Seminar and meetings in France

I'm giving a seminar in the Ecole Normale Supérieure (ENS) in Lyon, France the 6th of December. Just after that I'll be in Paris for 2 consecutive meetings:

• The French-Japanese meeting on Jamming, Glasses and Phase transitions
• Unifying Concepts in Glass Physics V,  where I will be presenting a poster.

Both seminar and poster are about the same stuff I talked about in Kanto-softmatter workshop and in a previous post. Here is the more formal abstract.

A link between local structural ordering and slow dynamics has recently attracted much attention from the context of the origin of glassy slow dynamics [1, 2]. There have been a few candidates for such structural order [3, 4], icosahedral order, exotic amorphous order, and crystal-like order. Each type of order is linked to a different scenario of glass transition. Thus, revealing the order responsible for slow dynamics is crucial for our understanding of the glass transition. Here we experimentally access local structural order in polydisperse hard spheres by its particle-level observation with confocal microscopy. We identify the key structures as icosahedral and face-centred-cubic(fcc)-like order, excluding any other simple local symmetry. We find that both types of order are statistically associated with slow particles. However, when approaching the glass transition, the icosahedral order does not grow in size whereas crystal-like structures grow. It is the latter that governs the dynamics and is linked to dynamic heterogeneity. This questions the direct roles of the icosahedral ordering in glassy slow dynamics and stresses the importance of the structural order compatible with the avoided first order transition, crystallization. Our finding also suggests that the growing lengthscale of structural order is essential for the slowing down of dynamics and the nonlocal cooperativity in particle motion.

References

1. Cavagna, A. Supercooled liquids for pedestrians. Physics Reports 476, 51124, 2009.
2. Berthier, L. & Biroli, G. Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 83, 587, 2011.
3. Steinhardt, P., Nelson, D. & Ronchetti, M. Bond-orientational order in liquids and glasses. Phys. Rev. B 28, 784805, 1983.
4. Tarjus, G., Kivelson, S. A., Nussinov, Z. & Viot, P. The frustration-based approach of super-cooled liquids and the glass transition: a review and critical assessment. J. Phys.: Condens. Matter 17, R114R1182, 2005.
5. Lubchenko, V. & Wolynes, P. Theory of structural glasses and supercooled liquids. Annu. Rev. Phys. Chem. 58, 235266, 2007.
6. Tanaka, H., Kawasaki, T., Shintani, H. & Watanabe, K. Critical-like behaviour of glass-forming liquids. Nature materials 9, 324Ð31, 2010.

Reconstruction from confocal microscopy coordinates. Only structured particles are shown for clarity.

Particle tracking I : from analog to digital

Pinpointing the positions and sizes of tens of thousands particles from pictures. I can't miss one, I can't detect a particle where there is none. The precision must be extremely high. That is what I am doing routinely as the basis of my research. If I don't get this step right, my research has feet of clay, standing on sand.

In 1905 Einstein published three papers founding or revealing three different fields of physics : relativity, quantum mechanics and Brownian motion. The last one is a major breakthrough in statistical physics because if it was true, then matter was discontinuous, made of particles like atoms or molecules. However an experimental proof was needed.

Jean Baptiste Perrin

Jean Perrin exhibited this proof by the following experiments around 1908 : he suspended microscopic gamboge particles in water and waited for them to settle. Obviously their were more particles at the bottom than at the top ; however, how many more ? Perrin took a microscope and counted : how many particles do I see in average in a drop of suspension taken at 1 cm from the bottom (do it for 1000 drops to get a good average) ? How many at 2 cm ? etc. The concentration profile he got was perfectly fitting with theoretical predictions and thus discontinuity of matter was proved. Jean Perrin got the Nobel prize in physics 1926 for that.

A century later, how do you do track particles ? First, you don't need to stick your eye to a microscope. You take a digital picture with a CCD camera adapted to the microscope. Of course you can take movies.

A typical image of a dense colloidal suspension, taken by confocal microscope.

Now you have about ten thousand pictures like that out of a single experiment. Of course, you can superimpose the picture with a grid, locate the coordinates of a particle by following the grid with your finger, write them down in a notebook and so on and so forth. Perrin could have done that during years, but we have computer slaves.

Crocker and Grier designed the following algorithm to track individual particles from pictures. It is probably easier to understand if we imagine the intensity of each pixel as an altitude. For example, the two pictures below are equivalent.

Noisy picture of particles

Corresponding intensity profile

Blur your image to remove noise and to smooth the particles' intensity profile. Each particle should become a peak with no flatness at the top.

Previous picture, blurred

Find the pixels that are local intensity maxima. Their must be one per particle + others due to noise.

Local maxima

If you have large areas without particles, you may find local maxima there due to noise. If you remove the local maxima that are not bright enough, you should be left with only particles, none from noise. Now you know the coordinates of each particle centre with discreet (pixel) precision.

To increase the precision, you can take the centre of mass (intensity) of the pixels surrounding each possible centre. This gives subpixel resolution (about 1/10th of a pixel).

This is an extremely quick and efficient algorithm used routinely by many groups either in 2D or in 3D (yes, you can take 3D pictures, I'll have a post about it). You can check the official web page for more information. My own code for that is on sourceforge.

So far so good if your particles have the same size ... something that almost never append in nature, and not that often in experiments. I'll write about the more-than-one-size case in an other post.

Kanto softmatter talk

A busy week is ending ... almost. I give a talk tomorrow at a workshop (yes, a Saturday !), on Monday I submit a research proposal to be paid from April. And after that I will have to work again on a paper that has been rejected.

Tomorrow is the kanto softmatter workshop, a very local meeting for the soft matter labs around Tokyo. Talks are only given by young researchers, not by big names. That is why I have an opportunity to talk. In larger conferences until now I only got poster presentations. Well, there is no bed of roses.

I will talk about my thesis work, in particular the content of the paper that was rejected: what are the local structures playing a role in a model of glass transition and which one is more important than the other. The answer is rather surprising. A glass is amorphous, so most people think that a glass is the opposite of a crystal. Therefore if glass has a structure this structure must be very different and incompatible with the crystal symmetry. That's why icosahedral order is often exhibited as a typical glass order.

A icosahedron is a solid with 20 identical faces. Like this dice used in Dungeons&Dragons.

via Wikimedia

13 particles forming a perfect icosahedron, from my thesis

As you can see, there are pentagons everywhere in that structure: icosahedron has 5-fold symmetries. The problem with five-fold symmetry is that it cannot pave space (at least in 2D and 3D). Try to pack them together and you will always have gaps.

By JF Sadoc via Wikimedia

However, the icosahedron is very dense and often maximises locally the interaction energy between the particles. Icosahedral order is locally the best structure, so it forms easily in a dense liquid, but cannot spread. That is what is called frustration.

What one can image in a supercooled liquid is icosahedral bits, probably forming a sort of network or fractal, and total disorder in the gaps. The icosahedral structure is stable, so is moves very slowly and slows the overall dynamics. If we are still in the liquid a given icosahedral bit will eventually disappears while order is formed elsewhere, but in the glass even that rearrangement is forbidden, too costly in energy to append in a reasonable time, so everything is stuck. Here is an explanation of the glass transition.

Another explanation (advertise by my boss, so my judgement may be biased) is that a supercooled liquid is by definition metastable to the crystal, so the liquids "wants" to become a crystal. Things are getting in the way (like icosahedron for example) so the crystal is not formed. However, there are stuffs in the supercooled liquid that look like a little bit like crystals. Not very healthy crystal if you pass me the expression; hunchbacks, twisted legs, broken faces, no arms ... still if you look close enough the local structure is closer to the crystal than anything else.

a) displacements b) crystalline order and c) number of neighbours in a 2D shaken granular supercooled fluid. From Keiji Watanabe and Hajime Tanaka,
Physical Review Letters (2008).

Once you have a method to detect these crystal-like stuffs, which has been done in an handful of models, you discover that they are slower than the rest of the liquid and that their size is growing when you get closer to the glass transition. Paradoxically isn't it the crystal that is responsible for the slowing down to the glass ?

Who is slowing down the system ? The locally favoured structure of the fluid or the influence of the crystal ? To answer this question I used a system that has independently icosahedra and crystal-like structures. In a few systems, people have found very slow icosahedral structures and some of them exhibited it as the proof that liquid order was the culprit. However others remarked that the "crystal" in these systems actually contains some icosahedral motifs. For example if the "crystal" is in fact a quasicrystal with five-fold symmetry, you cannot tell if the icosahedra that you see in the supercooled liquid come from the locally favoured structure of the liquid or as crystal-like stuff.

A Frank-Kasper phase, which is a crystal containing icosahedra (large blue spheres). From the Trebin lab in the university of Stuttgart.

A quasicrystal with icosahedral symmetry, via Wikimedia

To avoid that confusion, my system has a well known crystal of face centered cubic structure, without a glimpse of icosahedron in it. In addition, icosahedral order is locally favoured. In that situation, no mistake possible, the slower structure wins.

And at the end, I found that the icosahedral bits play very little role in the slowing down, the crystal-like bits are doing all the slowing work. Of course Icosahedral order plays a role : it is frustrating the crystallisation, and that is thanks to that frustration that we are able to supercool the liquid in the first place. However, that is the influence of the crystal that governs the slowing down and thus the glass transition.

Details in the paper to come ... when accepted.

PhD pre-defence training

At the end of this week one of my fellow lab member will know if he is able to write his PhD thesis. In our university this is probably the most decisive step in the process of getting a PhD.

How you get a PhD varies tremendously between countries, universities within the same country and sometimes even between departments within the same university. For example, in the US it is not uncommon to spend between 7 and 10 years in graduate school before getting the PhD. In France the distinction between undergraduate and graduate is fuzzy, but the line between Master and PhD is not: you need at least 3 years of PhD, often a few months more in science and a few years more in humanities. Here in Japan and in science/engineering departments the rules is 2 years of Master and 3 years of PhD. The PhD defence season is also tightly constrained modulo 6 months, so actually almost everybody abides by this 2+3 years minimum.

The fellow I am writing about has a quite unusual curriculum. He took a job in the industry after graduating from his Master, got sick of it and came back to the academia at the same time I was starting my PhD (the 3 last years). He had personal problems on the way and extended his PhD to 4 years. According to the training I attended on Monday, he will surely get his PhD with honours.

Defending a thesis is a rather formal - some would say "outdated" - ceremonial. It also depends a lot on the country/university. I heard that in the university of Utrecht in the Netherlands the candidate and the jury are dressed in 16-17th century outfits, family is invited and you never fail at your defence, neither do you get nasty questions. If you fail, that's before.

A PhD candidate in Utrecht

In France the dress code is less formal, but the jury can push you quite hard the D day. One of my friends in Belgium had to re-write his thesis after an inconclusive defence and defend it again a few month later.

Here in Japan everything is made to avoid last moment failure, thanks to a pre-defence. It's not a training strictly speaking. You are in front of the same jury as for the real defence, but it is before you wrote a single line of your thesis. You pack up everything you did in the last 2 years and a half into a 1h talk. The jury knows nothing of your work beforehand except the title and probably a short abstract. You don't want to obfuscate their minds or they tend to sleep. You don't want to appear shallow or you won't be able to write your thesis now. So you need to be ready, trained and mentored.

This is the decisive step. After that, you do your best to write your thesis, probably patch a few missing experiments/simulations/analysis, re-do everything just in case, etc. This easily eats the remaining 2 or 3 month before handing out the thesis, but the essential part is done. If you don't blow up during theses weeks of intense pressure and self-discouragement (I nearly did, but I was save by my family), you are done. You won't fail the D day anyway.

This fellow is going through the fire on Friday. His rehearsal on Monday was excellent (there were a few minor details to fix, but nothing important). Good luck.