Digital Commons Network^™

Optimizing Forest Harvest Cycles For Carbon Sequestration, Alex Landry, Margaret Lippsmeyer, Casey Wong

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

Our mathematical model aims to depict optimal harvest times for different types of forests based on the value they provide for carbon sequestration. We have developed three different models for the main forest types throughout the world, boreal forests, temperate forests, and tropical forests. For the model, we implemented a manipulated sine function for one period. By using a manipulated sine function, we are able to model the amount of carbon dioxide a tree is able to sequester over its lifetime as well as show the release of carbon dioxide back into the atmosphere when the tree dies and decomposes …

Optimal Race Strategies For Cyclists, Brendan Perez, Drew Altringer, Evan Fisette

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

For competitive cyclists, each course presents a unique set of factors and, in turn, leads to difficulty in choosing a racing strategy. Some courses confront cyclists with drastic changes in elevation while others are of a more consistent grade. Similarly, curvature varies from course to course.

Further, riders vary in their areas of strength. A rider’s power curve maps their instantaneous power output 𝑃 in W/kg over the amount of time that the rider can sustain that power level in seconds. The shape of a rider’s power curve indicates their riding style.

In this paper, we model the optimal …

How Drone Technology Can Help Minimize Natural Disaster, Carolina Gaspar, Kc Larranaga, Saumay Narayan

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

In this presentation, we demonstrate a model for determining how drone technology is able to be used most effectively in order to reduce the damage of natural disasters. Additionally, drones can enable response teams to be more effective and safe. Our model is based on the wildfires in Victoria, Australia, and our work was part of the 2021 Mathematical Contest in Modeling.

Effective Drone Usage For Wildfire Coverage In Victoria, Hitomi Uchiyama, Jakob Thomas Longbottom, Kellen Atkins

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

In this paper, we take a look at how drones can be used to efficiently help out with the communication between firefighters on the front line of wildfires with the operations center. We also take a look at how drones can also be used to survey the land, and how the wildfire is changing, to further instruct the operations center on how to most effectively disperse firefighters to control the fire. We look at the optimal positions for the drone placement in order to stay in signal range while also covering the most area possible. Using actual data from bushfires …

Tilings Of Modified Rectangles By Ribbon-Tile Pentominoes, Elizabeth Thompson

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

Which dimensions of a and b satisfy tilings of modified rectangles by ribbon tile pentominoes? We answer this question using tile invariants developed in prior research on the mathematics of tiling, as well as the use of inductive lemmas. The set of tiles we use for this study are height-1 ribbon tile pentominoes, which we later define. Modified rectangles are a-by-b rectangles with height a and width b, and the additional feature that the top left and bottom right squares are removed.

Sandcastles: A Math Modeling Adventure, Matthew Lemire, Joseph Simpson, Lottie Steward

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

Our presentation is about our experience participating in the 2020 COMAP Mathematical Contest in Modeling this past Spring. We briefly discuss the nature of the contest, followed by a summary of our specific experience. We selected Problem B, which was about finding the ideal geometric shape of the foundation of a sandcastle, and we achieved “Successful Participant” in the contest.

An Experience In Mentoring: Shaping Young Mathematical Minds, Andrea Hernandez-Gallo, Jennifer Moranchel, Ruben Saul Cruz, Jennifer Nordstrom

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

The Math PLUS program is a partnership between Linfield College and a local middle school which seeks to encourage more mathematics in local and regional science fairs. Linfield students are paired with middle school students to mentor science fair projects that are required to have a mathematical focus. We briefly discuss an overview of the program—its goals, structure and execution—before touching on our personal experiences as mentors for Yamhill-Carlton Intermediate School students. We also provide suggestions for improvements for those looking to implement similar programs at their own institution. The program is funded by a Dolciani Mathematics Enrichment Grant.

Big Data And The Stock Market: Distilling Data To Improve Stock Market Returns, William Shannon, Jennifer Moranchel, Xiaoyue Luo

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

In our modern competitive market, businesses are seeking efficient and innovative platforms to remain profitable and prepared, especially in the uncertain world of the financial stock market. One possible avenue for improving stock market returns that companies can turn to is harnessing a substantial volume of information, known as big data. However, because of the nature of big data, distilling and analyzing the vast amount of information can require complex analytical methods. Using a keyword selection process based on word frequency, we were able to filter out the data amongst the noise and derive a sector-specific keyword list. This list, …

Looking For A (Super)Resolution To An Image Processing Problem, Alleta Maier

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

In recent years sparse coding has been employed to efficiently process images. Since recovering sharp images from images corrupted with noise is a well-known ill-posed problem, small perturbations in the image lead to large deviations in the reconstructed image. We look to combine research in superresolution with that of sparse coding for elucidation.

Asymptotic Behavior Of Traveling Wave Solutions To Reaction-Diffusion Equations, Malley M. Nason

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

We will discuss travelling wave solutions to reaction-diffusion equations of the form:

u_t=u_xx+ u^p (1-u^q)

which can be used as a mathematical model for various biological phenomena, as well as to model problems in combustion theory. We identify conditions on the wave speed so that travelling wave solutions exist for the case p ≥1 and q ≥1. Moreover, we estimate the rate of decay of the travelling wave solutions. When p > 1 and q ≥1, this estimate requires center manifold theory because the typical linear methods fail to work. Through the mathematical analysis …

1-Relaxed Edge-Sum Labeling Game, Hang Do, Timothy Singer, Brent Moran

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

We introduce a new graph labeling and derive a game on graphs called the 1-relaxed modular edge-sum labeling game. Given a graph G and a natural number n, we define a labeling by assigning to each edge a number from {1,..., n} and assign a corresponding label for each vertex u by the sum of the labels of the edges incident to u, computing this sum modulo n. Similar to the chromatic number, we define L(G) for a graph G as the smallest n such that G has a proper labeling. We provide bounds for L(G) for various …

Searching For A Lost Plane, Yichen You, Yu Yan

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

Malaysia plane MH370 disappeared en route from Kuala Lumpur to Beijing on 8, March 2014. Besides considering the factors such as air piracy, weather, electromagnetic wave, and kinds of bugs of the airplane, in order to find the wreckage efficiently the growing concern is to confirm a limited area where the airplane probably fell, and then to find an optimum way to find the plane. It’s essential to build such a model involving both of the two layers mentioned above that can cover all the searching area by using the most efficient way.

The first layer is to confirm the …

Analysis Of Population Dynamics Of Terrorist Cells, Amanda Dorman

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

Applied mathematics connects many different fields of science. This research focuses on the population dynamics of terrorist organizations, namely Al Qaeda, by creating a mathematical model, while still considering social science fields, such as psychology. By considering psychological interrelations of a terrorist cell and their contact with citizens, we design a model that is a four-dimensional system of nonlinear differential equations to better understand the way in which recruitment ensues within such organizations. Using the computer program Mathematica, we are able to manipulate multiple parameters simultaneously in order to observe the impact of certain recruitment techniques on the general …

Traffic Flow: An Approach Towards Modeling The Right Lane Rule, James D. Knox, Alexander Ogle, Lauren Devore

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

We attempted to model and analyze the effect of the right hand rule for the 2014 COMAP Math Modeling Competition. In order to analyze the right hand rule we started with Greenshield’s macroscopic approach and modified it to simulate the effects of the right hand rule. By analyzing the resulting changes in the flow and density of the system we determined the performance of the rule in varying traffic densities. Next we looked at the performance by modeling traffic flow when the rule is strictly adhered to, as compared to an intermediate, where the rule is followed until the critical …

Competitive Tiling, Levi A. Altringer, Michael P. Hitchman, Charles Dunn, Amanda Bright, Greg Clark, Kyle Evitts, Brian Keating, Brian Whetter

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

Competitive tiling consists of two players, a tile set, a region, and a non-negative integer d. Alice and Bob, our two players, alternate placing tiles on the untiled squares of the region. They play until no more tiles can be placed. Alice wins if at most d squares are untiled at the end of the game, and Bob wins if more than d squares are untiled. For given regions and tile sets we are interested in the smallest value of d such that Alice has a winning strategy. We call this the game tiling number. In this project, we …

Tilings Of Annular Region, Kyle Evitts, Levi A. Altringer, Amanda Bright, Greg Clark, Charles Dunn, Michael P. Hitchman, Brian Keating, Brian Whetter

Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement

We present our summer research on mathematical tiling. We classified which rectangular annular regions are tileable by the set of T and skew tretrominoes. We present a partial proof of this result, and discuss some of the context for this problem.