Computer Modeling Project Topic (Help, please)

[Jelfish]

So I have this project where I need to write a report and code of some numerical method used in some specific area of physics modeling. The report deals mostly with the numerical method but requires that some specific physics application tied into it. An example would be the Crank-Nicholson method for solving the Schrödinger equation. I'm not really sure what topic I should choose and was wondering if any of you had a personal favorite. A side note - we've covered a few finite time stepping methods for partial diffs, so something other than that would be preferred. Also I'd like to know how difficult you feel it would take to implement the code.
Thanks! :!)

 

[neurocomp2003]

[]RigidBody Dynamics or Chris Hecker's Work.
[]Million-Body problem.
[]Some type of stellar physics model/planetary-geophysics modelling
like cloud dispersion or mountain formation.
[]Ising Model (thermo)

 

[Integral]

There are many simple Physics problems which should fill your needs.
1. Non linear pendulum
2. Multi spring/mass problem
3. RCL circuits.

You might consider choosing something with a known closed form solution so you can easily verify your numerical solution.

 

[saltydog]

May I suggest a project dealing with Emergence. Familiar with subject? Termites don't know what they're building yet they build marvelous clay cathederals. The santum "emerges" from the mud by way of non-linear effects between termite, pheremone, and mud. How can order arise from randomness? Try these two:

$$\frac{\partial a}{\partial t}=\frac{ca^2}{h}-\mu a+d_a \frac{\partial^2 a}{\partial x^2}$$

$$\frac{\partial h}{\partial t}=ca^2-\nu h+d_h \frac{\partial^2 h}{\partial x^2}$$


Oh yea . . . stars don't either.

 

[Jelfish]

Thanks - I'll check some of those out!

For reference, here's what I've done in class:

Euler Method: Pendulum

Runge Kutta Method: Pendulum, driven pendulum, a lot of other stuff with single deratives

FFT analysis: analyzing a wave, transforming the wave equation

Finite time centered space: numerically solving second order partial differential equations

Crank Nicholson Method: another method for solving second order partials (specifically the wave equation).


So you see, the main focus is the method and then a topic in physics from which it benefits.


Thanks for the replies so far. I'll do some research on the suggested topics. Any more would be welcome though!

 

[LeBrad]

Pick something simple that results in a HUGE system of structured linear equations. Then use clever system solving techniques (like sparse LU or GCR) to solve the system quickly.

 

[Jelfish]

That's a good idea, actually. Thanks!