# Ideas for simulation based physics paper in high-school

1. Aug 19, 2014

### Aaronaut

I have to write, with two friends, a simulation based physics paper at school.
The problem is, that will I am quite familiar with the concepts of calculus and algebra, my friends aren't.
So, we could find a good topic. The task is, to write a paper about a physical topic, with the use of a selfmade program. The development of the program shouldn't be a problem at all. we have a good programmer.
Any suggestions, for a topic that involves only pre-calculus math or only just some calculus?

2. Aug 19, 2014

### JorisL

How about a simple molecular dynamics simulation?
The setup is rather straightforward as you integrate the equations of motion for a system.
The hard part might be motivating the integrator to your fellow students as this is based on series expansions.
I'm sure there are some simple books out there that explain this in sufficient detail for the 3 of you to understand.

An example for a system here is simulating the orbit of the earth around the sun. Or any other orbit.
I wouldn't suggest simulating more difficult systems at first, get yourself acquainted with the methods first.
After that you can look at for example liquids e.g. a Lennard-Jones fluid as a prime example.

3. Aug 19, 2014

### Jano L.

Simulate motion of a set of spheres in rectangular container, bouncing of each other and off the walls. Since the motion of any sphere is a series of rectilinear motions interrupted by collisions, vector algebra (analytic geometry), basic mechanics and good programming skills should be sufficient. Since there are no forces in between the colissions, complicated numerical integration of differential equation is not necessary - the main hard part is handling the collisions. The mathematics involved should be tractable and physically this is interesting, since it is a model of a gas.

Why is it interesting? You can investigate whether the system obeys the equation of state from statistical physics
$$PV = Nk_BT,$$
where $P$ is pressure, $V$ si volume of the container, $N$ number of spheres and $T$ is kinetic temperature. Theoretically, it should be obeyed if the gas is rare enough, but with enough spheres packed, lower effective volume $V'$ is expected. You can investigate this decreased volume as a function of number of spheres $N$.

Another interesting thing: you can investigate whether the velocities of the spheres obey Maxwell's distribution. Just give all the spheres velocities with random direction and random magnitude initially and observe what happens to histogram of velocities. It should approach the Maxwell curve and stick to it.

Last edited: Aug 19, 2014
4. Aug 19, 2014

### Jorriss

This is what I would recommend, just write a molecular dynamics (MD) simulation from scratch. The thing about molecular dynamics is a bare bones MD code has very few features to implement but there is a lot of room to increase the complexity.

http://ocw.mit.edu/courses/material...sma-5107-spring-2005/labs/lab_assignment4.pdf

If you go down to extra credit the Professor indicates the ingredients to a bare bones code.