been ill

Apologies for yet another reader-losing break in posts. I've been ill. Nothing terrible, but I'm not getting as far down my priority list as I might otherwise.

Hopefully a spritely return in the next few weeks.

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).

Networks in Nature Physics

For those with access, looks like Nature Physics has a complexity issue. With articles by Barabási and Newman and the likes, it looks like it has a solid networks bent.

There's a paper on community structure by my favourite physicist, Mark Newman, that I'm looking forward to reading.

Enjoy!

We all do economics

The very interesting blog, Mind Hacks, has a post on a theory of a bipolar economy.

A 1935 Psychological Review article proposed a ‘manic-depressive psychoses’ theory of economic highs and lows based on the idea that the market has a form of monetary bipolar disorder.

I find it quite interesting how people like to reframe the problem of economic crashes in their own subject. In psychology it seems perfectly natural to ascribe the behaviour to individual human behaviour. As a physicist I'm completely convinced that it's a collective effect that arises from many relatively simple individuals, trying to win a game, interacting in a highly complex system. Of course one could possibly say the same about the brain itself.

I wonder if biochemists have some hormone explanation and neuroscientists some neurotransmitter reason. Perhaps all these perspectives are equally right (or wrong) – I guess the only thing for sure is that we don't really know!

A phase diagram in a jar

One of the things I love about colloids is just how visual they are. Be it watching them jiggling around under a confocal microscope, or the beautiful TEM images of crystal structures, I always find them quite inspirational, or at least instructional, for better understanding statistical mechanics.

Sedimentation

Just to prove I'm on the cutting edge of science, I recently discovered another neat example from 1993. At the liquid matter conference in Vienna Roberto Piazza gave a talk titled "The unbearable heaviness of colloids". As a side note there was a distinct lack of playful titles, maybe people were too nervous at such a big meeting. Anyway, the talk was about sedimentation of colloids.

Sedimentation is something I don't usually like to think about because gravity, as any particle physicist will agree, is a massive pain in the arse. Never-the-less, my experimental colleagues are somewhat stuck with it (well, most of them). As is often the way it turns out you can turn this into a big advantage. What Piazza did, and then others later, was to use the sedimentation profile of a colloidal suspension to get the full equation of state, in fact the full phase diagram, from a single sample.

The nicest example is from Paul Chaikin's lab (now in NYU, then in Princeton), where they used a colloidal suspension that was really close to hard spheres. They mixed a bunch of these tiny snooker balls in suspension, and then let it settle for three months. What they got is this lovely sample, with crystal at the bottom (hence the strange scattering of the light), and then a dense liquid which eventually becomes a low density gas at the top. It's as though the whole phase diagram is laid out before you.

Equation of State

This is a very beautiful illustration, but it's not the best bit. In the same way that atmospheric pressure is due to the weight of the air above you, if you can weigh the colloids above a particular point in the sample then you can calculate the pressure at that point. This is exactly what they did. There are many different ways to measure the density of colloids at a particular height, if you can do it accurately enough (which was the big breakthrough in Piazza's 1993 paper) then you can calculate the density as a function of pressure. In a system where temperature plays no role such as this, this is exactly the equation of state (EoS).

When compared with theoretical calculations for hard spheres the experimental data lies perfectly on the theory curves, complete with first order phase transition where it crystallises. This is really a lovely thing. EoSs are very sensitive to exact details, so in the same way that in my group we compare our simulation of the EoS to check our code, this showed very accurately that their colloids really were hard spheres.

So I think this is all very nice. I nicked the above images from Paul Chaikin's website, I recommend having a poke around, there's loads of great stuff (you really need to see the m&ms).

Back from the dead

Can't remember the number of times I've said I've been away because I've been busy, but this time it'll be different. Well it probably won't be different, it looks like I'm destined to be an inconsistent blogger!

It's now been three months since I arrived in the Netherlands for my new job and I'm enjoying it a lot here. The pace is much faster in the group than I'm used to but I'm enjoying the buzz of lots of interesting things getting done. Now I'm more settled I'm hoping for a spectacular return to blogging - there's certainly enough to talk about here!

The Dutch are good at science

In general the Netherlands has a fantastic history in the sciences. I was watching Carl Sagan's Cosmos the other day (best telly ever made), he loved the Netherlands it would seem. There's a whole episode where people dress up in pointy hats and reenact bits from Dutch scientific history.


I'm no historian so there's no point making a huge list. Some notable greats though include Cristiaan Huygens, famous for the wave theory of light, he worked on telescopes and even the pendulum clock. The microscope was invented in the Netherlands, allowing the Antonie van Leeuwenhoek to discover "a universe in a drop of water".

What about statistical mechanics?

Closer to the focus of this blog, the name Johannes van der Waals is never far away. His theories allowed us to begin to understand why matter undergoes phase transitions.Two names that are important for us here in Utrecht are Peter Debye and Leonard Ornstein.

Peter Debye is another one of those names that just seems to pop up all the time. It's littered through my thesis because of his work on phonons. Debye was professor at the university of Utrecht for a very short time. I believe the university didn't deliver on his startup money so he left. The picture is from our coffee room in the Debye Institute.

As well as working in the Debye Institute I also work in the Ornstein Lab, after Leonard Ornstein. For me his name is most famous from the Ornstein-Zernike relation in liquid state theory, however, I think he did a lot of varied stuff. He followed on from Debye at Utrecht in 1914 where he remained until 1940. Ornstein was Jewish and at the beginning of the war was dismissed from his position at the university. Only six months later he died. Seems to me it should be the Ornstein Institute, anyway, we also have his picture up.

Enough history

So the Dutch weren't too bad at science. The living ones aren't too shabby either. So hopefully lots of interesting things to be posted in the coming weeks.