Worked Problem Assignment 7#

Due 1 Dec 23

We have started to use probability and counting statistics to understand the behavior of systems. In this worked problem, you will explore a system of your choosing.

Updated Rubric

Remember that a worked problem means the scale of a detailed (e.g., parts a-h) homework problem.

Starting your Analysis#

You will need to orient us to your problem as there are many potential statistical models. You will need to develop an analytical tractable situation that can also be explored using the numerical methods we have developed. You will need to do the following:

  1. Write a paragraph or two describing the system you are investigating. Make sure to explain the parameters and variables.

  2. Explain what you are going to do and why. If you can point us to where things are being done, that’s helpful.

  3. You need to clearly set up your analytical problem. This means write down and explain the equations you are constructing.

Investigating the System#

After you set things up, please conduct an investigation using the tools we have developed in class. The order in which it proceeds is up to you, but make sure the flow is logical and clear. We want to understand how your investigations are going to help you be successful with your projects.

Assignment#

  1. Choose a statistical model associated with a physical system

  2. Write a paragraph or two describing the system you are investigating. Explain what you are going to do and why. If you can point us to where things are being done, that’s helpful.

  3. Conduct your analysis of that system and present equations and plots that help you understand the system.

  4. Graph any results and explain what you have found.

Looking ahead (earn extra credit)#

If you are looking into these systems and finding them interesting here’s two things you can do to earn extra credit.

  1. Investigate a statistical mechanics or quantum mechanical model.

  2. Run a number of simulations with a variety of parameters and compare the results. What do you notice?

Submitting your work#

You will upload your work to D2L. It should be a single PDF of your work. If you also write code, please submit the associated files as well. If you do all of this in a Jupyter notebook, please export the notebook as a PDF and submit the notebook and PDF file. If you have any questions, please ask. We want you to enjoy working on these problems.