Email me with a paragraph description of what you are planning for your project. due: Wednesday April 26 (end of day)
Project writeups. due: Friday May 5
Here is a selective list of titles from previous years' projects.
It's probably better NOT to pick from this list. But you can get some idea of what is possible.
The wikipedia article on dimensional analysis is quite complete and gives more info than you need.
The
Buckingham Pi-theorem
handout from OpenCourseWare at MIT course 2-25 (Fluid Mechanics) gives a very (perhaps too?) succinct descrition of dimensional analysis.
The double auction pricing article by Daniels et. al.
describes the dimensional analysis (top of page 2) they use to model double auction pricing.
They cite their previous article (section II.A) for details.
There are other similar articles cited (and citing) these articles.
None are able to really justify their choice of dimensions except to say that it is analytically tractible.
Summary of Dynamic Models: Big Picture Lessons we can take from this part of the course.
Chaos and Fractal Attractors
The Wikipedia article on the Lorenz Attractor has some good pictures and descritions.
Lorenz Simulator to show the attractor. Written in HTML5 instead of java applet for better security.
Lorenz Equations
simulation java applet from CalTech (May not work due to security on java applets).
Sensitive dependence using the Lorenz Equations. This applet allows you to track nearby trajectories to show that they separate (May not work due to security on java applets).
The Wikipedia article on the Attractors shows some attractors more generally than the Lorenz System.
Sugarscape was described in detail in a book "Growing Artificial Societies" 1996 by
Joshua Epstein and Robert Axtell, Brookings Press. The science library has a copy.
You can also read more at many websites about sugarscape including:
A NetLogo implementation of SugarScape originally created at University of Leicester
and adapted for this class.
After installing NetLogo,
download the SugarScape NetLogo Program.
You can Download NetLogo onto your computer
and run examples that way. NetLogo is also on the Math Department Computers.
Sugarscape models are in the Models Library under Social Sciences.
Artificial Stock Market models like the Levy, Levy Solomon model have a lot written
about them. Here's a reasonably readable article by Zschischang and Lux (2001).
A phase plane plotting java app.
Once at this page click on the "pplane.jar" link in the last paragraph. You should be able to
double-click on the downloaded file, but there might be security issues. If so, you can Right-click
(control-click on Mac) and choose "Open". After it opens once, you can just double-click after that.
If your system doesn't allow java programs to open, you should google how to change settings to allow java to run.
I wrote an AJAX version of pplane called pplaner.
It doesn't have all the features of pplane, but gets the basic job done.
The original pplane program was a Matlab program and you can still download pplane8.m after a google search for it.
My last attempt to do that didn't work with recent versions of Matlab. Your mileage may vary.