet Analysis, Nash Mcleod

Discovery Day - Daytona Beach

Investigating the Spatial Scales of Ionospheric Irregularities Using Wavelet Analysis:   Ionospheric radio wave scintillation arises from plasma density irregularities in Earth’s ionosphere. Consequently, rapid fluctuations occur in the phase and amplitude of Global Navigation Satellite System (GNSS) signals and can impact communication and navigation systems. These irregularities span from a wide range of spatial and temporal scales and evolve dynamically under the influence of magnetosphere-ionosphere (MI) processes. We investigate phase and amplitude scintillation events using Continuous Wavelet Transform (CWT) to study the spatial evolution of ionospheric irregularities. These irregularities are thought to be formed via different plasma mechanisms such as …

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Bounded Thunderstorm Tracking Of Lightning Events With Muon Detection, Skylar Wardlaw, Ainsley Helgerson, Maria Kaminska, Logan Velvet, Georgii Dubrov, Jackson Stewart, Aaron Jung, Nathaniel O’Hara, Amelia Koth, Nash Mcleod, Emaleth Wyckoff Aug 2026

Bounded Thunderstorm Tracking Of Lightning Events With Muon Detection, Skylar Wardlaw, Ainsley Helgerson, Maria Kaminska, Logan Velvet, Georgii Dubrov, Jackson Stewart, Aaron Jung, Nathaniel O’Hara, Amelia Koth, Nash Mcleod, Emaleth Wyckoff

Discovery Day - Daytona Beach

The muon is a high-energy particle that can be produced by cosmic rays and trigger upper-atmospheric particle cascades and energetic processes. It has been hypothesized that such cascades are at the onset of lightning. As such, muons serve as a valuable probe for investigating the underlying mechanisms of its initiation, whose full governing dynamics remain vastly unknown despite extensive research. Traditional approaches to lightning research involve simulations and observations of the discharge itself, but the role of high-energy particle interactions has yet to be fully constrained. The CosmicWatch Muon Detector design enables the detection of atmospheric muons through scintillation events, …

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Effect Of Anode Size On The Properties Of Constricted Hollow Anode Pulsed Plasma Source, Nirav Patel, Garret Seckinger Aug 2026

Effect Of Anode Size On The Properties Of Constricted Hollow Anode Pulsed Plasma Source, Nirav Patel, Garret Seckinger

Discovery Day - Daytona Beach

With the advent of ion thrusters, burns requiring large velocity changes can be performed with a fraction of the propellant required by traditional chemical rocket engines. However, current ion thrusters produce thrust in the order of millinewtons and thus cannot be viable for launching vehicles or burns requiring velocity changes in a small amount of time. Furthermore, current ion thrusters experience grid and component erosion, where the two grids at the termination of the nozzle slowly erode due to particle impact, and the hot electrodes degrade due to high thermal load. This limits the life of ion engines, which require …

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Stormtrack: A Regime-Aware Classifier-Router Architecture For Multi-Horizon Kp Index Forecasting, John Rendleman Aug 2026

Stormtrack: A Regime-Aware Classifier-Router Architecture For Multi-Horizon Kp Index Forecasting, John Rendleman

Discovery Day - Daytona Beach

STORMTRACK: A Regime-Aware Classifier-Router Architecture for Multi-Horizon Kp Index Forecasting Current algorithms in operational space weather face extreme difficultly predicting the Kp geomagnetic index beyond 24 hours, a lead time that is critical for protecting high-frequency communications and infrastructure. Most regression models are optimized for quiet conditions, which dominate the data, leading to systematic underpredictions of storm events that cripple space infrastructure. Probabilistic approaches and physics-based numerical models also falter due to the same class imbalance plaguing standard regressors at multi-day lead times. The ICARUS 6 architecture addresses this by splitting the forecasting component into quiet and storm regimes, which …

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Accelerating Search And Rescue Response: A Simulation Study On The Dynamic Efficiency Of Flocking-Enabled Drone Swarms, Sophia Beckwith, Carys Del Prete Aug 2026

Accelerating Search And Rescue Response: A Simulation Study On The Dynamic Efficiency Of Flocking-Enabled Drone Swarms, Sophia Beckwith, Carys Del Prete

Discovery Day - Daytona Beach

This project explores how imitations observed in animal group behavior, specifically flocking in birds, can be applied to the functionality of autonomous drone systems to aid in search and rescue efforts. The goal is to demonstrate how incorporating code based on the Boids, Vicsck and predictive control linear algebraic mathematical models for drone flight controls and the collective behaviors of flocks will increase the efficiency of drone maneuvers, allowing them to reorganize and fill gaps when one is removed. A MATLAB-based simulation was developed to model the behaviors using research conducted on the symmetric and synchronized behaviors observed from flocks …

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A Feedback Loop Control To Automate Cold Atmospheric Pressure Plasma Based Additive Manufacturing, Arineh Shahbazi Aug 2026

A Feedback Loop Control To Automate Cold Atmospheric Pressure Plasma Based Additive Manufacturing, Arineh Shahbazi

Discovery Day - Daytona Beach

Currently, nanoparticle annealing based additive manufacturing process requires high temperatures, making them unsuitable for a broad range of applications. By lowering the temperature and developing a process to use Cold Atmospheric Pressure Plasma (CAPP) for annealing, many more doors are opened to a wide range of materials, films, and environments for space, communication, and microelectronics. CAPP-based additive manufacturing technology is continually evolving, making projects like nanoparticle annealing more feasible. In this work, we designed a CAPP jet printer assembly consisting of a 0.25-inch outer diameter glass tube connected to a 3D printing nozzle. The flow of Argon gas in the …

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Climate Resilient Infrastructure: The Problem Shift, Tyler Lautieri, Isaiah Morrison, Harrison Totten Aug 2026

Climate Resilient Infrastructure: The Problem Shift, Tyler Lautieri, Isaiah Morrison, Harrison Totten

Discovery Day - Daytona Beach

Climate change is a heavily debated topic, but recent studies and data show that climate change is leading to an increase in the frequency and severity of hazards. Infrastructure systems are subjected to more compound and cascading events that lead to the degradation of the systems. More traditional infrastructure design relies on concern that the system will be subjected to single hazard issues, and the design focuses on preventing structural failure during these isolated events. These approaches often fail to account for long term degradation of the system, as well as the interacting hazards, and system interdependence, which makes resilience …

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Modeling Population Growth With Logistic And Modified Logistic Equations, Mihil Dimpal Patel Aug 2026

Modeling Population Growth With Logistic And Modified Logistic Equations, Mihil Dimpal Patel

Discovery Day - Daytona Beach

Population growth models are essential tools for understanding how biological populations change over time under environmental constraints. This study examines population dynamics by comparing the classical exponential growth model with the logistic growth model. While exponential growth assumes unlimited resources and results in unbounded population increase, the logistic model incorporates a carrying capacity that limits growth as resources become scarce. To better represent real-world conditions, the logistic model is extended by introducing modifications such as harvesting terms and time-varying carrying capacities, which account for external removal of individuals and changing environmental limits. The equilibria of these models are determined, and …

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Polymer Degradation And Their Environmental Impact, Addison Orr, Vanessa Gilbert Aug 2026

Polymer Degradation And Their Environmental Impact, Addison Orr, Vanessa Gilbert

Discovery Day - Daytona Beach

Synthetic polymer material usage has increased significantly within the last several decades due to their durability, resistance to mechanical wear, low density, and inexpensiveness. Despite these advantages, most synthetic polymers are not biodegradable and instead undergo slow degradation processes. The processes are multifaceted, involving physical, chemical, and biological mechanisms influenced by material properties and environmental conditions, such as soil, light, temperature, and moisture levels. As a result, the polymers break into microplastics and contaminate air, water, and soil, posing risks to human health and surrounding ecosystems. Additionally, polymer degradation can release harmful substances that disrupt food chains and can lead …

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Optimization Of Engine, Jordan Reed, Dev Shah Aug 2026

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 …

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Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Bianca Gerity, Arineh Shahbazi Aug 2026

Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Bianca Gerity, Arineh Shahbazi

Discovery Day - Daytona Beach

A seiche oscillation is a standing wave that oscillates in an enclosed body of water, like a lake or pool. Seiches are caused by strong winds, earthquakes, and rapid atmospheric changes. Seiches are an excellent real-world example of damped harmonic motion. The physics of these unique vibrations can actually be modeled using a second-order differential equation for damped oscillators of the general form mx''+cx'+kx=0, where m represents the mass of the vibrating water column, c represents the energy dissipation due to friction and viscosity, and k represents the force governed by gravity and the basin's geometry. The objective of this …

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Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Sharjeel Malik, Justin Della Aug 2026

Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Sharjeel Malik, Justin Della

Discovery Day - Daytona Beach

Combustion instability in liquid rocket engines is driven by coupling acoustic pressure oscillations and unsteady heat release. To achieve specific desired outcomes, small perturbations can be made to either decay or grow, depending on system dynamics and artificial parameters. Using a linearized eigenvalue framework, where eigenvalues determine growth/decay rates and frequencies, and eigenvectors describe spatial mode shapes and couplings between pressure, velocity, and heat release, a mathematical model can be derived to describe said behavior for a cross-section of the rocket engine. The Rayleigh criterion is used to identify conditions under which energy is added to oscillations, while flame transfer …

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Production And Analysis Of Lavender Essential Oil: Extraction, Composition, And Applications, Mary Zoeller Aug 2026

Production And Analysis Of Lavender Essential Oil: Extraction, Composition, And Applications, Mary Zoeller

Discovery Day - Daytona Beach

Steam distillation was performed to extract essential oil from lavender and analyze its chemical composition. Lavender is known to contain several compounds such as linalool, terpinen-4-ol, and linalyl acetate, which contribute to its characteristic aroma and biological activity. The purpose of this experiment was to isolate these compounds without decomposition and identify them using gas chromatography–mass spectrometry (GC-MS). Approximately 14.851 g of lavender was heated with water to generate steam, which carried the volatile compounds into a condenser where the vapor was cooled and collected. The distillate was transferred to a separatory funnel to isolate the organic layer from the …

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Navier Stokes Pressure Drop Derivation, Brayden Benedetti, Gedaliah Dimbert, Jaden Turobiner Aug 2026

Navier Stokes Pressure Drop Derivation, Brayden Benedetti, Gedaliah Dimbert, Jaden Turobiner

Discovery Day - Daytona Beach

Accurate prediction of pressure losses in propellant and fluid feed systems is essential for reliable design and operation of aerospace and industrial flow networks. This project presents a systematic derivation of a practical pressure drop calculator for a feed system using isopropyl alcohol, beginning from the fundamental conservation laws and culminating in an engineering-level computational model. Starting with the differential form of the Navier–Stokes equations for incompressible flow, the governing equations are simplified through a series of physically justified assumptions, including steady-state flow, negligible body forces, and fully developed internal flow within circular piping. The resulting momentum balance is reduced …

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Bridging Discrete And Continuous Systems: Fibonacci Sequences And Exponential Growth From Odes, Martyna Wojcik Aug 2026

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 …

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Application Of Navier Stokes In Cfd, Hayden Kerkhoff, Gavin Palmer, Garret Seckinger Aug 2026

Application Of Navier Stokes In Cfd, Hayden Kerkhoff, Gavin Palmer, Garret Seckinger

Discovery Day - Daytona Beach

This project investigates the use of 2-Dimensional Computational Fluid Dynamics (CFD) to analyze aerodynamic behavior, then compare data with the numerical solution of the Navier–Stokes equations run by MATLAB. By leveraging open‑source and possible industry CFD platforms—including OpenFOAM and commercial solvers such as ANSYS Fluent and Inventor Professional—the study evaluates how computational methods simulate, optimize, and predict key aerodynamic quantities such as lift, drag, stall angle, and Reynolds number.   The project focuses on modeling an airflow over specific parameters, such as different angles of attacks and ISA Atmospheric Conditions. Parametric variations in density, angle of attack, chord length, and temperature …

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Mechanical Vibrations And Damping, Axon Deadrick, Will Standish, Tanay Agarwal Aug 2026

Mechanical Vibrations And Damping, Axon Deadrick, Will Standish, Tanay Agarwal

Discovery Day - Daytona Beach

Mechanical vibrations occur in many engineering systems and can be described using second-order differential equations. In this project, the motion of vibrating systems is studied using the mass–spring model. The focus is on three types of oscillations: free vibrations, dampened vibrations, and forced oscillations. Free vibration describes how a system moves when it is displaced and then released without any external force. Damped vibration includes effects such as friction or resistance that cause the motion to gradually decrease over time. Forced oscillations occur when an external force acts on the system and continuously drives the motion. This project also examines …

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Numerical Modeling Of Badminton Shuttlecock Trajectories, Lola G. Torres, Cassandra Pumphrey, Jadyn Peterson, Domenic Barsotti Aug 2026

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 …

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Motion With Air Resistance, Gauge Mccain, Jacob Bealefeld, Francesca Wise Aug 2026

Motion With Air Resistance, Gauge Mccain, Jacob Bealefeld, Francesca Wise

Discovery Day - Daytona Beach

The motion of objects moving through air is influenced not only by gravity but also by air resistance, which affects the speed and acceleration of the object over time. This project examines the motion of a falling object by modeling it with an ordinary differential equation that accounts for both gravitational force and a resistive drag force proportional to velocity. Using Newton’s Second Law, a first-order differential equation is derived to describe how the velocity of the object changes as it falls. The solution of this equation demonstrates how the velocity increases initially and gradually approaches a constant value known …

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Steam Distillation Of Jasmine, Mikayla Hulvey, Meliah Martin Aug 2026

Steam Distillation Of Jasmine, Mikayla Hulvey, Meliah Martin

Discovery Day - Daytona Beach

This experiment aimed to isolate various components, including benzyl acetate, linalool, indole, and farnesene, from jasmine buds. The functional groups include an ester in benzyl acetate, an alcohol in linalool, an amine in indole, and alkenes in farnesene. Jasmine buds were combined with distilled water and steam distilled using a standard distillation apparatus. The distillate, containing hydrosol and trace amounts of essential oil, was then collected for extraction using methyl tert-butyl (MTBE) for a liquid-liquid extraction. The organic layer was then separated, washed using brine, dried over anhydrous sodium sulfate, and then transferred for later analysis. The essential oil obtained …

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A Differential Equation Approach To Heat Flow In A Thin Rod, Alexandria Krol, David Cardona, Collin Petrie Aug 2026

A Differential Equation Approach To Heat Flow In A Thin Rod, Alexandria Krol, David Cardona, Collin Petrie

Discovery Day - Daytona Beach

A Differential Equation Approach to Heat Flow in a Thin Rod examines how differential equations can be used to model and understand heat conduction in a fundamental physical system. Heat transfer in solids is a key concept in physics and engineering, particularly in systems where temperature changes over time. A thin rod provides a useful one-dimensional model for studying how heat moves through a material and how temperature varies along the rod as time passes. The primary objective is to develop a mathematical description of this process using differential equations. The analysis begins with physical principles such as conservation of …

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Numerical Analysis Of The Sir Model For Predicting Disease Spread, Victoria Gaibor, Isabel Tejada, Kate Moore Aug 2026

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 …

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Mechanical Vibrations And Damping – Structural Analysis, Kelsey Hunsicker, Sarah Kraus, Sophia Muller Martinelli De Souza Aug 2026

Mechanical Vibrations And Damping – Structural Analysis, Kelsey Hunsicker, Sarah Kraus, Sophia Muller Martinelli De Souza

Discovery Day - Daytona Beach

Mechanical Vibrations are crucial in understanding and structural analysis of engineering systems such as bridges and airplane wings. If not considered, these vibrations can lead to structural fatigue or failure. By using differential equations, structural vibrations will be examined. Researching the different kinds of vibrations and damping will help to find the vibration behavior of the system. For example, a mass-spring damper system will use second-order linear differential equations. The systems model can be shown to be underdamped, overdamped, or critically damped. These will compare the amplitudes and oscillation differences between the systems by using computational code. Analyzing these differences …

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