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Physical Sciences and Mathematics Commons™
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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Modeling Aircraft Takeoffs, Catherine Cavagnaro
Modeling Aircraft Takeoffs, Catherine Cavagnaro
CODEE Journal
Real-world applications can demonstrate how mathematical models describe and provide insight into familiar physical systems. In this paper, we apply techniques from a first-semester differential equations course that shed light on a problem from aviation. In particular, we construct several differential equations that model the distance that an aircraft requires to become airborne. A popular thumb rule that pilots have used for decades appears to emanate from one of these models. We will see that this rule does not follow from a representative model and suggest a better method of ensuring safety during takeoff. Aircraft safety is definitely a matter …
Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum
Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum
CODEE Journal
Common mechanistic models include Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models. These models in their basic forms have generally failed to capture the nature of the COVID-19 pandemic's multiple waves and do not take into account public policies such as social distancing, mask mandates, and the ``Stay-at-Home'' orders implemented in early 2020. While the Susceptible-Vaccinated-Infected-Recovered-Deceased (SVIRD) model only adds two more compartments to the SIR model, the inclusion of time-dependent parameters allows for the model to better capture the first two waves of the COVID-19 pandemic when surveillance testing was common practice for a large portion of the population. We find …
Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist
Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist
CODEE Journal
In this paper, I discuss two environmentally-focused writing assignments that I developed and implemented in recent integral calculus and differential equations courses. These models of carbon storage and PCB’s in a river provide interesting applications of one-compartment mixing problems. The assignments were intended to focus student attention on sustainability concerns while also developing other essential skills. I discuss these assignments and their effect on my students’ technical writing and environmental awareness. Detailed introductory instructions and mostly complete solutions to these assignments appear in the appendices, to include sample student work.
Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr
Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr
CODEE Journal
This paper presents mathematics relevant to the question whether voting should be mandatory. Assuming a static distribution of voters’ political beliefs, we model how politicians might adjust their positions to raise their share of the vote. Various scenarios can be explored using our app at https: //centrism.streamlit.app/. Abstentions are found to have great impact on the dynamics of candidates, and in particular to introduce the possibility of discontinuous jumps in optimal candidate positions. This is an unusual application of ODEs. We hope that it might help engage some students who may find it harder to connect with the more customary …
Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier
Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier
CODEE Journal
A Sand Tank Groundwater Model is a tabletop physical model constructed of plexiglass and filled with sand that is typically used to illustrate how groundwater water flows through an aquifer, how water wells work, and the effects of contaminants introduced into an aquifer. Mathematically groundwater flow through an aquifer can be modeled with the heat equation. We will show how a Sand Tank Groundwater Model can be used to simulate groundwater flow through an aquifer with a no flow boundary condition.