Physical Sciences and Mathematics Commons^™

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.

Brazilian Pepper's Impact On Barrier Island Biodiversity, Grayson Mccormick

Undergraduate Journal of Mathematical Modeling: One + Two

The Brazilian pepper is an invasive plant responsible for destruction of habitats of species native to Florida. We attempted to measure the impact of the Brazilian pepper on native plants by studying how it affects the biodiversity of Honeymoon Island, one of Florida's barrier islands. For this purpose we determined the population sizes of the Brazilian pepper along with five other species of plants on two quadrats of land laid out in Honeymoon Island State Park. Both Simpson's Index of Diversity and Shannon-Wiener Index were used to estimate the biodiversity and assess the impact of the Brazilian pepper on the …

Light Attenuation At Molasses Reef, Ashley Earls

Undergraduate Journal of Mathematical Modeling: One + Two

Estimating the amount of light available at different depths of the ocean is important for gaining a better understanding of coral reefs. It is especially useful to be able to get such estimates without having to perform direct measurements. Although accurate, the direct measurements are costly, time consuming, and usually limited to relatively small areas of interest.

One statistic that could be useful for estimating the amount of available light is the rate at which it declines with depth (the rate of light attenuation). In this project, this rate is calculated for four different wavelengths using data for 30m water …

Motion Of A Pendulum, Jared Wynn

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project is to derive and solve the equation of motion for a pendulum swinging at small angles in one dimension. The pendulum may be either a simple pendulum like a ball hanging from a string or a physical pendulum like a pendulum on a clock. For simplicity, we only considered small rotational angles so that the equation of motion becomes a harmonic oscillator.

Optimal Location Of An Oil Storage Facility, Giovanni Quiel

Undergraduate Journal of Mathematical Modeling: One + Two

Given three oil drilling sites, we devise a method to determine the optimal location for a storage facility such that the total length of pipeline required to connect each site to the facility is minimized. First we represent the total distance of piping as the sum of the individual distances between the storage facility and each oil well. From this, both the optimal overall pipeline length and the location of the storage facility which realizes the minimal length can be determined through the first and second partial derivative tests.

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 …

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 …

2010 File Geodatabase Containing Aerial Photos, Pete Reehling, Richard Mckenzie, City Of Tampa Department Of Sanitary Sewers Bay Study Group

Images

The Bay Study Group was created by the City of Tampa in 1976 to monitor the effects of pollution abatement that occurred in Hillsborough Bay when the city’s wastewater treatment plant was upgraded from primary to advanced treatment in 1979. The Bay Study Group documented a remarkable restoration of water quality parameters and biological indicators in Hillsborough Bay from the mid 1980s until 2009, when it was disbanded. This zip Geodatabase file contains the aerial photos for the year 2010.

Pasteurization Of Milk, Alejandro Barbosa Alzate

Undergraduate Journal of Mathematical Modeling: One + Two

We determined the time it takes milk, which is heated from 60°F to 150°F, to achieve pasteurization and compared this result with the standard pasteurization process of heating milk at a constant temperature of 150°F for 30 minutes. Instead of directly quantifying the bacterium population, we considered the bacteria to milk concentration ratio. To solve for the unknown time, we equated the final bacterium concentration ratio achieved through both varied temperature and constant temperature. After equating the final pasteurization concentrations we were unable to find an analytical solution, so we used numerical techniques to find the unknown heating time.

Optimization Of A Chemical Reaction Train, Bahar Sansar

Undergraduate Journal of Mathematical Modeling: One + Two

This project consists of the optimization of a chemical reactor train. The reactor considered here is the continuous stirred tank reactor (CSTR), one of the reactor models used in engineering. Given the design equation for the CSTR and the cost function for a reactor, the following values are determined; the optimum number of reactors in the reaction train, the volume of each reactor and the total cost.

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 …

Finding The Area Of An Irregularly Shaped Room, Justin Walls

Undergraduate Journal of Mathematical Modeling: One + Two

This experiment utilized integration in a practical sense by determining the floor area of an irregularly shaped room. By taking the integral summation of three sections formed from semi-circles, the desired areas as well as positive results were found. The final data determined that the floor area of the irregularly shaped room was around 580 square feet.

Canal Lock Displacement, Rick Blanton

Undergraduate Journal of Mathematical Modeling: One + Two

In this project we determine the time needed for a pump to raise the water level in a canal lock in order for a boat to continue upstream. Using calculus methods and elementary physics, it was determined that it would take roughly 5 minutes for a single 60 horsepower pump to raise the water level the required 10 feet. We conclude that the lock is fairly efficient but offer some suggestions to increase the time efficiency of the lock system.

Automated Determination Of A Package's Center Of Mass, Ayaz Hemani

Undergraduate Journal of Mathematical Modeling: One + Two

In order to address the issue of increased efficiency and better planning for parcel shipments, an automated computer program was developed in Microsoft Excel that calculates center of mass and moments of mass with greater speed and reliability than currently implemented systems. This simple program requires only a variable density function and limits of integration for a given object as input within the spreadsheet system. Once the required input has been provided, a series of chain calculations, with the help of a Visual Basic for Applications (VBA) script, is able to process the input, which is done through integration and …

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.

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, …

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.

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.

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.

Total Number Of Synapses In The Adult Human Neocortex, Thai Nguyen

Undergraduate Journal of Mathematical Modeling: One + Two

The brain is composed of glial cells and neurons where synapses form connections between neurons and other cells. Since synapses are very small, so either a light or electron microscope is required to see them. Unlike other mammals, synapses in the human brain deteriorate rapidly upon death making them difficult to study. This project constructs a simple model for the number of synapses in the human neocortex by age and sex based on the amount of neurons. This hypothetical model can also be used to study the impact of Alzheimer's disease and other forms of dementia that are marked by …

Spatial Distribution Of Soda Straws Growth Rates Of The Coufin Cave (Vercors, France), Yves Perrette, Stéphane Jaillet

International Journal of Speleology

The Choranche Cave system (Vercors, France) is an excellent locality for measuring the growth rates of large numbers soda straws. This is especially the case for the Coufin Cave, as enlargement of the cave entrance in 1875 led to a change in stalactite color from brown to white, thus providing a reliable chronomarker. The date of this brown-to-white calcite transition has been confirmed by lamina counting. We measured and georeferenced the growth-lengths of 306 soda straws in a 1m² area of the roof of the Coufin Cave entrance chamber. Because of the very slow and sometimes inexistent water feeding …

Revelations Of Adaptive Technology Hiding In Your Operating System, Kathleen P. King

Leadership, Counseling, Adult, Career and Higher Education Faculty Publications

Pre-publication version of a chapter about the assistive technology tools and resources available for free in Windows OS and Mac OS. Introducing higher education faculty to free resources, features and programs which they can recommend to their students or perhaps use for themselves (for instance for fading eyesight or hearing). In addition, the chapter briefly shares strategies and examples of how they might be used.

The book will have an entire chapter dedicated to assistive technology as well. This is a popularized assistive technology chapter for generalist, NON special education, faculty to become acquainted with readily available and free resources. …

Glacier (?) National Park, Judy Mcilrath

School of Geosciences Faculty and Staff Publications

In this Spreadsheets Across the Curriculum activity, students examine data pertaining to the disappearing glaciers in Glacier National Park. After calculating percentage change of the number of glaciers from 1850 (150) to 1968 (50) and 2009 (26), they move on to the main glacier-monitoring content of the module--area vs. time data for the Grinnell Glacier, one of 26 glaciers that remain in the park. Using a second-order polynomial (quadratic function) fitted to the data, they extrapolate to estimate when there will be no Grinnell Glacier remaining (illustrating the relevance of the question mark in the title of the module). Introductory …

Yellowstone! A National Park On A Hot Spot, Judy Mcilrath

School of Geosciences Faculty and Staff Publications

This Spreadsheets Across the Curriculum activity introduces Geology of National Parks students to Yellowstone National Park. The module takes a broad overview of volcanic features of the park, including the line of calderas along the up-drift hot spot trace, the mapped area of tuffs produced by their cataclysmic eruptions, and the hydrothermal features for which the park is so well known. Students calculate the rate that the North American Plate has been moving over the hot spot, the relative volume of the materials produced in the cataclysmic eruptions, their recurrence interval, and probability of eruption in any given year. The …

Green Local Governments In Florida: Assessment Of Sustainability Performance, Naimish Upadhyay, Robert Brinkmann

School of Geosciences Faculty and Staff Publications

The sustainability performance of local governments that adopted the Florida Green Building Coalition’s Green Local Government standard was evaluated using a web-based review and survey of 26 local governments within the context of the Three Es of environment, equity, and economic development. The results indicate that while many local governments exhibit a broad commitment to sustainability as evidenced by the inclusion of sustainability in formal documents, such efforts are not present across all government functions or departments. In addition, while local issues are often addressed, interrelated sustainability goals of equity and economic development are not clearly articulated. Most local governments …

Karst Geology And Cave Fauna Of Austria: A Concise Review, Erhard Christian, Christoph Spötl

International Journal of Speleology

The state of cave research in Austria is outlined from the geological and zoological perspective. Geologic sections include the setting of karst regions, tectonic and palaeoclimatic control on karst, modern cave environments, and karst hydrology. A chapter on the development of Austrian biospeleology in the 20th century is followed by a survey of terrestrial underground habitats, biogeographic remarks, and an annotated selection of subterranean invertebrates.

Teaching Resources In Speleology And Karst: A Valuable Educational Tool, Jo De Waele

International Journal of Speleology

There is a growing need in the speleological community of tools that make teaching of speleology and karst much easier. Despite the existence of a wide range of major academic textbooks, often the caver community has a difficult access to such material. Therefore, to fill this gap, the Italian Speleological Society, under the umbrella of the Union International de Spéléologie, has prepared a set of lectures, in a presentation format, on several topics including geology, physics, chemistry, hydrogeology, mineralogy, palaeontology, biology, microbiology, history, archaeology, artificial caves, documentation, etc. These lectures constitute the “Teaching Resources in Speleology and Karst”, available online. …

Do Karst Rivers “Deserve” Their Own Biotic Index? A Ten Years Study On Macrozoobenthos In Croatia, Biljana Rađa, Sanja Puljas

International Journal of Speleology

In this study we present the results of a ten year survey of the aquatic macroinvertebrate fauna along four karst rivers: Jadro, Žrnovnica, Grab and Ruda, all of them situated in the Middle Dalmatia region of Croatia, in an attempt to construct the Iliric Biotic Index, which will be more applicable for the water quality analysis than the most frequently applied biotic index in Croatia, the Italian Modification of Extended Biotic Index. The rivers geologically belong to the Dinaric karst, unique geological phenomena in Europe. Benthic macroinvertebrates were collected along each river at 15 sites by standard methods of sampling …

Candoluminescence Of Cave Gypsum, John R. Sweet, John W. Hess, William B. White

International Journal of Speleology

A selection of gypsum specimens from a variety of caves as well as CaSO₄ synthesized in the laboratory emit both a green and yellow candoluminescence when excited by a hydrogen diffusion flame. The green emission is attributed to dehydration of gypsum to bassanite and the yellow emission appears upon further dehydration to anhydrite. The source of the luminescence is ascribed to minor concentrations of Mn²⁺ in the gypsum.