Digital Commons Network^™

Calculus Application To Topographic Mapping, Veronica Zapata

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of the paper is to find the volume of water in a ditch. An example image of ditch is given in Appendix C. The first act that before any calculation can be performed is to record the field work. Once at the property the ditch must be identified. Three points of elevations per section should be measured by the surveyor; one point is at the center of the ditch (the lowest point) and the two ones are at the ends (the highest points). The sections are detailed in Appendix A. Using the elevation points from the property, we …

Using The Sir Epidemiology Model With Vector Transmission To Predict The Effectiveness Of A Viral Marketing Campaign And The Spread Of Product Adoption, Michael Freed

Undergraduate Journal of Mathematical Modeling: One + Two

Stevelab, LLC is working on an app that will be released within the year. For planning purposes, the company needs to be able to predict how well the app will spread in its initial phase. Because the pilot launch will be limited to Hillsborough County, FL, there is a limited population. The marketing strategy is to sell the application to places where people gather to mingle and socialize, with a particular focus to the bar scene. Customers of the bar can use the app for free. In addition to our direct sales efforts, we can expect the bar owners to …

Equilibrium Ratio Of Polymers To Monomers In Cooperative Polymerization Of Amyloid-Β Protein, Tina Gagliardo

Undergraduate Journal of Mathematical Modeling: One + Two

Amyloid-β42 is a protein polymer that catalyzes the formation of pathogenic amyloid plaques that are a prominent feature in the brain tissue of patients who suffer from Alzheimer’s disease. Aβ42 polymerizes via a nucleation-elongation mechanism; several monomers must first congregate into a nucleus before it can elongate into a polymer. The nucleation step is energetically unfavorable since a nucleus smaller than 7 to 8 monomeric units is unstable, therefore the pieces tend to dissociate faster than they can bond together. A solution of Aβ42 will consist of 100% monomers and oligomers smaller than the nucleus when the total concentration is …

Calculating Water Wavelength Using Dispersion Relation And Approximation, Chantelle Lee

Undergraduate Journal of Mathematical Modeling: One + Two

The dispersion relation equation is used to directly compute wave number and wave length to compliment water wave pressure sensor readings. Waves are measured to help coastal engineering to better mitigate coastal infrastructures. Various given wave periods and water depths are used to show how the dispersion relation equation could compute wave length. Also, shallow and deep-water approximations are formulated from the dispersion relation equation and the results are compared.

Effects Of Change In Tire Pressure Upon Efficiency Of A Vehicle, Haider Ali Khan

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this paper is to compare the difference in the efficiency of acceleration, of a 2018 Audi A8, in two distinct scenarios where the tire pressure is kept at a maximum and partial level. The approach towards solving the issue is multi-faceted, the efficiency is dependent on the difference in the time it takes for the car to accelerate, thus to obtain the elapsed time, the foundational basis is set by the relations between Torque/Force, and RPM/Speed of the vehicle. All the calculations are completed by using the data extracted from the car’s specifications set (Automobile Catalog). Newton’s …

Population And Mortality Predictions Of The Florida Manatee – Ten Year Watercraft Mortality, Dylan Lehigh

Undergraduate Journal of Mathematical Modeling: One + Two

The West Indian Manatee is currently listed as a threatened species by the U.S Fish and Wildlife service. A threatened designation means population levels still are at risk of becoming endangered again in the foreseeable future. This project seeks to forecast how many manatees would perish from watercraft strikes (the greatest threat to their survival) based upon the most current method utilized for projecting manatee population growth.

The latest version, known as the Core Biological Model (version 6) or CBMv6, was employed along with the most current manatee population data, which was provided by Dr. Jeffrey A. Hostetler. Dr. Hostetler …

A Mathematical Model For The Upper Limits Of Thyroid Volume In Adolescents, Jacob Treanor

Undergraduate Journal of Mathematical Modeling: One + Two

This paper describes a mathematical model that relates age to the volume of the thyroid gland, given in milliliters, of adolescents based on data from a 1997 study by the World Health Organization (W.H.O.) (World Health Organization, 1997). Using the upper limit per age group provided by the data, a model was constructed through integration of the second derivative of the data for males and females, ages 6-15. It was concluded that the upper limit for the thyroid volume could be expressed by one of two second order polynomial equations, depending on gender, with any values significantly larger than those …

Locating Centers Of Mass With Image Processing, Amina Gahramanova

Undergraduate Journal of Mathematical Modeling: One + Two

The center of mass of a rigid body is a unique point that represents the mean position of all matter that composes it. Allowing representing complex bodies as a single point, this concept is underlying the basis of all essential mechanical calculations, and is therefore a crucial consideration in engineering. The paper shows how to devise a fast and convenient way of locating the centroid of planar objects of different shapes. For several shapes that can be represented as regions bounded by graphs of functions, this point can be found by using integral calculus. However, solving for the center of …

Using Moment Of Inertia And Observable Planetary Features To Approximate The Two-Layer Structure Of Earth, Jupiter, And Neptune, Selena Kimball

Undergraduate Journal of Mathematical Modeling: One + Two

This paper examines the interior structure and composition of Earth, Jupiter, and Neptune by using moment of inertia (MoI) and observable planetary features to create approximate two-layer interior structure models. The moment inertia of a uniform sphere, hollow sphere, and a sphere with a shell are derived to calculate the radius and density variables that identify the relationship between the different radii and densities of the two layers. A two-layer model of the planet’s interior can then be formulated based on the radius, density, known MoI factor and the surface density or the assumed composition density of the planet. The …

Using Matrices To Balance Chemical Reactions And Modeling The Implications Of A Balanced Reaction, Emilee Barrett

Undergraduate Journal of Mathematical Modeling: One + Two

This paper explores an alternative way to balancing equations of chemical reactions and understanding why it is necessary to use balanced equations in science. To balance a chemical equation chemists often guess the coefficients that would balance the equation and check if it works. An alternative method is to use matrices to determine the coefficients of a balanced chemical reaction through solving a system of linear Diophantine equations. After determining the coefficients, a balanced chemical reaction can be formed and used to model how the different coefficients impact the overall reaction. Then it can lead to larger applications within the …

Bicycle Speed Through Different Gears With Drag, Ian Larson

Undergraduate Journal of Mathematical Modeling: One + Two

When riding a bicycle, the rider experiences two forces: the force of the road that acts upon the rear wheel while pedaling, and an opposing force that exerts on the bicycle/cyclist, called aerodynamic drag force (drag). When adjusting Newton’s equation in the second law of motion, the instantaneous change in velocity is equal to the object’s net force divided by its mass. The corresponding differential equation has not been solved analytically. With the bicycle starting at rest at t=0, we solved the equation numerically for any time t by using what is known as Euler’s Method to plot the …

Integrating The Equation Of Hydrostatics For Groundwater Under Non-Isothermal Conditions, Megan A. Levine

Undergraduate Journal of Mathematical Modeling: One + Two

Groundwater is an important area of study for several scientific fields and is relevant to many problems in our everyday life. One way the study of groundwater has become different in this age of technology is through modeling. Modeling is used in numerous fields to visualize complex problems and view inaccessible areas, such as under the Earth. An essential part of groundwater modeling is to know water pressure at any depth underground. The difficulty in calculating this is that there are several variables that affect water pressure, all of which are affected by one another and all are calculated by …

Calculating The Electromotive Force Through A Loop, Esteban Leal

Undergraduate Journal of Mathematical Modeling: One + Two

This is a short article which utilizes the equations of Faraday’s law, Ampere’s law, and Ohm’s law. We manipulate the formulas to solve a practical application in which the electromotive force must be calculated. With the successful calculation of the electromotive force, we can use this technique in larger applications.

Acid-Base Titration, David Pierre

Undergraduate Journal of Mathematical Modeling: One + Two

Titration is an analytical method used in biomedical sciences and analytical chemistry laboratories to determine the quantity or the concentration of a known or unknown substance. There are many kinds of titrations, but this investigation is fundamentally based on acid-base titration, in which the development of a mathematical titration model is explained and determined. In a titration experiment, the concentration and volume of the base added is proportionally equal to those of the acid. The concentration of the substance is determined by following this principle. Moreover, these calculations are usually approximate. Thus, the construction of a titration model is done …