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Articles 91 - 120 of 182
Full-Text Articles in Mathematics
Rocket Flight Path, Jamie Waters
Rocket Flight Path, Jamie Waters
Undergraduate Journal of Mathematical Modeling: One + Two
This project uses Newton’s Second Law of Motion, Euler’s method, basic physics, and basic calculus to model the flight path of a rocket. From this, one can find the height and velocity at any point from launch to the maximum altitude, or apogee. This can then be compared to the actual values to see if the method of estimation is a plausible. The rocket used for this project is modeled after Bullistic-1 which was launched by the Society of Aeronautics and Rocketry at the University of South Florida.
Fukushima: A Model Study, Melinda Kathryn Mckell
Fukushima: A Model Study, Melinda Kathryn Mckell
Undergraduate Journal of Mathematical Modeling: One + Two
This article investigates the radiation dispersion modeling system available to Japanese authorities during the response phase of the Fukushima Dai-Ichi incident.
Modeling Rocket Flight In The Low-Friction Approximation, Logan White
Modeling Rocket Flight In The Low-Friction Approximation, Logan White
Undergraduate Journal of Mathematical Modeling: One + Two
In a realistic model for rocket dynamics, in the presence of atmospheric drag and altitude-dependent gravity, the exact kinematic equation cannot be integrated in closed form; even when neglecting friction, the exact solution is a combination of elliptic functions of Jacobi type, which are not easy to use in a computational sense. This project provides a precise analysis of the various terms in the full equation (such as gravity, drag, and exhaust momentum), and the numerical ranges for which various approximations are accurate to within 1%. The analysis leads to optimal approximations expressed through elementary functions, which can be implemented …
Survival Analysis - Breast Cancer, Minh Hoang Pham
Survival Analysis - Breast Cancer, Minh Hoang Pham
Undergraduate Journal of Mathematical Modeling: One + Two
In this study we used the parametric survival approach to analyze the survival time of African American breast cancer patients. In research about the survival time of patients, the Cox Proportional Hazard model, a semi-parametric method, is primarily used, but this approach does not rely on the distributional assumptions. The parametric method is more consistent with a theoretical approach compared to a semi-parametric approach. We observe that the survival time of African American breast cancer patients follows the Weibull Probability Distribution. First, we fitted the model to represent the survival ability of the general population (African American women diagnosed with …
High Jump Analysis, Paige Cooke
High Jump Analysis, Paige Cooke
Undergraduate Journal of Mathematical Modeling: One + Two
This project presents a mathematical analysis of the high jump, a popular track and field event. The first and second stages of the high jump correspond to the athlete’s run along two distinct trajectories. The third stage is the actual jump. We propose an individual model for each of these stages and show how to combine these models to study the dynamics of the entire high jump.
A Simplified Model Of The Internal Combustion Engine, Christofer Neff
A Simplified Model Of The Internal Combustion Engine, Christofer Neff
Undergraduate Journal of Mathematical Modeling: One + Two
This project further investigates a model of a simplified internal combustion engine considered by Kranc in 1977. Using Euler’s method for ordinary differential equations, we modeled the interaction between the engine’s flywheel and thermodynamic power cycle. Approximating with sufficiently small time intervals (0.001 seconds over a period of 12 seconds) reproduced Kranc’s results with the engine having an average angular velocity of 72/sec.
Volatilization Of Benzene In A River, Eric Dunlop
Volatilization Of Benzene In A River, Eric Dunlop
Undergraduate Journal of Mathematical Modeling: One + Two
Benzene is a volatile organic compound: when it contaminates a river, some of the substance will evaporate as it flows through. We examine the volumetric flow rate to find how volatilization affects the concentration levels of benzene as the substance flows through several consecutive sections of a river, using a specific example to illustrate the general method.
Adiabatic Flame Temperature For Combustion Of Methane Ii, Rebeca Pupo
Adiabatic Flame Temperature For Combustion Of Methane Ii, Rebeca Pupo
Undergraduate Journal of Mathematical Modeling: One + Two
We calculate the adiabatic flame temperature of a mixture of methane and oxygen in the presence of a diluent gas then determine the mole fractions of methane without respect to nitrogen and solve for the moles of oxygen present. Knowing the moles of methane and oxygen, allows us to calculate the moles of nitrogen present at four constant mole fractions of nitrogen, and the adiabatic flame temperature is determined from the energy released by the reaction. Lastly, we produce several graphs to compare the adiabatic flame temperatures at different mole fractions of nitrogen.
Diffusion Of Vitamin B12 Across A Mesoporous Metal Organic Framework, Veronica Valencia
Diffusion Of Vitamin B12 Across A Mesoporous Metal Organic Framework, Veronica Valencia
Undergraduate Journal of Mathematical Modeling: One + Two
We measure the rate of uptake and the rate of release of a Vitamin B12 solution (dissolved in water) at 2 different temperatures (room temperature and 37°C) by the mesoporous metal organic framework TbMOF-100 at 1-hour intervals using a spectrophotometer. Using the Beer-Lambert law, we calculate the concentration of the stock solution based on the absorbance values obtained with the spectrophotometer. These values allow for the quantification of the initial rate of uptake and the rate of uptake at a random incubation time of the Vitamin B12 by the TbMOF-100. We also calculate the value of the coefficient of diffusion …
Study Of Dieldrin In Coralville Reservoir, Jeremy Smith
Study Of Dieldrin In Coralville Reservoir, Jeremy Smith
Undergraduate Journal of Mathematical Modeling: One + Two
Using existing experimental data taken over a period of roughly 12 years that documents the concentrations of dieldrin levels in the environment and fatty tissue of the fish, we construct a model of the total dieldrin concentration decline. Comparisons between the experimental data and speculative data can be made using calculus and elements of statistics in order to better understand the movement of dieldrin in the reservoir. Because of the potentially harmful exposure effects of dieldrin to humans as well as the environment, it is important to be able to predict when stability has been restored to the ecosystem.
Finding The Area Of A Major League Baseball Field, Jacob Courchaine
Finding The Area Of A Major League Baseball Field, Jacob Courchaine
Undergraduate Journal of Mathematical Modeling: One + Two
Using a Major League Baseball (MLB) baseball field template for guidelines, we estimate the cost of building the largest possible field accepted under MLB standards. This includes finding the areas of both the clay and grassy regions and determining how many bags of clay and fertilizer are required to cover the field.
Modeling Flow Rate To Estimate Hydraulic Conductivity In A Parabolic Ceramic Water Filter, Ileana Wald
Modeling Flow Rate To Estimate Hydraulic Conductivity In A Parabolic Ceramic Water Filter, Ileana Wald
Undergraduate Journal of Mathematical Modeling: One + Two
In this project we model volumetric flow rate through a parabolic ceramic water filter (CWF) to determine how quickly it can process water while still improving its quality. The volumetric flow rate is dependent upon the pore size of the filter, the surface area, and the height of water in the filter (hydraulic head). We derive differential equations governing this flow from the conservation of mass principle and Darcy's Law and find the flow rate with respect to time. We then use methods of calculus to find optimal specifications for the filter. This work is related to the research conducted …
The Elevation To Area Relationship Of Lake Behnke, Kaitlin Deutsch
The Elevation To Area Relationship Of Lake Behnke, Kaitlin Deutsch
Undergraduate Journal of Mathematical Modeling: One + Two
The objective of this project was to determine the area-to-depth relationship in Lake Behnke, which acts as the principal stormwater drainage basin for the University of South Florida campus in Tampa, Florida. Data previously collected in a stormwater management study by Jeffery Earhart illustrated a linear correlation between the lake's area and depth; however, that study was conducted in 1998, and this present work serves to double check that correlation. We analyzed a bathymetric map of Lake Behnke that displayed several contour lines indicating depth and approximated the area inside each closed curve with a contour integral. The resulting relationship …
Overfishing Of The Common Snook, Allison Ashcroft
Overfishing Of The Common Snook, Allison Ashcroft
Undergraduate Journal of Mathematical Modeling: One + Two
The chief aim of this project is to determine if the populations of the common snook, Centropomus Undecimalis, in the Atlantic and Gulf coast are being affected by overfishing. This is established by evaluating the intrinsic rate of change for these populations and their carrying capacities. It turns out that the carrying capacity for the population of the Atlantic coast is approximately one million snook and its intrinsic rate is 0.00621, while the carrying capacity of the Gulf coast's population is 2.9 million snook and its intrinsic rate is 0.00165. The decline of both populations is most likely due …
Complexity Of Mitochondrial Genome Sequences, Brandon Toun
Complexity Of Mitochondrial Genome Sequences, Brandon Toun
Undergraduate Journal of Mathematical Modeling: One + Two
The purpose of this project is to compare the complexities of different species' mitochondrial genome sequences. Using an implementation of Deflate compression algorithm from Java standard library, we were able to compress mitochondrial genomes of nine different species. The complexity of each sequence is estimated as a ratio of the original sequence length to the length of the compressed sequence. In addition, we show how a notion of topological entropy from symbolic dynamics can be used as another complexity measure of nucleotide sequences.
U.S. Oil Reserves And Peak Oil, Trang Luong
U.S. Oil Reserves And Peak Oil, Trang Luong
Undergraduate Journal of Mathematical Modeling: One + Two
We use calculus methods to estimate the quantity of U.S. oil reserves. We consider a model that consists of an exponential function with four unknown constants. We fit real oil production data to determine the unknown constants. With the constants determined we use the function to find the year in which the U.S. oil production reached its peak. We also estimate the amount of petroleum produced until the end of 2006, and the undiscovered oil reserves to be produced in the future.
The Subset Sum Problem: Reducing Time Complexity Of Np-Completeness With Quantum Search, Bo Moon
The Subset Sum Problem: Reducing Time Complexity Of Np-Completeness With Quantum Search, Bo Moon
Undergraduate Journal of Mathematical Modeling: One + Two
The Subset Sum Problem is a member of the NP-complete class, so no known polynomial time algorithm exists for it. Although there are polynomial time approximations and heuristics, these are not always acceptable, yet exact-solution algorithms are unfeasible for large input. Quantum computation offers new insights for not only the Subset Sum Problem but also the entire NP-complete class; most notably, Grover's quantum algorithm for an unstructured database search can be tailored to identify solutions to problems within mathematics and computer science. This paper discusses the physical and conceptual feasibility of quantum computation and demonstrates the utility of quantum search …
Speleothem Laminae Counting And Growth Rate, Corey Wilson
Speleothem Laminae Counting And Growth Rate, Corey Wilson
Undergraduate Journal of Mathematical Modeling: One + Two
The goal of this project is to determine if there is a correlation between annual laminae in speleothems and Uranium dating. To do this, we counted laminae using high-resolution images and calculated a line of the best fit for the resulting data. We found that our data could supplement Uranium dating, but unless more data is obtained, laminae counting gives relatively imprecise age and growth rate estimates.
Blood Alcohol Content, Chris Ludwin
Blood Alcohol Content, Chris Ludwin
Undergraduate Journal of Mathematical Modeling: One + Two
Given a set of differential equations describing blood alcohol content as a function time, we integrated the equations to obtain a general solution. The general solution equation depends on three free parameters: the initial concentration of alcohol in the stomach after ingestion, the rate of alcohol absorption into the blood stream and the rate at which the alcohol is metabolized by the liver. We fitted our solution to experimental data to determine the unknown parameters for a particular subject.
Correlation Among Different Variables And Life Expectancy, June Liu
Correlation Among Different Variables And Life Expectancy, June Liu
Undergraduate Journal of Mathematical Modeling: One + Two
The purpose of this project is to show how heart rate, blood pressure, and weight of different species correlate with their life expectancy. We perform graphical analysis and compute Pearson's Product-Moment Correlation Coefficient to show that the heart rate has the highest degree of correlation with life expectancy.
Retroactive Interference And Forgetting, Vinishaa Ankala
Retroactive Interference And Forgetting, Vinishaa Ankala
Undergraduate Journal of Mathematical Modeling: One + Two
Retroactive interference is the amount of information that can be forgotten by a person over time due to newly learned material. In this paper we establish a relationship between the amount of information forgotten by college students while they read and watch television and the time taken to forget it. We equate these numerical equations to solve for the unknown constants. By doing so, we can find the exact equation and also the amount of forgetting information due to retroactive interference.
Mathematical Analysis Of Genomic Evolution, Cedric Green
Mathematical Analysis Of Genomic Evolution, Cedric Green
Undergraduate Journal of Mathematical Modeling: One + Two
Changes in nucleotide sequences, or mutations, accumulate from generation to generation in the genomes of all living organisms. The mutations can be advantageous, deleterious, or neutral. The goal of this project is to determine the amount of advantageous mutations it takes to get human (Homo sapiens) DNA from the DNA of genetically distinct organisms. We do this by collecting the genomic data of such organisms, and estimating the amount of mutations it takes to transform yeast (Saccharomyces cerevisiae) DNA to the DNA of a human. We calculate the typical number of mutations occurring annually through the organism's average life span …
Optimization Of A Wall Built On A Slope, John Hanna
Optimization Of A Wall Built On A Slope, John Hanna
Undergraduate Journal of Mathematical Modeling: One + Two
This project focuses on optimizing the construction of a wall with identical segments built on a slope. Faced with certain variable and fixed cost limitations, one can find the width of a segment that will minimize the total production cost. In this case, the lowest total cost comes from using 10 segments of width 3m.
Study Of Consciousness, Samuel Lee
Study Of Consciousness, Samuel Lee
Undergraduate Journal of Mathematical Modeling: One + Two
The human brain is a powerful organ that controls most of the body. Researchers around the world have long tried to uncover how the brain operates, how memories are formed and stored. Our understanding of neurological diseases such as Alzheimer's and Parkinson's disease has been rapidly improving, yet much remains to be done. In this work, we attempt to study changes in intracranial pressure (ICP) for a 12-hour period and discuss whether the resulting estimates could be used as a measure of consciousness.
Blood Glucose Levels, Carlos Estela
Blood Glucose Levels, Carlos Estela
Undergraduate Journal of Mathematical Modeling: One + Two
The purpose of this study was to establish a mathematical model which can be used to estimate glucose levels in the blood over time. The equations governing this process were manipulated with the use of techniques such as separation of variables and integration of first order differential equations, which resulted in a function that described the glucose concentration in terms of time. This function was then plotted, which allowed us to find when glucose concentration was at its highest. The model was then used to analyze two cases where the maximum glucose level could not exceed a certain level while …
Arc Length Of A Pipe Needed For A Directional Drill, Kenneth Cabana
Arc Length Of A Pipe Needed For A Directional Drill, Kenneth Cabana
Undergraduate Journal of Mathematical Modeling: One + Two
Underground contracting has come a long way in recent years. As communities and buildings are being built, services like water, sewer, and gas are needed to allow people to perform their day to day activities. This research has led to the idea and design of a way to find the arc length of the pipe put into the ground at given points. The pipe length was estimated using the formulas for distance and arc length together with two different modeling methods: Lagrange interpolation and polynomial regression. Both techniques yielded similar results; however this may be situational and in other circumstances …
Pallet Physics, Lauren Woodbridge
Pallet Physics, Lauren Woodbridge
Undergraduate Journal of Mathematical Modeling: One + Two
This project explores whether it is safe to unload a 907kg pallet from a supply truck with a bed 1.5m off the ground by sliding it down a metal ramp. First we calculated the critical angle for which the pallet would overcome the friction of the wood on the metal and begin to slide. Next we calculated velocity of the pallet as it reaches the bottom of the ramp. Finally we calculate the distance the pallet travels on the concrete after leaving the ramp. Based on these calculations of acceleration, velocity, and displacement, we conclude that it would not be …
Sizing Of An Ammonia Discharge Tank, Tuliagenda Beckfords
Sizing Of An Ammonia Discharge Tank, Tuliagenda Beckfords
Undergraduate Journal of Mathematical Modeling: One + Two
Phosphate companies use well-stirred tanks to regulate the concentration of ammonia they discharge via their wastewater, preventing ammonia spikes from exceeding the cap set by the Environmental Protection Agency. This report discusses the methods used to determine the minimum possible volume of the tank required to regulate wastewater discharge. With this information, it was determined that the use of a stirring tank is an efficient and cost effective way to regulate ammonia discharge. Based on these results many other companies may use this method to decrease the negative effects of ammonia on the environment.
Comparison Of First Gear Performance For Manual And Automatic Transmissions, Kyle Stottlemyer
Comparison Of First Gear Performance For Manual And Automatic Transmissions, Kyle Stottlemyer
Undergraduate Journal of Mathematical Modeling: One + Two
The purpose of this project is to compare the first gear performance of an automobile for both its manual and automatic transmission options. Each transmission type has a different gear ratio, which yields a different acceleration curve for each transmission throughout the torque-rpm curve of the engine. The method of integral calculus was used to find an equation which could be used to solve for time at any point in the car's acceleration. The automobile velocity versus time was then graphed to compare each transmissions acceleration trend. This process is similar to that which automotive companies may use when determining …
Optimization Of A Pressure-Treating Process, Josean Velez
Optimization Of A Pressure-Treating Process, Josean Velez
Undergraduate Journal of Mathematical Modeling: One + Two
A company that pressure-treats wood wants to minimize its annual cost without using more than 250 days of operation per year. In addition, they want to find the corresponding value of time, batches and cost for each category. We develop an expression in terms of boards per batch to model the total cost of the treatment process. We then take the derivative and use Newton's Method to find the number of boards per batch that minimizes total cost.