Mathematics Commons^™

Nerve Cell Deterioration Associated With Alzheimer's Disease, Yaping Tu

Undergraduate Journal of Mathematical Modeling: One + Two

Alzheimer's disease is an extremely serious condition that is challenging to diagnose. We have used experimental data to compare the rate of decay of entorhinal cortex (EC) neurons in various stages of Alzheimer's. We observed that the rate of EC neuron decay in the patients without Alzheimer's is close to zero, linear in mild cases, and quadratic in severe cases. We believe that described estimates may help to diagnose the disease as well as its stage.

Calculating Optimal Inventory Size, Ruby Perez

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of the project is to find the optimal value for the Economic Order Quantity Model and then use a lean manufacturing Kanban equation to find a numeric value that will minimize the total cost and the inventory size.

Predator-Prey Modeling, Shaza Hussein

Undergraduate Journal of Mathematical Modeling: One + Two

Predator-prey models are useful and often used in the environmental science field because they allow researchers to both observe the dynamics of animal populations and make predictions as to how they will develop over time. The objective of this project was to create five projections of animal populations based on a simple predator-prey model and explore the trends visible. Each case began with a set of initial conditions that produced different outcomes for the function of the population of rabbits and foxes over an 80 year time span. Using Euler's method, an Excel spreadsheet was developed to produce the values …

Volume Of An Industrial Autoclave, Nicholas Madaffari

Undergraduate Journal of Mathematical Modeling: One + Two

We were able to determine the volume of an industrial autoclave sterilization tank using a technique learned in calculus. By measuring the dimensions of the tank and roughly estimating the equation of curvature at the ends of the tank, we were able to revolve half of the end of the tank around the x axis to get its fluid volume. Adding the two volumes of the ends and the volume of the cylindrical portion on the tank yielded the total volume.

The Aerodynamics Of Frisbee Flight, Kathleen Baumback

Undergraduate Journal of Mathematical Modeling: One + Two

This project will describe the physics of a common Frisbee in flight. The aerodynamic forces acting on the Frisbee are lift and drag, with lift being explained by Bernoulli‘s equation and drag by the Prandtl relationship. Using V. R. Morrison‘s model for the 2-dimensional trajectory of a Frisbee, equations for the x- and y- components of the Frisbee‘s motion were written in Microsoft Excel and the path of the Frisbee was illustrated. Variables such as angle of attack, area, and attack velocity were altered to see their effect on the Frisbee‘s path and to speculate on ways to achieve maximum …

Embedded Systems - Missile Detection/Interception, Luis Cintron

Undergraduate Journal of Mathematical Modeling: One + Two

Missile defense systems are often related to major military resources aimed at shielding a specific region from incoming attacks. They are intended to detect, track, intercept, and destruct incoming enemy missiles. These systems vary in cost, efficiency, dependability, and technology. In present times, the possession of these types of systems is associated with large capacity military countries. Demonstrated here are the mathematical techniques behind missile systems which calculate trajectories of incoming missiles and potential intercept positions after initial missile detection. This procedure involved the use of vector-valued functions, systems of equations, and knowledge of projectile motion concepts.

The Sir Epidemiology Model In Predicting Herd Immunity, Joanna Nicho

Undergraduate Journal of Mathematical Modeling: One + Two

The Simple Epidemic Model uses three states to describe the spread of an infection: the susceptible (S), the infected (I), and the recovered (R). This model follows the trend of an infection over time and can predict whether an infection will spread. Using this model, epidemiologists may calculate the percentage of the population that needs to be vaccinated in order to provide a population immunity from a disease. This study will compare the vaccination percentage required for herd immunity to measles, mumps, and rubella against the current percentage of vaccinated individuals.

Locomotion Of A Running Quadruped Robotic System, Bradley Savon

Undergraduate Journal of Mathematical Modeling: One + Two

Very little is known about the locomotion of quadruped robotic systems. In Latin, the term quadruped means 'having four feet'. The robotic system analyzed in this project was a software simulation program modeled after a horse. Simulation data was recorded to resolve the relationship between foot position and impulses required to accelerate or to decelerate the system while trotting. These sets of data were then analyzed in MATLAB to produce graphical representations which allowed for a better understanding of the robot's motion in the simulation environment. A function was fit to the graph of discrete data values measured in the …

Pollination Of A Canary Tree Flower, Abbie O'Hern Weeks

Undergraduate Journal of Mathematical Modeling: One + Two

Pollination is an essential part of the life cycle of flowering plants. We perform an experiment to determine how long a canary tree flower is accessible to pollinating insects so that fertilization can take place. We conducted an observational study where we measured the size of the same flower and charted its growth each day. With the observational data we constructed a scatter plot and from the graph we fit a cubic function to the data. We conclude that in the lifespan of a canary tree flower, pollination begins at 5 1/2 days and ends approximately 9 days later.

Dosimetry Calculations Of Radiopharmaceuticals, Kelbe Jahnke

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of this project is to determine the absorbed dose of radiation to a patient using ^99mTc-MAA as a tracer for a lung scan using the MIRD formula accounting only for the radiation dose contributed by the target organ. The radiation dose for other organs to the target organ is considered negligible as the uptake of ^99mTc-MAA from other organs is less than 1%. In addition to calculating the absorbed dose of radiation, the initial dose rate was also calculated by back solving to determine the total mass of the lungs. The radiation dose to the patient …

Maximum Power From A Solar Panel, Michael Miller

Undergraduate Journal of Mathematical Modeling: One + Two

Solar energy has become a promising alternative to conventional fossil fuel sources. Solar panels are used to collect solar radiation and convert it into electricity. One of the techniques used to maximize the effectiveness of this energy alternative is to maximize the power output of the solar collector. In this project the maximum power is calculated by determining the voltage and the current of maximum power. These quantities are determined by finding the maximum value for the equation for power using differentiation. After the maximum values are found for each time of day, each individual quantity, voltage of maximum power, …

Escape Velocity, Nikola Vlacic

Undergraduate Journal of Mathematical Modeling: One + Two

In this project, we investigated if it is feasible for a single staged rocket with constant thrust to attain escape velocity. We derived an equation for the velocity and position of a single staged rocket that launches vertically. From this equation, we determined if an ideal model of a rocket is able to reach escape velocity.

Using Calculus To Model The Growth Of L. Plantarum Bacteria, Erin Carey

Undergraduate Journal of Mathematical Modeling: One + Two

Experimental data for the growth of Lactobacillus plantarum bacteria have been obtained over time, creating the need for mathematical means to model this data. We use the Gompertz model because it is a sigmoid function for a time series, where growth is slowest at the start and end of a time period. The Gompertz model is especially useful because it defines specific parameters that characterize the S-shaped curve. In addition, the Gompertz model uses relative growth, which is the logarithm of the given population compared to the initial population. This reflects the fact that bacteria grow exponentially. The important parameters …

Detecting Edges, Sam Maniscalo

Undergraduate Journal of Mathematical Modeling: One + Two

In human vision the first level of processing is edge detection. Edges are determined by the transitions from dark points to bright points in an image. For this paper, we consider an edge profile model representing a boundary or edge in an image. From this model we can determine the strength of the edge, the width of the edge, and either the transition from dark to bright to dark or the transition from bright to dark to bright. Our first step was to take the given edge profile and determine the type of edge that is represented and the characteristics …

Determination Of Azeotropy, Kyle Cogswell

Undergraduate Journal of Mathematical Modeling: One + Two

The ultimate goal of this paper is the determination of an azeotrope within a methanol-acetone system. An azeotrope is the point in a chemical system at which coexisting compositions of vapor and liquid phases are equal. The importance of this point lies in the fact that azeotropes are undesirable; they prevent one from completely separating a mixture through distillation. This state can occur over a range of temperatures and for the purposes of this paper there is only one azeotrope for each given temperature. All azeotropes occur at relative extrema in pressure. By finding these extrema, we find the mole …

Infection Of A Homogeneous Population By A Known Bacterium, Arthur Maknenko

Undergraduate Journal of Mathematical Modeling: One + Two

In order for the development of antibiotics and vaccines to be successful, the lifecycle and infection pattern of a pathogen must be studied well. In this paper, we study the rate of replication and the pattern of infection in a homogeneous population, which may or may not have an effective immunity or immunization program against the pathogen. We utilize three functions: one will determine the rate with which the pathogen replicates; the second will show the result of an infection by a single individual of a susceptible population without a removal rate; and the third will include the removal rate …

2009 Ford Mustang Performance Test, Daniel Fernandes

Undergraduate Journal of Mathematical Modeling: One + Two

Our goal is to find the time required for a 2009 Ford Mustang to accelerate from rest to 88 feet per second. We begin with three equations involving force, velocity, and force inverse, which is a value derived from Newton's Law, F=ma. The Mustang has three gears with three different gear ratios that must be used as the car accelerates. We found results from 2000 to 6000 RPMs for all three gears. Once the force inverse was found, we plotted the force inverse vs. velocity graph. The area beneath this curve from 0 to 88 feet per second is the …

Modulus Of Subgrade Reaction And Deflection, Austin Potts

Undergraduate Journal of Mathematical Modeling: One + Two

Differential equations govern the bending and deflection of roads under a concentrated load. Identifying critical parameters, such as the maximum deflection and maximum bending moments of a street supported by an elastic subgrade, is key to designing safe and reliable roadways. This project solves the underlying differential equation in pavement deflection and tests various parameters to highlight the importance in selecting proper foundation materials.

That's A Drag: The Effects Of Drag Forces, Shane Maxemow

Undergraduate Journal of Mathematical Modeling: One + Two

Drag is a force that opposes motion due to an object's shape, material, and speed. This project defined what drag force is, derived the governing equation for drag and listed some applications of drag forces. Derivation of the drag equation was achieved using the Buckingham π theorem, a dimensional analysis tool. Lastly, this project explored the problem of how long and how far a dragster takes to stop once its parachute is deployed.

Biodiversity In A Florida Sandhill Ecosystem, Samantha Robertson

Undergraduate Journal of Mathematical Modeling: One + Two

This project compares two transects of land in the University of South Florida's Botanical Gardens for their biodiversity. The transects were chosen to represent a Florida sandhill ecosystem and the individual Longleaf Pine, Saw Palmetto, Turkey Oak, Laurel Oak and Live Oak specimens were counted. All other species above waist height were counted as "other"?. Once the individuals were counted, the Simpson's and Shannon-Wiener indices were calculated. Since the Shannon-Wiener index incorporates several diversity characteristics, it is typically more reliable than Simpson's. However, both biodiversity indices agreed that transect B was more diverse than transect A.

Repeatability Estimates Of Sloped Scattered Data, Angelique Waller

Undergraduate Journal of Mathematical Modeling: One + Two

Repeatability is the variance in data accumulated under fixed conditions. It is important for quality control as it costs both time and money to recalibrate tools and remanufacture machines. This project compares three methods for approximating the repeatability of a sloped scattered data set. The first method uses a linear approximation, the second involves rotating the data points, and the third calculates distance using right triangles. The methods are compared for both precision and ease of use.

Robotics Potential Fields, Jordi Lucero

Undergraduate Journal of Mathematical Modeling: One + Two

This problem was to calculate the path a robot would take to navigate an obstacle field and get to its goal. Three obstacles were given as negative potential fields which the robot avoided, and a goal was given a positive potential field that attracted the robot. The robot decided each step based on its distance, angle, and influence from every object. After each step, the robot recalculated and determined its next step until it reached its goal. The robot's calculations and steps were simulated with Microsoft Excel.

Arsenic And Growth Of Amphistegina Gibbosa, Elise Keister

Undergraduate Journal of Mathematical Modeling: One + Two

A laboratory tested various concentrations of arsenic on the growth of foraminifera and recorded their findings. Upon examination, the plotted probability density function for each of these trials resembled a similar shape. The plots were then characterized in a general model composed of linear segments. Using calculus, statistics such as the expected value, variance and standard deviation were calculated to interpret the collected data. The statistics revealed that arsenic limits the growth of ocean life.

Call Forecasting For Inbound Call Center, Peter Vinje

Undergraduate Journal of Mathematical Modeling: One + Two

In a scenario of inbound call center customer service, the ability to forecast calls is a key element and advantage. By forecasting the correct number of calls a company can predict staffing needs, meet service level requirements, improve customer satisfaction, and benefit from many other optimizations. This project will show how elementary statistics can be used to predict calls for a specific company, forecast the rate at which calls are increasing/decreasing, and determine if the calls may stop at some point.

Transportation Of Machinery Through A Confined Space, Diana Atwood

Undergraduate Journal of Mathematical Modeling: One + Two

Our goal in this paper is to determine whether a packaging machine of negligible width will fit through a hallway and into a certain room (see page 4 for comments about negligible width). Given the width of the hallway and the room, we apply calculus to find the minimum length available between the two. We determine that the machine will successfully fit into the room.

Buoy Dynamics In Subsurface Zones, Randy Guillen

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this paper is to find the tension acting on a line that anchors a buoy submerged just beneath the surface of the ocean. Since the problem statement only gives the geometric shapes and dimensions of the buoy, we must use calculus to find its volume and surface area through integration of the volumes and surfaces of revolution formed by the specific parts of the buoy along an axis. The volume and surface area determine the buoyancy force and force of gravity, the two forces acting on the buoy that affect the tension in the line. After calculating …

Reconstruction Of Brooksville Ridge Cave Temperatures From Speleothem Samples, Amor Elder

Undergraduate Journal of Mathematical Modeling: One + Two

A problem was proposed to use an adjusted version of Dorale's speleothem delta function to model the temperature fluctuations in the Brooksville Ridge Cave from the Medieval Warm Period to the present. The temperature values reconstructed by the model can be compared to the known temperature trend during the same selected time period. If the results matched the trend, it indicates that the cave's temperature was the dominant influence. If not, a different variable was the main influence of the cave.

Using δ¹⁸O values gathered from a speleothem, past temperatures of the cave were modeled. Results show that …

Calculating Power Of A Co2 Compressor, Jennifer Wedebrock

Undergraduate Journal of Mathematical Modeling: One + Two

In this project the goal is to find the power of a CO₂ compressor used in a process of storing CO₂ underground. Although the compressor is not 100% efficient and does not exist under ideal conditions, the power can first be calculated as if it were under ideal conditions by calculating its enthalpy and entropy. Residual terms are then added to both the enthalpy and the entropy to account for the behavior of CO₂ under non-ideal conditions. Since the sum of the change in entropy under ideal conditions and the residual terms for entropy is zero, a …

Collection Of Nitrate In A Denuder, Hannah Feig

Undergraduate Journal of Mathematical Modeling: One + Two

Data are given for aerosol nitrate (NO_3-) size distributions in the atmosphere as recorded by a cascade impactor and by an annular denuder. Using this data, our goal is to find the percent of nitrate in the atmosphere that the denuder is able to detect. This requires that we find the size distribution of nitrate that enters the denuder. From these data and calculations, we find that 32.8% of nitrate in the atmosphere can be detected by the denuder. Nitrate was measured to study its affects on seagrass in the Tampa Bay and to compare nitrate levels with …

Critical Axial Load, Walt Wells

Undergraduate Journal of Mathematical Modeling: One + Two

Our objective in this paper is to solve a second order differential equation for a long, simply supported column member subjected to a lateral axial load using Heun's numerical method. We will use the solution to find the critical load at which the column member will fail due to buckling. We will calculate this load using Euler's derived analytical approach for an exact solution, as well as Euler's Numerical Method. We will then compare the three calculated values to see how much they deviate from one another. During the critical load calculation, it will be necessary to calculate the moment …