Mathematics Commons^™

Design Of Nozzle For High-Powered Solid Rocket Propellant, Jackson Stephenson

Undergraduate Journal of Mathematical Modeling: One + Two

This paper presents a preliminary nozzle design for a high-altitude rocket to be built by SOAR, the Society of Aeronautics and Rocketry. The equations and methods used for analysis came from professional sources via text or informational videos. The equations in focus will look at the temperature/pressure/area-Mach relationships for isentropic flow, pressure expansions in selected materials, and finding other characteristic properties using safe chemical property assumptions using CEARUN. The equations were used under the assumption of an isentropic flow under sea level conditions. If the design and the projected results look promising, they will be implemented soon for machining and …

Organic Agricultural Analysis: Efficiency Of Common Practices, Bradley Biega

Undergraduate Journal of Mathematical Modeling: One + Two

To analyze the efficiency of common watering practices in an organic agriculture setting we use Sweetwater Organic Farm’s conventional methods for irrigation and land allotment as well as some algebra and calculus technique. Sweetwater’s operation is limited to their largest growing field. A mathematical model is built to determine the current efficiency of the rotary head sprinkler system. Then the efficiency of this system is compared to a new drip line system. Several variables like soil porosity, absorption rates, and areas where no plants are located, are taken into consideration. Our results show that the current irrigation in place wastes …

Using The Entropy Rate Balance To Determine The Heat Transfer And Work In An Internally Reversible, Polytropic, Steady State Flow Process, Savannah Griffin

Undergraduate Journal of Mathematical Modeling: One + Two

The entropy rate equation for internally reversible steady state flow process has been used to calculate the heat transfer and work in an internally reversible, polytropic, steady state flow process.

Geochemical Modeling Of Fractional Magma Crystallization, Luke Varner

Undergraduate Journal of Mathematical Modeling: One + Two

Modern day geologists use many different modeling programs such as Geospatial Information Systems in addition to R (programming language) for a wide array of applications such as: projecting collected data for mapping, visualization, and trend prediction. Computational power for these modeling programs is derived from Calculus, Probability, and Statistics. The purpose of this paper is to provide a site-specific geochemical analysis of an igneous rock formation composed of two specific compositions allowing for the predictions of rock formation derived from the resultant geochemical model.

Comparing Two Flywheel-Piston Linkages, Anthony Sanchez

Undergraduate Journal of Mathematical Modeling: One + Two

The main idea of this paper is to compare two different ways of linking a flywheel to a piston: the Scotch Yoke linkage and the Eccentric linkage. The Scotch Yoke linkage is a way to convert the linear motion of a piston into rotational motion by using a flywheel, or vice versa. The Eccentric mechanism, on the other hand, consists of a circular wheel that is fixed to a rotating axle that makes it rotate. We compare two methods by expressing both motions as functions of three variables (R, L and θ) and use these functions to …

Efficacy Of Acute Normovolemic Hemodilution In The Setting Of Chronic Anemia, Andrew Vieira

Undergraduate Journal of Mathematical Modeling: One + Two

A theoretical model for calculating hematocrit as it relates to blood volume loss was used to test the theoretical impact of acute normovolemic hemodilution prior to surgery in a chronically anemic patient. The technique of hemodilution is intended to decrease red blood cell loss that occurs as the result of surgical intervention, however its impact may be decreased in an anemic patient. An equation to find change in hematocrit resulting from blood volume loss was elucidated via integration. This equation was then applied to a theoretical patient with 5 L of blood and a hematocrit of 32 percent which revealed …

Diagnosing Breast Cancer With A Neural Network, John Cullen

Undergraduate Journal of Mathematical Modeling: One + Two

Fine needle aspiration (FNA) is a minimally invasive biopsy technique that can be used to successfully diagnose types of cancer, including breast cancer. Immediately, it is difficult for a human to spot any trends in the cell level data gathered during a fine needle aspiration procedure. One way to predict the type of tumor a patient has, is to use a computer to develop a mathematical model based on known data. This project utilizes the Diagnostic Wisconsin Breast Cancer Database (DWBCDB) to create an accurate mathematical model that predicts the type of a patient’s tumor (Malignant or Benign). A neural …

Alternative Typing Learning Curves, Marcel Kreuzer

Undergraduate Journal of Mathematical Modeling: One + Two

Typing is a part of everyday life for many people. However some people have difficulty in doing it. For example, for people who are blind and those who have carpal tunnel or cerebral palsy, a standard keyboard would not be effective to type. Alternative options include voice recognition and keyless keyboards. We focus on orbiTouch keyboard which has no keys, only two knobs which allow a person to type. Which alternative way of typing would be most effective given a person’s condition is discussed.

Danger Of Snow In The Sunshine State, Dmitrii Karpenko

Undergraduate Journal of Mathematical Modeling: One + Two

The main purpose of the project is to investigate the maximum deflection of a rectangular 16 x 8 inches beam, supported on both ends under uniform loading stress under snow pressure in the event that Tampa experiences snowfall. The required information for the project is the material of the beam and its dimensions, measurement of the area of the roof that would accumulate snow, and calculations of the Moment of Inertia and Uniform Distributed Load for the beam. The maximum deflection of the beam can be calculated using the information above.

The outcome of the research shows that the roof …

Application Of Simple Harmonics Modeling A Shock, Kai Raymond

Undergraduate Journal of Mathematical Modeling: One + Two

This project entails modeling a spring-shock absorber system in order to evaluate the position of a mass when this system is acted upon by outside forces. We will restrict our attention to the linear case where it is assumed that Hooke’s law gives the force exerted by the spring, and the resistance of the system will be proportional to the velocity of the mass. We analyze the time and frequency domain of the absorber system and compute its impulse response.

Approximating Surface Area Of Fluctuating Lipid Leaflets Using Weighted Grid Tessellation, Ahnaf Siddiqui

Undergraduate Journal of Mathematical Modeling: One + Two

The surface area per lipid is an important quantity useful in characterizing lipid bilayer structure and dynamics. However, simply dividing the flat surface area covered by the number of lipids does not give a sufficient characterization of surface dynamics in cases where parts of the lipid leaflets have curvaceous trajectories in three dimensions. An algorithm is proposed for modeling surface area per lipid using a three-dimensional tessellated grid. In this way both the vertical, as well as the more commonly considered the horizontal, fluctuations of lipids are used to accurately determine the area covered. This algorithm can reveal differences in …

Rudimentary Model Of Glucose Response To Stress, Nasha Rios-Guzman

Undergraduate Journal of Mathematical Modeling: One + Two

A simplistic multifactorial model was crafted to represent change in plasma glucose concentrations after increases in stress hormones above baseline. A sample application of the predictive use of this model was demonstrated, and a reflection on possible models in diabetic populations was described. The potential for use of this model in conjunction with current models is discussed, as well as the issues pertinent to such a basic model.

Analysis Of Rainfall In Tampa, Amy Polen

Undergraduate Journal of Mathematical Modeling: One + Two

Rainfall for a region is very important to define, because it affects an ecosystem health, wildlife, and even human behavior. Using data obtained from National Oceanographic and Atmospheric Administration (NOAA) at the Tampa Bay International Airport and graphing it, the total rainfall for a year was estimated by both a rough trapezoidal Riemann’s sum approximation and a definite integral generated by polynomial regression. It was determined that both approximations gave an underestimate of the total rainfall that was measured, but the polynomial integral gave a reasonable estimate with a small percent error. It was seen through the graphical representation of …

Analyzation Of The Resistor-Inductor-Capacitor Circuit, Martin D. Elton

Undergraduate Journal of Mathematical Modeling: One + Two

Starting with the basics of what a Resistor-Inductor-Capacitor circuit (RLC) is, i.e. its fundamental components, and ending with practical applications using advanced calculus to aid in predetermining the results and circuit design, this paper analyzes the RLC circuit via an advanced calculus based approach.

The Solow Model And Standard Of Living, Eric Frey

Undergraduate Journal of Mathematical Modeling: One + Two

All across the world, living standards vary significantly. The Solow growth model, developed by Nobel Prize winning economist Robert Solow in 1956, is still one of the most commonly used models in economics to explain economic growth. This paper will outline the Solow growth model, and its assertion that increases in total factor productivity (TFP) can lead to limitless increases in the standard of living in a country. Much of the mathematical notation and explanation has been derived from Stephen Williamson of Washington University. Additionally, it will provide empirical examples illustrating the model’s ability to match real-world data.

The Forces Affecting A Sailboat, Kelly Stukbauer

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project is to determine the specific effects of the various forces acting on a sailboat. Through this project, a greater understanding of both the physics behind sailing, and the calculus behind that physics, shall be gained.

Optimization Of A Fuel Cell, Eduardo Gines

Undergraduate Journal of Mathematical Modeling: One + Two

Fuel cells are devices that generate energy from a chemical reaction that takes place inside the cell. The main parts of these devices are two electrodes and an electrolyte solution. The project consists of determining the area of the electrodes for the fuel cell at which the cell produces its maximum amount of power. This was done with the performance curve of the fuel cell which was in terms of voltage vs current density. The performance curve was turned into terms of power density vs current density, and through this curve the maximum power was determined by identifying the maximum …

Electrical Efficiency Of A Solar Cell, Johnnie Cairns

Undergraduate Journal of Mathematical Modeling: One + Two

Our goal was to determine the electrical efficiency of a solar cell, specifically a CuInGaSe2 solar cell. Solar cells work by converting energy from the sun in the form of photons to electrical energy in the form of electrons. However, the solar energy converted into electrical energy is limited by a property of solar cells called the quantum efficiency. The quantum efficiency of a solar cell is the fraction of photons hitting the cell that are converted into electrons; quantum efficiency varies as a function of wavelength. Another key component which also varies as a function of wavelength is spectral …

Analysis Of Adiabatic Batch Reactor, Erald Gjonaj

Undergraduate Journal of Mathematical Modeling: One + Two

A mixture of acetic anhydride is reacted with excess water in an adiabatic batch reactor to form an exothermic reaction. The concentration of acetic anhydride and the temperature inside the adiabatic batch reactor are calculated with an initial temperature of 20°C, an initial temperature of 30°C, and with a cooling jacket maintaining the temperature at a constant of 20°C. The graphs of the three different scenarios show that the highest temperatures will cause the reaction to occur faster.

Hydrolysis Of Acetic Anhydride In A Cstr, Veronica N. Coraci

Undergraduate Journal of Mathematical Modeling: One + Two

To find the optimal reactor volume and temperature for the hydrolysis of acetic anhydride at the lowest possible cost with a 90% conversion of acetic anhydride, a formula for the total cost of the reaction was created. Then, the first derivative was taken to find a value for the temperature. This value was then inputted into the second derivative of the equation to find the sign of the value which would indicate whether that point was a minima or maxima value. The minima value would then be the lowest total cost for the optimum reaction to take place.

Optimization Of An Agitated Extractor, Evan Zapf

Undergraduate Journal of Mathematical Modeling: One + Two

In this scenario, we use calculus to determine the optimal operating specifications of a chemical extraction process. The results are achieved by first developing an expression that yields the total annual cost of the process. Factoring in electricity, vessel, agitator, and solvent costs, an annual cost expression was fabricated. AGIEX company manufactures a certain amount of a product, A, which has an impurity that it wishes be reduced. By engineering an optimally sized vessel to perform the extraction of impurity, the company will save costs by ensuring no inefficient spending on power or excess solvent occurs. A specific amount of …

Temperature Of The Central Processing Unit, Ivan Lavrov

Undergraduate Journal of Mathematical Modeling: One + Two

Heat is inevitably generated in the semiconductors during operation. Cooling in a computer, and in its main part – the Central Processing Unit (CPU), is crucial, allowing the proper functioning without overheating, malfunctioning, and damage. In order to estimate the temperature as a function of time, it is important to solve the differential equations describing the heat flow and to understand how it depends on the physical properties of the system. This project aims to answer these questions by considering a simplified model of the CPU + heat sink. A similarity with the electrical circuit and certain methods from electrical …

Size And Concentration Analysis Of Gold Nanoparticles With Ultraviolet-Visible Spectroscopy, Sanim Rahman

Undergraduate Journal of Mathematical Modeling: One + Two

Spherical gold nanoparticles (GNPs) are synthesized by Turkevich Method and PEL 35 UV-VIS spectrophotometer recorded the wavelength and absorption of the Surface Plasmon Resonance (SPR) peak. The diameter and concentration of solute GNPs are calculated. The concentration of GNPs is done with Beer’s law. The average diameter of GNPs is done via the ratio of SPR peak to the absorbance at 450 nm. The diameters are compared to SEM scan of synthesized GNPs and Sigma-Aldrich values.

Maximum Efficiency Of A Wind Turbine, Marisa Blackwood

Undergraduate Journal of Mathematical Modeling: One + Two

The concept of a wind turbine is not new technology, however, in a day and age where renewable energy is popular, the interest in wind turbines has increased dramatically. This project investigates multiple aspects of a wind turbine and will derive the maximum power efficiency of an ideal wind turbine, first introduced by Albert Betz in 1919. This project will also calculate the size of a wind turbine at maximum efficiency given certain parameters and determine the optimum outlet velocity as a function of wind speed to maximize the mechanical energy produced. These equations will be derived by using concepts …

Spintronic Circuits: The Building Blocks Of Spin-Based Computation, Roshan Warman

Undergraduate Journal of Mathematical Modeling: One + Two

In the most general situation, binary computation is implemented by means of microscopic logical gates known as transistors. According to Moore’s Law, the size of transistors will half every two years, and as these transistors reach their fundamental size limit, the quantum effects of the electrons passing through the transistors will be observed. Due to the inherent randomness of these quantum fluctuations, the basic binary logic will become uncontrollable. This project describes the basic principle governing quantum spin-based computing devices, which may provide an alternative to the conventional solid-state computing devices and circumvent the technological limitations of the current implementation …

Optimum Gear Ratios For An Electric Vehicle, Scott Parkinson

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of this project is to determine the optimal gear ratios for a vehicle containing a four-speed transmission. This vehicle is required to reach a speed of 30 m/s in the minimum time possible. Equations for the velocity at each shift point were found. An equation for the total time that the vehicle took to reach 30 m/s was then derived and equations for the times spent in each gear were found through integration of the provided formula for acceleration. The optimal gear ratios were then found by taking the partial derivatives of the total time equation with respect …

Comparative Analysis Of Gps Data, Kiel Von Lindenberg

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of this project is to calculate the distance traveled during a bike ride around the University of South Florida using information gathered by a GPS (Global Positioning System) application on a smartphone. We calculate the route distance in two ways: from latitudes and longitudes using the haversine formula and 2) from velocities and times using the trapezoidal rule. These computed distances were compared to the distance given by the smartphone application.

Voltage Smoothing With A Capacitor, Martin Copello

Undergraduate Journal of Mathematical Modeling: One + Two

A rectifier is an electrical circuit that converts alternating current to direct current, e.g., a half wave rectifier removes lower valleys of the AC voltage wave. If a capacitor is placed in parallel with a half wave rectifier, the transition from voltage peak to peak is smoothed to closer resemble constant DC voltage. The objective of this project was to model the voltage changes of a half wave rectifier with a parallel capacitor. It was found that the smoothness of the voltage waves increased as the capacitance of the capacitor increased.

Calculating The Solar Energy Of A Flat Plate Collector, Ariane Rosario

Undergraduate Journal of Mathematical Modeling: One + Two

The amount of solar energy that could be obtained by a flat plate solar collector of one square meter dimension is calculated in three different locations: Tampa FL, Fairbanks AL, and Pontianak Indonesia, considering the varying sunset time for each day of the year. The results show that if the collectors are placed near the equator, more total energy could be obtained. In fact, by placing a solar collector in Pontianak, Indonesia 12.42% more solar energy can be obtained than by placing it in Tampa and 96.9% more solar energy than Alaska.

Florida Sinkholes And Grout Injection Stabilization, Charles Hunt Griffith Ii

Undergraduate Journal of Mathematical Modeling: One + Two

Florida has a major problem when it comes to sinkholes. These sinkholes can become very hazardous to people, homes, and to the landscape as a whole. Florida sits on a carbonate platform which is highly indicative of sinkholes. There are three main types of sinkholes which occur in Florida: dissolution, cover subsidence, and cover collapse. I will compare these types of sinkholes to the underlying formation beneath Florida to see if there is a connection between the types of sinkholes that occur. I will also create a 3D model of grout injection stabilization and calculate its volume to compare to …