Hacker News Reader

Comment by matt-attack | Hacker News Reader

It’s funny that he first described his method of random atoms bounding around until they found the exit. He then suggested adding a “fan” to the start to hell blow the atoms in the right direction.

The thing is, that’s exactly what his first solution was. A fan. His first solution is literally how air blows through the maze. (I suppose it’s technically when happens when you release air into an evacuated mass but still).

Also he suggests that collisions are needed to add “pressure”. Not true. He had pressure in his first modeling and no collisions are necessarily to model.

View on HN

You're mistaken about the simulation they're actually running. They are doing simple Brownian motion rather than a gas/fluid simulation, so there's no pressure differential anywhere and the particles don't interact with each other but rather with a theoretical other gas of consistent pressure.

You can see it by noting that the molecules that are very far apart are still bouncing around as though hitting other molecules (and they also mention it at 3m19s or so).

So there isn't a fan and they couldn't realistically add one. If they did, they'd essentially have to bias particles towards a prior-knowledge correct path through the maze (which is solving a maze by already having a solution), or actually run a gas simulation.

> Also he suggests that collisions are needed to add “pressure”. Not true.

If there are no inter-molecule collisions, there is effectively 0 pressure. (Ignoring the pressure that the walls of the container "feel", which is presumably not being modeled)

>Ignoring the pressure that the walls of the container "feel", which is presumably not being modeled

But that is exactly what pressure (of an ideal gas) is? No intermolecule collisions are required to model the behavior of a gas as we know it.

No, free molecular flow is a very different regime with very different behavior.

If you assume the gas is spread evenly throughout the space, you can model the pressure the gas exerts on the container it is in without intermolecule collisions. You (somewhat obviously) cannot model the pressure the gas exerts on itself this way, which is important if you're looking at the dynamics of how the gas will respond to a non-uniform distribution (the steady-state will still be uniformly distributed, but a gas with intermolecular collisions will spread out faster than one without: this is actually extremely relevant to achieving an ultra-high vacuum: when pressures are low enough you can't easily pump a volume out through a small hose, you need the pump to occupy a large enough part of the surface area of the volume you're pumping for the molecules flying around to actually hit it).

The thermodynamic definition of pressure is just how much work it takes to compress the system. This definition still works locally, you can just imagine compressing a small volume of gas.

I'm not 100% sure if fluid dynamics uses a subtly different definition (though how hard the medium is to compress is a fairly universal definition).

Obviously thermodynamics does break down if you've only got a small number of particles, but then 'pressure' also kind of stops working as a concept when you've got mostly vacuum.

An ideal gas still exerts pressure, even though in theory it has no interactions between particles.

Roughly speaking if you put a bunch of bouncing particles in a box then even if they don't hit each other they're going to hit the walls of the box more often if you decrease the volume. This means pressure is proportional to density so inversely proportional to volume i.e. pV is constant.

I don't think that's quite right actually. The first solution is like releasing gas molecules into a vacuum. They random walk and collide their way gradually diffusing out. That is taking a long time, as you can observe.

If the maze were already filled with a gas, and a fan were pressurizing the whole thing from one end, a pressure wave would be traveling through the maze towards the exit, sending the first particle out the door much faster.

Notably, they are not colliding with each other, I don't think. That is what he meant by adding pressure. If you made it more like a "flood fill" of the maze, where new particles are pushing into the maze, that would be similar. Though, I would guess that the earlier particles added would be higher probability to get out first. (Which would fit the intuition.)

Is it? Without pressure forcing molecules in an average direction, it isn't a fan. Right?

Notably, a fan would first saturate all dead ends closest to it. Basically turning deadends into walls at their entrance. But, again, this only works if you have pressure. Right?

I assume he meant pressure as, if there are already a bunch of particles stuck in a dead-end branch lower the chance of going there.

I took his idea of a "fan" blowing air to be like a sort of bias applied to the vector in a certain direction, perhaps a small bias for not going "backward".

Still sounds like, with the wrong maze, they would tend to pile up in certain nooks.

I think that is an idea behind many air filters. You will get build up in areas of the "maze", but ideally the lighter portions of the air will be able to basically bounce out and through. Some bigger particles will get lucky and find an exit.

Reply on news.ycombinator.com