Self-Jamming Cars

This week I wanted to try another Complex Systems-style simulation, this time based on something I had originally seen on Mythbusters, but others have tried with similar results: Traffic jams that appear out of nowhere simply due to drivers varying their speed. The system is fairly simple: Some number of cars drive on a circular track, trying to go as fast as possible while maintaining a safe stopping distance and obeying the speed limit. However, they may not all accelerate at the same speed, and can brake unexpectedly. These error factors result in some interesting effects, including waves of slow speed that travel backwards around the track.

To simplify things, I assumed the cars were either accelerating at maximum, or braking at maximum. They would decide based on the stopping distance from the car ahead of them:

where v is the car's velocity, and a_b is the braking acceleration. If the distance to the next car is less than this, we brake, otherwise we continue accelerating.

The controls you'll find below are the number of cars on the track, the maximum speed they'll go, the rate of acceleration, the rate of braking, the size of the variation in acceleration rate, and the rate at which that variation changes. This last factor is needed because if we change the acceleration error at every step, it tends to average out and have little effect. There's also a brake button that makes the red car slow while holding it down. As with many of these Complex Systems topics, I'm always surprised by the dynamics that emerge with just a few simple rules. Be sure to post a comment if you find something particularly weird!

Dreamt of in Your Philosophy

This week, I got several questions from Papou about the Big Bang and thermodynamics:

Is the Universe a closed system?

In order to answer this, we need to define what is meant by a "closed system": This is where no matter or energy enters or leaves the system under consideration. That means that the Earth, which gets energy from the Sun and radiates it back into space, is not a closed system. The Universe, however, which contains all matter and energy observed, is a closed system.

A different question, which uses confusingly similar terms, is whether the Universe is open or closed in the geometric sense. This refers to what happens if you travel in a straight line: Do you eventually come back to where you started, like you would on the surface of the Earth? Due to the influence of dark energy, for our universe the answer is no, it is geometrically open, whatever Modest Mouse may tell you.

How do the Laws of Thermodynamics apply to the Big Bang Theory?

Before we dive into this, let's talk about what the laws of thermodynamics are:

1. The energy in a closed system remains constant.
2. In any process, the entropy of the system must increase or stay the same.
3. As temperature approaches absolute zero, entropy approaches a constant

These are sometimes summarized as

1. You can't win.
2. You must lose.
3. You have to play the game.

I've mentioned entropy a couple of times on this blog, each time in a slightly different context. In this case, it can be thought of as energy that can no longer be used for work. As an example, if you have a bottle of compressed air, you could use it to propel a cart or turn a pinwheel, but if everything's at the same pressure, the air won't flow. This is actually the plot of a short story I read recently called Exhalation, about robots powered by compressed gas.

The Big Bang theory states that all matter and energy in the Universe started at a single point, which expanded outward. We can check off the first law, since the theory isn't saying anything about where that point came from – The Universe started with some fixed energy, and that energy is still here, just more spread out. That last part applies to laws 2 and 3 – Spreading out means more possible states for the matter, and lower temperature. It's these laws that lead to the heat death of the Universe, which I described before.

What is the impact of the Laws of Thermodynamics on Evolution?

The laws I outlined above are sometimes used as an argument against evolution: Evolution makes things more ordered, but that violates the increasing entropy requirement. The key is that the second law doesn't say entropy everywhere increases, just that it increases in the system as a whole. It's true that a human body has less entropy than a pile of microbes of the same mass, but that skips all the entropy generated in producing a human body. For a (slightly) more detailed discussion, I found this page, written by Robert Oerter at George Mason University.

Can there ever be enough Hawking Radiation to eliminate a Black Hole?

Yes! Hawking radiation is a process by which black holes can emit particles, but according to the first law up above, that means the black hole must lose energy/mass. If this happens over enough time, or the black hole is small enough, it can eventually evaporate. When the Large Hadron Collider first started up, some people (not scientists) were afraid it would create a black hole that would swallow the Earth. Experts were confident that if it did create one of the hypothesized microscopic black holes, they would quickly evaporate under Hawking radiation.

Thanks for more great questions, Papou!