Digital Commons Network^™

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 …

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.

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 …

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.

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 …

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 …

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 …

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 …

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 …

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 …

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.

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.

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.

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.

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.