Each group will choose one of the options below as a project. You will have most of the quarter to work on your problem of choice and will submit both a Preliminary and Final Report as a group. Methods and techniques you learn in this course will be applicable to these projects and will requre you to read ahead to identify them. If you wait until the topic is discussed in class you will likely not have sufficient time to complete your project and prepare your report. You MUST use something from this course in your model!
Remember, these are GROUP projects. That does not mean you "divy" up the work. It means that you work together. That is, every member of the group should be able to explain the model and report. For example, if you use a computer simulation to test your model, every member of the group should be able to explain the simulation. Learn from the members of your group!
Please feel free to use computer simulations, collect physical data, and do experimentation whenever safe, reasonable, and applicable.
In the United States, the passenger pigeon was heavily hunted until the late nineteenth century. Unfortunately for the passenger pigeon (as well as modern day avid bird watchers and zoo-goers alike) the passenger pigeon could only breed successfully when the population was above a certain "threshold" value. As a consequence, despite the fact that the total number population numbers were still quite large up until the late 1880's - early 1900's, it was not sufficiently dense to maintain the breeding population and this species of bird is now extinct. Create a dynamic for the population of passenger pigeons at the turn of the century and incorporate this idea of a "threshold" value. What can you say about the dynamics? Was there a way to save the passenger pigeon? Can you apply this model to modern day "endangered" or "at-risk" species?
Wild sources of ocean life, such as salmon, halibut, crab, etc., are usually thought of as "renewable" resources. However, many of these resources appear to be dwindling and consequently, the fishery industry is experiencing a crisis. One possible explanation for the decrease in population sizes is over-fishing. That is, if too many fish/crab are caught, there are not enough to reproduce and sustain the population. Model one such population as a "renewable resource." What can you say about over-harvesting? What about under-harvesting? What advice would you give the fisheries and/or governmental agencies?
Consider an infectious disease which can be carried by people who are asymptomatic (a.k.a. "carriers"). A classic example of this would be Typhoid Fever. Model the spread of such a disease? What are the effects of transmission via a "carrier" on the population dynamics? How is this different from the dynamics of a system where all infectious individuals are symptomatic?
Consider the following thought experiment. Suppose you have a mass, m, attached to a spring. How are the dynamics of this mass-spring system different here on earth than they would be, say, in orbit (e.g. in microgravity)? How would the dynamic change if the experiment were completed in a gravity-free environment (e.g. deep space)?
Model the dynamics of an electrical current, I, in a simple series circuit. What is the relationship between the current and the resistance, R? What is the relationship between the current and the impressed voltage, E? Can you solve this system? If so, what does the solution tell you? (Hint: consider Kirchhoff's second law).
Propose your own project. If you choose this option, you must have your topic approved by me before you submit the preliminary report.