I got our fix working and ran a few examples, and reported the results to the group who made a few observations about the simulation behavior that didn't look right: gravity didn't seem to be doing its job. We tried a few more things to fix it by exploring the effect of a few of the parameters in the simulation like the strength of gravity, initial speeds, initial concentration of bodies, and body sizes. This led to some good discussion, which I hope helped also solidify some concepts from the simulation strategy, which we will still need going forward. Here is an example animation.

As it turns out, I had a mistake that meant the forces weren't being calculated at all, so the students were right on with their observations! Here's an example animation with the corrected forces...as we can see, it makes more sense but there is still some work to be done.

Diffusion and Brownian motion

We then switched gears to concepts closer to the physics of fluids. We introduced 2 main concepts: diffusion and Brownian motion.

To introduce diffusion, which is the concept that "particles" migrate from regions of high concentration to regions of low concentration, we watched the first half of this video.

To introduce Brownian motion, we watched a movie of pollen grains suspended in water, much as the original experimenter Robert Brown (a botanist) would have seen in 1827

And another video that had some good animations of what causes Brownian motion (no, it's not that the pollen is alive and moving itself)

Finally, we watched an experiment that gives a clue into how the 2 phenomena are related

We had very interesting conversations and discussion around these concepts. Everyone had heard of diffusion before, but Brownian motion was new. The students were asking many excellent questions, and the best part is that sometimes they were answering each others' questions quite well! One example was Luka's question of why a thrown ball will eventually slow down due to friction with the air molecules, even though it should be struck by air molecules behind it...doesn't Brownian motion imply that collisions from the front and back are just as likely? It was Alex who answered using a fun analogy of a running person as the ball, and little children running around as the air molecules that slow the runner down.

The final concept we discussed was the relationship of Brownian motion to our solar system simulator. I hope I got across the idea that the solar system simulation is basically the same as the simulator we would need for Brownian motion — all we need to do is exchange the force of gravity for random forces in random directions at every time step!

Next time, we will start to see the relationship between Brownian motion and diffusion by thinking about the spreading of ink in water (like the last youtube video) in 2 completely different ways: many individual ink particle motions simulated under random "Brownian" forces (which we know how to do thanks to the solar system simulator), and as a continuum concentration field governed by partial differential equations---very similar to but simpler than the ones governing fluid flow, which we had our first taste of during our flow through tubes experiments.

Until then!

Thanks,
Alex