Just hurry up and sit down!

As a semi frequent flyer, and incredibly impatient stand-behinderer I couldn't resist linking to this - Time needed to board an airplane: A power law and the structure behind it from a Norwegian group, Vidar Frette and Per Hemmer.

Boarding strategy is of great importance to airlines, where the turn around time of planes – especially short haul – can make a real dent in profits. For the authors of this paper, however, it seems they just think it's a neat model to test out 1D problems where the particles are distinguishable, rather than the more common indistinguishable particles. In a traffic model the cars are usually identical, whereas here the passengers have a specific seat booking. Statistically this makes a difference.

Of course many people do look at specific strategies. For example here, it seems that it's difficult to think up a strategy that beats random loading. One would think that loading back-to-front would be better but this is not the case. A quick google search finds this nice page from Menkes van den Briel. There you can see videos of all the different strategies.

Unfortunately the best strategy seems to involve seating people in order of window/middle/aisle. Not great if you're sitting next to your kids.

All of which did remind me that it is much quicker boarding when you don't have seat bookings. When I fly to England using a certain orange-themed airline, that doesn't book seats, there's an initial mêlée followed by reasonably rapid sitting down. On a certain royal blue-themed airline it takes forever for a plane half the size to get sat down.

My suggestion is that I should be allowed to starting poking, with increasing frequency and verbal abuse, anyone that I deem to be taking too long to put their bag away.

Clustering in sea-ice floes

I started writing this post as a long winded account of the difference between equilibrium and non-equilibrium statistical mechanics. It turns out that that is hard to discuss without waffling on, so instead I will just talk about an interesting paper from the world out of equilibrium - which is most of the real world.

I've been walking around with this interesting paper, "Molecular-dynamics simulation of clustering processes in sea-ice floes" by Agnieszka Herman, in my bag since November. It was picked up in the spotlight section, in Phys. Rev. E (loosely the stat-mech/complexity section). My attention was grabbed by the idea that simple ideas in granular gases could hold sway in the icy seas of the Arctic.

Marginal ice zone

Roughly speaking, it's always icy at the top of the earth and then as you go south it turns into ocean. Around the transition between icy and not icy (only the best technical explanations for my readers) is the so called marginal ice zone (MIZ). This is where bits of ice break away from the main ice pack and float around in the sea. Understanding how this ice moves around, and the effect of external forcing, is important if we're to best understand the impact of global climate change.

The ice-floes studied in this paper are in an intermediate region between densely packed and very low density. The sizes of the ice fragments are roughly distributed with a power-law tail and they float about and hit each other inelastically. It is here that one can make the link to something closer to my own field, it is a 2D granular gas.

Granular gases

In the world of the small everything is constantly being battered by random thermal noise. It's so random that it, in fact, becomes rather predictable and Boltzmann distributed. In the world of a bit bigger, this thermal noise doesn't really affect the individual particles any more and we're now dealing with grains. I've talked about this before in the context of colloids – the last bastion of thermodynamics before everything goes granular.

In a granular context the ice fragments are particles that move ballistically in between collisions, and when they collide energy is lost. This system, of dissipative colliding grains is known to have interesting dynamics including the clustering of particles and other complicated correlations.

The really nice thing about this paper is that what Agnieszka Herman has done is to simulate such a granular gas, but adding in realistic numbers for all sorts of effects such as friction, wind, currents, restitution coefficient (how inelastic it is) and to see if it can reproduce what is observed in the oceans. This can not have been easy to set up!

Comparing to real life

The image below is the sort of sea ice clustering that is seen in the MIZ. One sees that the smaller floes tend to accumulate on one side of the larger floes.

This is also seen in the simulations results. This is because, as well as losing energy in collisions, the floes are being driven by wind and currents. The larger floes catch up with the smaller ones pushing them along for a while until they fall off. The colour bar shows the velocities of the different floes.

At higher densities – more collisions – you can still see the gaps behind the large floes, although the distribution of velocities is now narrower.

I don't know how rigid this system is, it'd be interesting to know if there's a breakout point where the ice floes can suddenly escape. It's really neat to think that you can connect such different systems, not to mention such different scales, and still be able to say something sensible.

Big thanks to Agnieszka for providing the colour images. Images, copyright APS, are reproduced with permission from the paper Phys. Rev. E 84, 056104 (2011).