Mathematics and Natural Sciences

Frances Resweber, Becca Collings

Faculty Sponsor: Dr. Dave Wessner

Marshall Brady

Faculty Sponsor: Shyam Gouri Suresh

This paper draws data from all fifty states over a period of four years in an attempt to study the effect that government controlled economic variables, such as various taxes and the minimum wage, has on interstate migration rates in the United States. Several other variables that are not directly decided by state governments are included in the model to act as controls. It was predicted that those variables that increased one’s disposable income would increase migration and those that decreased one’s disposable income would decrease migration. Overall, the variables in question proved to match the theory at the ten percent significance level.

Evan Pritchard

Faculty Sponsor: Dr. Michelle Kuchera

Black holes and the motion of objects of mass around them are important concepts to understand when talking about the universe. The azimuthal, or radial angle, radius, the initial angular speed, and the initial change in radius are values needed to calculate the trajectory of their path. Changing any of these values creates a vastly different trajectory. It was found that the most regular change between graphs changed when the dɸ/dt was changed by an interval of .01 from .01 to .07. The Fourth-Order Runge-Kutta method was used to compute the differential equations that explain the motion. The pylab package in the Spyder Python IDE was used to complete the computations graph the trajectory of an object.

Andrew Hoyle

Faculty Sponsor: Dr. Michelle Kuchera

Since the crew of Apollo 11 first landed on the moon in 1969, humanity has sought to further extend its reach to other celestial bodies. By far the most commonly thought of target for such an expedition is Mars. In recent years the goal of sending a manned mission to Mars has seemed much closer to reality thanks to advancements not only by NASA and other federal space agencies around the globe, but also private space agencies such as Space-X. One question still remains, though. What exactly would a manned mission to Mars have to look like? Therefore, the goal of this project is to help answer this question by simulating the physics behind such a mission. This will be done by simulating first the motion of the planets, Earth and Mars, using Newton’s Laws and Fourth Order Runge-Kutta, then incorporating the same methods to simulate visually and mathematically the movement of a manned command module.

Malcolm Wynter

Faculty Sponsor: Michelle Kuchera

Bailey Autry

Faculty Sponsor: Dr. Michelle Kuchera

Airliners are likely our main mode of transportation to cover long distances, with a large airliner such as a Boeing 747-200 being able to transport 400 or more people over more than 7500 miles. However, climate change and rising fuel prices are some of the main concerns surrounding commercial aircraft.
My goal for this project is to plot the fuel consumption of an airliner over time and show that, while the environmental concerns are valid and large jets burn tons of fuel, they can be a very efficient mode of transporting hundreds of people across the globe. My equation for rate of fuel burn has four variables, each of which has its own equation. The goal of this project is to plot the fuel consumption of aircraft over time and show how it varies according to several factors, such as the weight of the aircraft, altitude, and current flight phase.
Below is a graph for fuel consumption in a similar type of aircraft to the one I have plotted so far. It looks different because I I have yet to account for short flights being given a lighter fuel load, which decreases rate of fuel consumption. If I have time, I plan on comparing the fuel efficiency of this engine type (high bypass turbofan) to others, such as a turboprop. I will also try to include the descent, which will use more fuel per mile than cruise flight despite decreasing altitude.

Kevin Andrews

Faculty Sponsor: Michelle Kuchera

This Project models shows the process used to calculate the trajectory of a soccer ball including forces of friction, and the Magnus Effect using Python.

Eleni Tsitinidi

Faculty Sponsor: Michelle Kuchera

This program adapts the Monte Carlo Random Walk algorithm to calculate the energy for the ground state of a finite square well. It also plots the unnormalized wave function and the Energy vs V for a range of V from 1 to 200. It changes the algorithm of random walk Monte Carlo as presented in “An Introduction to Computer Simulation Methods Applications to Physical System” to calculate different potentials (currently finite square well), runs in python and changes aspects of the algorithm such as when the “random walkers” are being added (adds multiple at a time). The energy estimate for the ground finite square potential well with the inputs of the user’s choosing is printed to the console. In addition a plot of the unnormalized wave function is returned along with a plot of how the energy ranges with different V values. The results are not very accurate numerically, they seem to be off by a magnitude of 10 but the graphs seem correct in shape. The method can and will be improved by using the Diffusion Monte Carlo improved algorithm.

This program adapts the Monte Carlo Random Walk algorithm to calculate the
energy for the ground state of a finite square well. It also plots the unnormalized wave function and the Energy vs V for a range of V from 1 to 200. It changes the algorithm of random walk Monte Carlo as presented in “An Introduction to Computer Simulation Methods Applications to Physical System” to calculate different potentials (currently finite square well), runs in python and changes aspects of the algorithm such as when the “random walkers” are being added (adds multiple at a time). The energy estimate for the ground finite square potential well with the inputs of the user’s choosing is printed to the console. In addition a plot of the unnormalized wave function is returned along with a plot of how the energy ranges with different V values. The results are not very accurate numerically, they seem to be off by a magnitude of 10 but the graphs seem correct in shape. The method can and will be improved by using the Diffusion Monte Carlo improved algorithm.