tag:blogger.com,1999:blog-54575143845572689342024-02-07T15:42:12.083+00:00Kinetically ConstrainedAnonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.comBlogger70125tag:blogger.com,1999:blog-5457514384557268934.post-24787571986418093772014-08-26T18:29:00.000+01:002014-08-26T18:36:51.538+01:00Post post doc<p>Continuing what has become a quarterly theme here is summer's post:</p>
<p>One reason for a drop in blogging productivity is that I have been severely distracted by that thing that many postdocs are -- career. It's a pretty neat job being a postdoc. Like a PhD you've got more time to dig deep into a topic but you're more on top of your skills. It's flexible, it's a great way to get work abroad, you can wear a T-shirt to work and so on. It's a nice job.</p>
<p>Eventually you do start to want a permanent position. Now in academia these are hard to get and there's very little geographic control. Many have written long and angrily about this, that's not what I want to get into. It is what it is. From a practical point of view it as an excellent time to think about whether you really want that academic job -- do you want to stick of twist? In my case I've gone for twist.</p>
<p>This autumn I'll be making the move from statistical physics to statistical, er, statistics. My physics work was gradually slipping towards data science and I can't resist any longer (it's the <a href="http://www.forbes.com/sites/gilpress/2012/09/27/data-scientists-the-definition-of-sexy/">sexiest job</a> of the <a href="http://blogs.nature.com/naturejobs/2013/03/18/so-you-want-to-be-a-data-scientist">21st century</a> don't you know!). Actually I want to post about that physics/data work at some point but need to wait for reviews etc.</p>
<p>I'm really excited about my new position and all the new things I'll be learning. If possible I'd like to keep this blog going, I think there's a decent cross over with what I'll be doing next. The themes might switch more towards data than soft matter but statistics are statistics. It'll be a little sad leaving physics but I'll always see the world through a stat-mech lens, which is no bad thing for anyone in my opinion.</p>Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-8205053849682651342014-05-15T16:43:00.000+01:002014-05-16T18:58:20.757+01:00Journals for e-readersOne thing that makes me cross is that despite the terrifying amount of money our library pays to buy back our research in the form of journals, they're still not terribly easy to read. I've got an e-reader now and I'd like to read things on that, just the sort of value-added that the publishers could do. Unfortunately everything is still just a pdf file only to be printed on A4.<br />
<br />
There are <a href="http://willus.com/k2pdfopt/">some utilities</a> for coping with this but it's not really ideal.<br />
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I wanted to see how tough it is. So I tried to convert my last paper into something that would look nicer on an e-reader (in my case a kindle). The paper was written for an <a href="http://www.aps.org/publications/journals">APS</a> journal using the <a href="https://journals.aps.org/revtex">REVTeX 4.1</a> package. This makes it very easy to write papers formatted for APS (and possibly some others as well). The answer is that this was the best I could get it using REVTeX.<br />
<br />
<a href="http://people.bath.ac.uk/da246/publications/papers/Ashton2014_ereader.pdf">Ashton2014_ereader.pdf</a><br />
which originally looked like this:<br />
<a href="http://arxiv.org/pdf/1401.2064v1.pdf">http://arxiv.org/pdf/1401.2064v1.pdf</a><br />
or <a href="http://link.aps.org/doi/10.1103/PhysRevE.89.031301">here if you have access</a><br />
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It's actually not too bad! The abstract's gone a little wrong and the font is not strong enough, but it's not a disaster. It proves to me that the guys who make REVTeX could quite easily make a beautiful e-reader mode full of useful options. I made the citations clickable links for example.<br />
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To get this working I simply replaced this line<br />
<pre>\documentclass[aps, prl, twocolumn,superscriptaddress,amsmath,amssymb,floatfix]{revtex4-1}</pre>
<br />
<br />
with these lines<br />
<pre>\documentclass[12pt,a5paper,superscriptaddress,amsmath,amssymb,floatfix]{revtex4-1}
\usepackage[papersize={4.5in,6in},margin=0.5cm]{geometry}</pre>
<br />
Without the second one it doesn't seem to work very well. If you've got a better (and just as easy method) then leave a comment. I could have made it better by dropping REVTeX and customising every detail. Frankly that was proving a lot of work and that's not what I believe LaTeX should be about.<br />
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From now on I'll be uploading an e-reader version as well as an A4 version for my papers.<br />
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UPDATE:<br />
Royal Society of Chemistry, with a bit of fiddling looks fantastic on the kindle:<br />
<a href="http://people.bath.ac.uk/da246/publications/papers/Ashton2013_ereader.pdf">Ashton2013_ereader.pdf</a><br />
Had to dig about a bit to get this one-column (there's a \twocolumn[ half way down the page in the template that needs removing). Fiddled with the margins and widths a lot. See the <a href="http://people.bath.ac.uk/da246/publications/papers/ereader.tex">.tex file here</a>. Might go back to the APS paper and reduce the paper size even more. This seems to work quite nicely:<br />
<br />
<pre>\usepackage[papersize={9cm,12cm},margin=0.5cm]{geometry}</pre>
<pre></pre>
UPDATE2:
<br />
Got the RSC send-to-kindle button working and this just sends the two-column pdf. I guess the best hope is converting the html version then.<br />
<br />
FINAL UPDATE:<br />
I've found the best way I think now. It's to skip pdf altogether and go via html. Using htlatex I compiled the same original latex file into this webpage:<br />
<a href="http://people.bath.ac.uk/da246/papers/Ashton2014/">http://people.bath.ac.uk/da246/papers/Ashton2014/</a><br />
It's a bit broken here and there (you must use revtex4 and not revtex4-1, one day I'll go back through and work out all the settings needed to properly convert a revtex made file. Mostly it works.<br />
<br />
Next step was to download the <a href="http://www.amazon.com/gp/feature.html?docId=1000765211">KindleGen</a> utility and use that to convert the html to a .mobi file format. This is what I then put onto my kindle. If you download this and put it onto your kindle<br />
<a href="http://people.bath.ac.uk/da246/papers/Ashton2014/Ashton2014.mobi">http://people.bath.ac.uk/da246/papers/Ashton2014/Ashton2014.mobi</a><br />
you'll see that this is basically perfect for what you want from a Kindle version of a paper. For sure some things need fixing, for example the equations are a bit small. I'll work all of that out and make a separate post.<br />
<br />
The bottom line for this whole thing is that if I, a mostly lazy man, can get half way decent conversions of my LaTeX files onto an e-reader in an evening, then the journals could easily do this.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com1tag:blogger.com,1999:blog-5457514384557268934.post-64092914671813416442013-06-14T22:53:00.000+01:002013-06-14T22:53:43.418+01:00Networks of networks<div dir="ltr">
This week the Bath centre for<a href="http://www.bath.ac.uk/research/cncb/index.html"> "Networks and Collective Behaviour"</a>, of which I'm a member but by no means an official spokesman, had its official launch event. A fun two day meeting on "Uncertainty in interaction networks". For people such as myself who are in to statistical mechanics and the collective behaviour of systems with many parts, networks are a natural extension to what we do. It's a wonderfully interdisciplinary field with lots of cool problems to solve. Besides, networks is where I started out.</div>
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So, due to all this, my first few posts on my return from paternity leave might be networks based. From this week's meeting one thing that got me interested was people who are turning their attention to "multiplex networks". This is a word that means lots of things to me so to be more clear we're talking about separate networks that interact (this interaction is key). Usually it is assumed it is the same set of nodes with different sets of edges representing different relationships between them.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTpi4aAd9f7bJwQHSZ00xzC-jfP-KVn103WgZawKRqVkZoLfbeJZebu2paL61htwgfKCKnqAAdXGUQxrUKYYnKkhs217LYy3ouJ9t_H_Z8Gm7nGWGqm8TxQ7sHDHKOM7uCrYuSKd8wU6Yj/s1600/multiplexnet.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTpi4aAd9f7bJwQHSZ00xzC-jfP-KVn103WgZawKRqVkZoLfbeJZebu2paL61htwgfKCKnqAAdXGUQxrUKYYnKkhs217LYy3ouJ9t_H_Z8Gm7nGWGqm8TxQ7sHDHKOM7uCrYuSKd8wU6Yj/s320/multiplexnet.png" width="257" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Cartoon of a multiplex network with two different types of link</td></tr>
</tbody></table>
<div dir="ltr">
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An example given at the meeting was the power grid which is interacts with the water supply network and other services. Another example could be your social network where you distinguish between work colleagues and friends or family. Transport networks (for example bus and tube in London) will clearly interact in their function even though they are separate networks. </div>
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<br /></div>
<div dir="ltr">
Ginestra Bianconi from Queen Mary's gave a nice talk, in which she cited this <a href="http://www.pnas.org/content/107/31/13636">PNAS</a> on a network of computer gamers in a massively multiplayer online game. Data can be obtained for different types of interaction. Things such as friendship, trade, communication (positive) or enmity and attacks (negative). The authors claim that in order to properly understand the social structure one must consider all these different types on interaction. Among the things they found was that positive relationships tended to be clustered exponential networks whereas negative networks were not clustered and had powerlaw degree distributions. This means that a small number of players have a large number of negative connections. Also, different players had important roles in different networks. It certainly seems that with this extra layer of data one is in a better position to fully understand the network.</div>
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<div dir="ltr">
Ginestra's own work (in this <a href="http://iopscience.iop.org/0295-5075/102/1/16002/">EPL</a>) was concerned with political affiliation networks. This imagined two networks representing social connections in two political parties. Nodes can be active in both networks but will tend to become inactive in the opposite network to their current opinion closer to an election. There is a stat-mech model where "tend to" is represented by a field (call it temperature) that couples to how happy a node is (call it energy). I'm going to come back to this theme.</div>
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<br /></div>
<div dir="ltr">
I think multiplex networks are going to be really fun to work with. Seeing as networks are a useful simplification of reality multiplex networks seem to represent the next level of detail.</div>
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Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-24475040039732672022013-01-30T14:34:00.000+00:002013-01-30T14:34:08.241+00:00Back in the summerI realise things have gone pretty quiet around here. It turns out having a baby takes away pretty much any spare time you thought you had.<br />
<br />
I still have big plans for this blog and as the number of times I'm wide awake at 3am decreases I can see the light at the end of the sleep deprived tunnel. So I'm planning to have a quiet relaunch in the summer when I'll hopefully get some regularity back.<br />
<br />See you soon.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-36131988559815295302012-05-07T12:52:00.000+01:002012-05-07T12:52:25.508+01:00Journal Club: A New Blog<div class="tr_bq">
I've just started a new blog <a href="http://www.scmjournalclub.org/">www.scmjournalclub.org</a>. It's definitely in what you'd call the beta phase right now. I will certainly be changing the layout and gradually adding more permanent content over the next few weeks.<br />
<br />
Contributions welcome to <a href="mailto:submissions@scmjournalclub.org">submissions@scmjournalclub.org</a>.</div>
<br />
While I do sometimes get a bit technical, Kinetically Constrained is hopefully of interest to people inside and outside of the field. The idea for the journal club is that it is aimed at people working in the area of soft matter and statistical mechanics. In particular I want it to be useful for postgraduate students who would find it helpful understanding papers they may have found a bit impenetrable otherwise.<br />
<br />
How it will all work will hopefully evolve. I hope one day enough people check it out that the following scenario happens. A PG student presents a paper as best they can that they might be having trouble understanding. A comment thread follows and the problems get sorted out. Everyone wins.<br />
<br />
I also suspect that hundreds of journal clubs happen each week in different universities. While I understand people might not want this to be public, for those that don't mind they could put their presentation on SCM journal club where it can benefit even more people.<br />
<br />
To kick things off <a href="http://www.scmjournalclub.org/2012/05/new-hard-sphere-equation-of-state.html">I've started with a recent paper</a> on the arXiv by Andrés Santos on one of my favourite topics – hard spheres.<br />
<blockquote>
<b>Brief Summary</b><br />
In liquid-state theory the hard sphere equation of state is of particular importance because it is a fantastic reference system for a whole host of molecular and in particular colloidal liquids. The hard sphere equation of state (EoS) tells you what pressure you need to compress a your spheres to get a given density. With an analytical form for the EoS one can calculate any thermodynamic property one desires.</blockquote>
<blockquote>
Percus-Yevick (PY) is a way to close to the Ornstein-Zernicke (OZ) equation – an exact relation between correlation functions – and is usually solved by either the compressibility route or the virial route. You’re basically choosing how your approximation enters. Here Santos has taken a different route, following the chemical potential, and it gives a slightly different closure to OZ.
</blockquote>
<blockquote>
Carnahan-Starling is an incredibly simple EoS for hard spheres which is in common use (fluid phase). It can be written as a 1/3-2/3 mix of the compressibility and virial PY routes. In a similar way Santos writes a 2/5-3/5 mix of compressibility and chemical potential routes and gets a similarly simple expression – which is ever-so-slightly better than Carnahan-Starling.</blockquote>
<div>
I'm more than happy to take contributions. I think it's nicer if people say who they are but I'll hold back the name if that's the barrier to submitting (provided it's not an anonymous destruction of a rival's paper). You can submit via <a href="mailto:submissions@scmjournalclub.org">submissions@scmjournalclub.org</a>. For interested regulars I can look into direct posting via blogger.</div>Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-52011912307625002892012-04-25T09:50:00.003+01:002012-04-25T10:01:21.857+01:00The Renormalisation GroupA new video which more or less completes the critical phenomena series. <a href="#zoom">Jump straight to</a> it if you want to skip the background.<br />
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One of my favourite topics is the critical point. I've posted many times on it, so to keep this short you can go <a href="http://www.kineticallyconstrained.com/2009/05/critical-point.html">back here for a summary</a>. In brief, we're looking at a small point on the phase diagram where two phases begin to look the same. The correlation length diverges and all hell breaks loose. Well, lots of things diverge. At the critical point all length scales are equivalent and, perhaps most remarkably, microscopic details become almost irrelevant. Different materials fit into a small number of <a href="http://www.kineticallyconstrained.com/2011/07/universality-at-critical-point.html">universality classes</a> that share broad properties such as symmetry or dimensionality.<br />
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For a long time this universal nature was known about but it couldn't be said for sure if it was a truly universal thing, or just a really good approximation. Then along came the renormalisation group (RG), which gave a strong theoretical basis to critical phenomena and sorted everything out.<br />
<br />
The renormalisation group is usually at the back end of an advanced statistical mechanics course, and that is not the level I'm going for with this blog. However, when making the videos for the demonstration of <a href="http://www.kineticallyconstrained.com/2009/05/critical-point.html">scale invariance</a> and <a href="http://www.kineticallyconstrained.com/2011/07/universality-at-critical-point.html">universality</a> it became apparent that, even just making the pictures for these videos, I had to use RG. Even if I didn't realise it.<br />
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First I'll try to explain schematically what RG aims to do. Then I'll show how this is similar to how I make my pictures, and finally we'll get to a demonstration of RG flow at the end. I'll try not to dumb it down too much but I also want to be as quick as possible.<br />
<h4>
Renormalisation group</h4>
Let's look at how we do this with the Ising model. A simple model for a magnet where spins, sigma, (magnetic dipoles) can point up or down, $latex \sigma=\pm 1$, and like to align with their neighbours through a coupling constant, $latex J$. The energy is a sum over nearest neighbour pairs<br />
<br />
<div style="text-align: center;">
$latex \displaystyle E=\sum_{ij} -J \sigma_i \sigma_j$</div>
<div style="text-align: center;">
<br /></div>
Where RG enters is to say that, if the physics is the same on all length scales, then we should be able to able to rescale our problem, to cast it on a different length scale, and get back the same thing. In real-space RG this is done by blocking. We bunch a group of our spins up together and form a new super spin that takes on the majority value of its constituents. It's as though the spins in the block get together and vote on how they want to be represented, and then we can deal with them as one.<br />
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Here's what it looks like. Take an Ising model configuration<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdzn5pj60idoB6Eb_a6V5d-NaTppDXwGKsWerFk1icQVu99Rhcddjt-qkReM2EyDkdo5Z4VQiS4S7X8XKGSzEcwN5TCd9V_7rX2e7HhumblQyMVnTXEnzNO_V8UkHEDmrNEHZqDdGYwNMe/s1600/rgising1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdzn5pj60idoB6Eb_a6V5d-NaTppDXwGKsWerFk1icQVu99Rhcddjt-qkReM2EyDkdo5Z4VQiS4S7X8XKGSzEcwN5TCd9V_7rX2e7HhumblQyMVnTXEnzNO_V8UkHEDmrNEHZqDdGYwNMe/s320/rgising1.png" width="320" /></a></div>
Block them together<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2wXYz0hogmESrXc1eoppHetlJoCU1cIueTzyemJrWUYsV5QK73o5tgTzMJ7m2XtxtWsQTQRR3ik5uxslpn_Ub4ZXydw6w4Zd92dVtjKT8Mvl1elBWaaZ7YrEC9632ZLpLTJF5IKzYjCCn/s1600/rgising2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="288" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2wXYz0hogmESrXc1eoppHetlJoCU1cIueTzyemJrWUYsV5QK73o5tgTzMJ7m2XtxtWsQTQRR3ik5uxslpn_Ub4ZXydw6w4Zd92dVtjKT8Mvl1elBWaaZ7YrEC9632ZLpLTJF5IKzYjCCn/s320/rgising2.png" width="320" /></a></div>
<br />
And vote<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKW0FlvfegIU7Koi7UesMS6OIt4D7CZvQa_doKMniMVNTDOwFAqRJJCrKa__4WCUMsSIml-fsEzaQh4K3CVnPG4bV61Pm09F4osULrHFCor_YKe3HPrhARJGlUK_d9W9WPVZcrZRmtLpGs/s1600/rgising3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="297" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKW0FlvfegIU7Koi7UesMS6OIt4D7CZvQa_doKMniMVNTDOwFAqRJJCrKa__4WCUMsSIml-fsEzaQh4K3CVnPG4bV61Pm09F4osULrHFCor_YKe3HPrhARJGlUK_d9W9WPVZcrZRmtLpGs/s320/rgising3.png" width="320" /></a></div>
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We're left with a pixelated version of the first picture. Now here I will slightly deviate from RG as standard. The next step is to ask, if these super spins were a standalone Ising model, what temperature would they have? If our initial system is right on the critical point then the renormalised (blocked) system should have the same temperature because it should look exactly the same – scale invariance. If you're even slightly off then the apparent temperature, let's call it $latex T_{RG}$, will flow away from the critical point towards a fixed point.<br />
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These fixed points are the ferromagnet (all spins the same, $latex T_{RG}=0$) or the paramagnet (completely random, $latex T_{RG} \rightarrow \infty$) as shown below.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcVKubq-vOYZH_oPFPeXwEK467GKo1vP3LouPqUV9b6FADjI-QrbwLOkdUFAG9QkWwRyTvYQ7NGFxS0vIeMe0m4-UylaEtX15h5zkdtUKg3TYr9_0AavcgSppfkRuxRaSVwNplR3kJkQZA/s1600/rgising4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="140" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcVKubq-vOYZH_oPFPeXwEK467GKo1vP3LouPqUV9b6FADjI-QrbwLOkdUFAG9QkWwRyTvYQ7NGFxS0vIeMe0m4-UylaEtX15h5zkdtUKg3TYr9_0AavcgSppfkRuxRaSVwNplR3kJkQZA/s400/rgising4.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
Normally RG is done in terms of coupling constants rather than temperature. However, I think in our case temperature is more intuitive.<br />
<h4>
Zooming out</h4>
<div>
By now the link between RG and the pictures I make may already be clear. The configurations I will show below are made of something like $latex 10^{10}$ spins. Clearly I can't make a 10 Giga pixel jpeg so I have to compress the data. In fact the way I do it is an almost identical blocking process. Spins are bundled into $latex b \times b$ blocks and I use a contrasting function (a fairly sharp tanh) that is not far away at all from majority rule as described above.<br />
<br />
If we start by zooming in to a 768x768 subsection then each pixel is precisely one spin. As we zoom out we eventually need to start blocking spins together. In the video below there are three systems: one ever-so-slightly below $latex T_c$, one ever-so-slightly above $latex T_c$ and one right on the money. At maximum zoom they all look pretty much the same. If you had to guess their temperatures you'd say they're all critical.<br />
<br />
As we start to zoom out we can see structure on length scales, and the apparent temperatures start to change, in fact they flow towards the fixed point phases. Video below, recommend you switch on HD and watch it full screen<a href="http://draft.blogger.com/blogger.g?blogID=5457514384557268934" name="zoom">.</a><br />
<br />
<iframe allowfullscreen="" frameborder="0" height="335" src="http://www.youtube.com/embed/MxRddFrEnPc?rel=0" width="450"></iframe><br />
<br />
So there it is. RG in action. If you're not precisely on the critical point then you will eventually find a length scale where you clearly have a ferromagnet or a paramagnet. At the critical point itself you can zoom out forever and it will always look the same. The renormalisation group is a really difficult subject, but I hope this visualisation can at least give a feeling for what's going on, even if the mathematical detail is a bit more challenging.</div>
<div>
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<div>
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<br />Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-43277568751522370072012-04-18T16:51:00.001+01:002012-04-22T10:40:13.447+01:00The thermodynamic limit<div>
This post has been at the back of mind for a while and written in small, most likely disjoint pieces. I wanted to think about connecting some of the more formal side of statistical mechanics to our everyday intuitions. It's probably a bit half baked but this is a blog not a journal so I'll just write a follow-up if I think of anything.<br />
<br />
I'm often accused of living in a rather idealised world called the thermodynamic limit.</div>
<br />
This is completely true.<br />
<br />
To see why this is a good thing or a bad thing I should probably say something about what I think it is. I'll start at the colloquial end and work up, first let's say that in the thermodynamic limit everything is in equilibrium.<br />
<h4>
Nothing ever changes around here</h4>
If you put enough stuff in a jar, keep it sealed in a room that stays the same temperature, and give it enough time then it will eventually end up in its equilibrium state. One could argue that the real equilibrium is the grey mush at the end of the universe so clearly I'm going for some time scale that's enough to let everything in the jar settle down but not so much that I get bored waiting for it. For atoms and molecules this usually gives us a window between roughly a picosecond (10^-12 seconds) and lets say a 100 seconds (I get bored pretty easily). Once it is in equilibrium the contents of the jar will stay in the same state forever – or until it gets kicked over. The point is that in equilibrium nothing changes.<br />
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Or does it? To our eyes we may see no change, but the atoms inside the jar will be wriggling furiously, perhaps even diffusing over great distances. How could such great change on the small scale be consistent with eternal boredom on the macroscopic length scale? The answer has two parts. Firstly, the atoms that make up the world are all frighteningly similar. So if one diffuses away it will quickly be replaced by an indistinguishable substitute. The second part motivates the "enough stuff" part of the previous paragraph.<br />
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Listen to a group of people talking and the conversation will ebb and flow, and sometimes go completely quiet. Sit in a busy cafe and all you can hear is general noise. A sort of hubbub that you can easily identify as conversation, maybe you can even get a feel for the mood, but you can't tell what anyone is saying. In the thermodynamic limit there are so many atoms that all we can see is a sort of average behaviour. We can tell what sort of state it is (a liquid, a solid, a magnet – the mood) but the individuals are lost.<br />
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So as we lumber towards a stricter definition of the thermodynamic limit we should think about what we mean by a state. I've <a href="http://www.kineticallyconstrained.com/2009/02/entropy.html">talked about this before</a>. In statistical mechanics there is a huge difference between a 'state' and a 'configuration'. By configuration we mean the exact position (and sometimes velocity) of every particle in the jar. We're doing this classically so we won't worry about uncertainty. A state, in the stat-mech sense, is an ensemble of configurations that share some macroscopic property. For example their density, or magnetisation, or crystal structure.<br />
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To be the equilibrium state, the corresponding configurations must satisfy at least one of two criteria (ideally both). Firstly they should have a low energy compared to the other configurations. If particles attract they should be close, if dipoles point the same way they should try to do that. This is intuitive, balls roll down hill, systems like to lower their potential energy. Secondly there should be a lot of them. An awful lot of them. This is often referred to as entropy, but really I'm just saying you need to buy a lot of tickets to guarantee winning a prize.<br />
<h4>
A bit more mathematical</h4>
This combination of potential energy, U, and entropy, S, is known as the free energy. You can write it down as:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhABmTDhV2ifDEPwSp67k1eVJhkG2nQpsI3iodjWQ-4GCRnV8gjcMiX5dCeTpFjXTQSROiOnndMm9QGh6H1Hpx5erdwP9ga_X47PITtlim_rGTbBJogLSAgewpaaO0jI1pzrwhXLH3iN0er/s1600/eqFreeEnergy.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhABmTDhV2ifDEPwSp67k1eVJhkG2nQpsI3iodjWQ-4GCRnV8gjcMiX5dCeTpFjXTQSROiOnndMm9QGh6H1Hpx5erdwP9ga_X47PITtlim_rGTbBJogLSAgewpaaO0jI1pzrwhXLH3iN0er/s1600/eqFreeEnergy.png" /></a></div>
High temperatures, T, favour high entropy (lots of configurations), low temperatures favour low energy. In statistical mechanics, unlike normal mechanics, systems lower their free energy and not just their energy. The state with the lowest free energy is the equilibrium state. No exception.<br />
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The aim with statistical mechanics is to write down equations that take interactions on the individual particle level and relate this to the probability of finding the particles in a particular configuration. In the mathematical sense the final step is known as "taking the thermodynamic limit", and this means taking the number of particles in your equation, N, to infinity.<br />
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It is these infinities that make states formally stable, and give us phase transitions. Infinitesimal changes in conditions, such as temperature, can lead to dramatic changes to the equilibrium state. Of course there are not infinity particles in the real world. However, with roughly 10^24 water molecules in my cup of tea it's a pretty good approximation.<br />
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To be in the thermodynamic limit, therefore, we an infinite amount of stuff sitting for an infinite amount of time. The system must be able to explore all configurations to decide which state to settle on. You can see where we're going to run into problems.<br />
<h4>
Back to the real world</h4>
Getting back to the start of this post, why are my accusers being so accusatory? Most likely because the real world, for the most part, is massively out of equilibrium. From stars and galaxies, down to swimming bacteria. Then there are materials, such as glasses, where the relaxation time has become so long that the equilibrium state can't be reached in times longer than the age of the universe. Or some say forever – but I'll come back to ergodicity at a later date.<br />
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In colloid land things get quite interesting. As mentioned in a <a href="http://www.kineticallyconstrained.com/2011/02/colloids-are-just-right.html">previous post</a>, colloids that are big enough to easily see take about a second to move around enough to start equilibrating. That's very close to me getting bored, so if it's a dense system or there are strong attractions one can expect colloids to quickly fall out of equilibrium.<br />
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The theoretical framework for life out of equilibrium is hugely more complicated that at equilibrium. Even quantities such as temperature start to lose their meaning in the strictest sense. In fact, while people are working hard and no doubt making progress, it's safe to say that it will never be as elegant – or let's say as easy – as what we have in the thermodynamic limit.<br />
<h4>
All is not lost</h4>
So this means everything we study in equilibrium is useless? It clearly doesn't exist. Well it's true nothing in the universe meets the strict definition of infinite time and infinite stuff, but in reality it's usually alright to have a lot of stuff and enough time. In fact we regularly study systems with only hundreds of particles and correctly predict the phase behaviour. It's usually the enough time part that is the problem.<br />
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Knowing what the equilibrium state should be is a bit like knowing the destination but not the journey. In many many cases this is enough, atoms can rearrange themselves so quickly that it doesn't really matter how they get where they're going. Of course in many cases that we worry about today we need to know both where the system is going, and how it will get there. It could be that on the way to the true equilibrium state we get stuck in a state with low, but not the lowest, free energy. A bit like settling on your favourite restaurant before going to the end of the street and trying them all. In this case we can maybe plot a different route through the phase diagram with controls such as pressure and temperature.<br />
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Increasingly these pathways to self-assembly are the focus for many in the statistical mechanics community. We want to design new materials with exotic thermodynamic ground states (equilibrium states), so it is really important to know what will happen in the thermodynamic limit – we will always need phase diagrams. But with colloids, they're pretty impatient and will easily settle for the wrong state, so we also need to think carefully about how we will get to the ground state. It's an exciting time right now because experimentally we're even able to mess around with the fundamental interactions between particles in real time, numbers that we usually take as constants can suddenly be changed. it really is possible to control every stage of the assembly process from the start all the way to the end.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com2tag:blogger.com,1999:blog-5457514384557268934.post-5775789707676911142012-04-13T13:53:00.000+01:002012-04-13T13:53:03.636+01:00Less illMy spritely return has been a bit slower than I thought. However, thanks to the lovely people who work in the Dutch medical system I'm pretty much back.<br />
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Long winded post on the thermodynamic limit coming very shortly, then a follow up on ergodicity that I've been toying with. I've also got a new spin on the criticality videos that demonstrates the renormalisation group in action – I'm really really pleased with this video. Oh, and I'm at a conference next week so I'll round up some of the nice talks. There are a couple on critical Casimir forces so I may be compelled to put something down about that.<br />
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So lots coming up.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-30079138952194866372012-03-06T17:31:00.000+00:002012-03-06T17:31:05.186+00:00been illApologies 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.<br />
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Hopefully a spritely return in the next few weeks.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-7134403059388907562012-01-21T11:36:00.000+00:002012-04-22T10:40:46.312+01:00Just hurry up and sit down!As a semi frequent flyer, and incredibly impatient stand-behinderer I couldn't resist linking to this - <a href="http://link.aps.org/doi/10.1103/PhysRevE.85.011130">Time needed to board an airplane: A power law and the structure behind it</a> from a Norwegian group, Vidar Frette and Per Hemmer.<br />
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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.<br />
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Of course many people do look at specific strategies. For example <a href="http://www.sciencedirect.com/science/article/pii/S0377221701002946">here</a>, 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 <a href="http://menkes76.com/projects/boarding/boarding.htm">Menkes van den Briel</a>. There you can see videos of all the different strategies.<br />
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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.<br />
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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.<br />
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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.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com2tag:blogger.com,1999:blog-5457514384557268934.post-76227454011701184962012-01-15T18:26:00.001+00:002012-04-22T10:40:58.986+01:00Clustering in sea-ice floesI 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.<br />
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I've been walking around with this <a href="http://dx.doi.org/10.1103/PhysRevE.84.056104">interesting paper</a>, "Molecular-dynamics simulation of clustering processes in sea-ice floes" by Agnieszka Herman, in my bag since November. It was picked up in the <a href="http://physics.aps.org/synopsis-for/10.1103/PhysRevE.84.056104">spotlight section</a>, in <a href="http://pre.aps.org/">Phys. Rev. E</a> (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.<br />
<h4>
Marginal ice zone</h4>
<div>
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.</div>
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<div>
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.</div>
<h4>
Granular gases</h4>
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 <a href="http://www.kineticallyconstrained.com/2011/02/colloids-are-just-right.html">context of colloids</a> – the last bastion of thermodynamics before everything goes granular.
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<br />
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.<br />
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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!<br />
<h4>
Comparing to real life</h4>
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.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjY9a2ZoznfHO9dvkk6FPGBMPJ7dnOLsmWrOonTAc9HjIc00V3qMzHvrjDQMnZ0_EKILaHT8rht49WNctu190Q3GXjfKbY-xJlM4ifIfGa7mcm5-TNmhGZtrQNrRrP01XwCKhGGRcBHI6wr/s1600/seaice.png" imageanchor="1"><img border="0" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjY9a2ZoznfHO9dvkk6FPGBMPJ7dnOLsmWrOonTAc9HjIc00V3qMzHvrjDQMnZ0_EKILaHT8rht49WNctu190Q3GXjfKbY-xJlM4ifIfGa7mcm5-TNmhGZtrQNrRrP01XwCKhGGRcBHI6wr/s320/seaice.png" width="320" /></a></div>
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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.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjttR8y3Wqi_SNIm4HZR6Dbj6u1h0AyR6oHcaOGfZzBmM67j1KZmdJj9N-ROy_hGL-HSfUMJVSHi5-1ZZQ-xkZ6Qdjo6P75UOWqLMRBipsftjNYrc9P0f2mcJLdxS7VlGyf7eOcVo60yU09/s1600/Herman_A0.60.jpg" imageanchor="1"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjttR8y3Wqi_SNIm4HZR6Dbj6u1h0AyR6oHcaOGfZzBmM67j1KZmdJj9N-ROy_hGL-HSfUMJVSHi5-1ZZQ-xkZ6Qdjo6P75UOWqLMRBipsftjNYrc9P0f2mcJLdxS7VlGyf7eOcVo60yU09/s400/Herman_A0.60.jpg" width="400" /></a></div>
At higher densities – more collisions – you can still see the gaps behind the large floes, although the distribution of velocities is now narrower.
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjM3542eWfUtxryLv2cOCO7UmVnLQM1_sc2abZjFcl4qpeYmfDIYV5BZh4S_lFf0T91doujOmgxS0EgXBgBtonCNrla3StTgIQ0HRE-8K6YAbauwWFA5oaoSBpacNpm1_2x17sJRqyVr4l3/s1600/Herman_A0.85.jpg" imageanchor="1"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjM3542eWfUtxryLv2cOCO7UmVnLQM1_sc2abZjFcl4qpeYmfDIYV5BZh4S_lFf0T91doujOmgxS0EgXBgBtonCNrla3StTgIQ0HRE-8K6YAbauwWFA5oaoSBpacNpm1_2x17sJRqyVr4l3/s400/Herman_A0.85.jpg" width="400" /></a></div>
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.
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Big thanks to Agnieszka for providing the colour images. Images, copyright APS, are reproduced with permission from the paper <a href="http://pre.aps.org/abstract/PRE/v84/i5/e056104">Phys. Rev. E 84, 056104 (2011)</a>.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-86417410429520799102011-12-22T16:25:00.003+00:002011-12-22T16:25:49.196+00:00Networks in Nature PhysicsFor those with access, looks like Nature Physics has a <a href="http://www.nature.com/nphys/journal/v8/n1/index.html">complexity issue</a>. With articles by Barabási and Newman and the likes, it looks like it has a solid networks bent.<br />
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There's a paper on community structure by my favourite physicist, <a href="http://www.nature.com/nphys/journal/v8/n1/abs/nphys2162.html">Mark Newman</a>, that I'm looking forward to reading.<br />
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Enjoy!Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com4tag:blogger.com,1999:blog-5457514384557268934.post-66411654421074587312011-11-15T09:32:00.001+00:002014-05-18T14:35:35.702+01:00We all do economicsThe very interesting blog, Mind Hacks, has a post on a <a href="http://mindhacks.com/2011/11/12/a-theory-of-the-bipolar-economy/">theory of a bipolar economy</a>.<br>
<blockquote class="tr_bq">
A 1935 Psychological Review <a href="http://dx.doi.org/10.1037/h0059138">article</a> 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.</blockquote>
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.<br>
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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!Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-31819702267352839892011-11-07T14:25:00.001+00:002011-11-14T11:08:18.218+00:00A phase diagram in a jarOne of the things I love about colloids is just how visual they are. Be it watching them jiggling around under a <a href="http://www.chm.bris.ac.uk/pt/paddy/movie.swf">confocal microscope</a>, or the <a href="http://physics.nyu.edu/pine/Pine___Res___Clusters.html">beautiful TEM</a> images of crystal structures, I always find them quite inspirational, or at least instructional, for better understanding statistical mechanics.<br />
<h4>
Sedimentation</h4>
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 <a href="http://www.chem.polimi.it/people/faculty/roberto-piazza/">Roberto Piazza</a> 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.<br />
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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, <a href="http://www.nasa.gov/centers/glenn/about/fs12grc.html">most of them</a>). As is often the way it turns out you can turn this into a big advantage. What <a href="http://link.aps.org/doi/10.1103/PhysRevLett.71.4267">Piazza did</a>, and then <a href="http://link.aps.org/doi/10.1103/PhysRevB.53.5043">others later</a>, 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.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrLZBjeMl-jo5dOy-3nXr_3H-NrRIWCEuZ4KbwEop2yquRxbKlMD66d47qzG-S_VQsgaMjMNvs9W1wTc320OQh9Qnit2uqkwDe7xjzBepVNKbo6ucF-Dinky_f0GGy-99zhPx8OtW8Xjur/s1600/phase_rutgers.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="223" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrLZBjeMl-jo5dOy-3nXr_3H-NrRIWCEuZ4KbwEop2yquRxbKlMD66d47qzG-S_VQsgaMjMNvs9W1wTc320OQh9Qnit2uqkwDe7xjzBepVNKbo6ucF-Dinky_f0GGy-99zhPx8OtW8Xjur/s320/phase_rutgers.jpg" width="320" /></a></div>
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The nicest example is from <a href="http://physics.nyu.edu/~pc86/index.html">Paul Chaikin's</a> 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.<br />
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<h4>
Equation of State</h4>
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).
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0WZCtSIVUe0H4gzx3QmpmfsQRtcHx17HEvoa4pttDaYg2MIrLOKet2Teay9bLNM0n7ct88anPcWjescliL36o5CU815yk-NBzLXu8M63EvjenhRbBXyUI56kCGLGkznkRcY0O224fsb2C/s1600/eos_rutgers.jpg" imageanchor="1"><img border="0" height="302" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0WZCtSIVUe0H4gzx3QmpmfsQRtcHx17HEvoa4pttDaYg2MIrLOKet2Teay9bLNM0n7ct88anPcWjescliL36o5CU815yk-NBzLXu8M63EvjenhRbBXyUI56kCGLGkznkRcY0O224fsb2C/s400/eos_rutgers.jpg" width="400" /></a></div>
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.
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So I think this is all very nice. I nicked the above images from <a href="http://physics.nyu.edu/~pc86/index.html">Paul Chaikin's website</a>, I recommend having a poke around, there's loads of great stuff (you really need to see the m&ms).<br />
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<br /></div>Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com2tag:blogger.com,1999:blog-5457514384557268934.post-20936100689886907352011-11-04T19:04:00.001+00:002011-11-04T19:04:06.724+00:00Back from the deadCan'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!<br />
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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!<br />
<h4>
The Dutch are good at science</h4>
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.<br />
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<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/GvY8dQQI13Q" width="420"></iframe>
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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".<br />
<h4>
What about statistical mechanics?</h4>
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.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyLrDTTDvCbj-OS7WCcf-_pIA_Ol1u731XWCkjxymjaim2-clPEIuLu1T0-g3pB5lm4BJw-IFe83DwufqHwv2VEvV6nXaXhZz15bioIbxEk8JJLiW6UFdBwbv-NeIJzYP7-1EaV01juQeB/s1600/IMG_0322.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyLrDTTDvCbj-OS7WCcf-_pIA_Ol1u731XWCkjxymjaim2-clPEIuLu1T0-g3pB5lm4BJw-IFe83DwufqHwv2VEvV6nXaXhZz15bioIbxEk8JJLiW6UFdBwbv-NeIJzYP7-1EaV01juQeB/s200/IMG_0322.JPG" width="200" /></a></div>
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<a href="http://en.wikipedia.org/wiki/Peter_Debye">Peter Debye</a> 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.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjun3NqiNbLQBLyybRJHKGjvI7xGaS6LCTPZ-EyHeY0s0jc65y8wkXSflaX-LT_kfCMOJNjsHFNlVoZVblvJtftx2fCMvkhILodJjAdmAGH_vJ85a6qVJj_hsTjaGr6npM5-N3a815NSEeY/s1600/IMG_0323.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjun3NqiNbLQBLyybRJHKGjvI7xGaS6LCTPZ-EyHeY0s0jc65y8wkXSflaX-LT_kfCMOJNjsHFNlVoZVblvJtftx2fCMvkhILodJjAdmAGH_vJ85a6qVJj_hsTjaGr6npM5-N3a815NSEeY/s200/IMG_0323.JPG" width="150" /></a>As well as working in the Debye Institute I also work in the Ornstein Lab, after <a href="http://en.wikipedia.org/wiki/Leonard_Ornstein">Leonard Ornstein</a>. 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.</div>
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<span class="Apple-style-span" style="font-weight: bold;">Enough history</span></div>
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.Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-5457514384557268934.post-8860550784829445522011-07-09T00:26:00.000+01:002011-07-09T00:26:34.156+01:00Universality at the critical pointTime for more critical phenomena.<br />
<h4>Another critical intro</h4>I've talked about this <a href="http://www.kineticallyconstrained.com/2009/05/critical-point.html">a lot</a> <a href="http://www.kineticallyconstrained.com/2009/08/biological-membranes.html">before</a> so I will only very quickly go back over it. The phase transitions you're probably used to are water boiling to steam or freezing to ice. Now water is, symmetrically, very different from ice. So to go from one to the other you need to start building an interface and then slowly grow your new phase (crystal growth). This is called a first order phase transition and it's the only way to make ice.<br />
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Now water and steam are, symmetrically, the same. At most pressures the transition still goes the same way – build an interface and grow. However, if you crank up the pressure enough there comes a special point where the distinction between the two phases becomes a bit fuzzy. The cost of building an interface goes to zero so there's no need to grow anything. You just smoothly change between the two. This is a second order, or continuous, phase transition and it's what I mean by a critical point.<br />
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As I've demonstrated before, one of the consequences of criticality is a loss of a <a href="http://www.youtube.com/watch?v=fi-g2ET97W8">sense of scale</a>. This is why, for instance, a critical fluid looks cloudy. Light is being scattered by structure at every scale. This insight is embodied in the theory of the renormalisation group, and it got lots of people prizes.<br />
<h4>Universality</h4>A second feature of critical phenomena is universality. Close to the critical point it turns out that the physics of a system doesn't depend on the exact details of what the little pieces are doing, but only on broad characteristics such as dimension, symmetry or whether the interaction is long or short ranged. Two systems that share these properties are in the same universality class and will behave identically around the critical point.<br />
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At this stage you may not have a good picture in your head of what I mean, it does sound a bit funny. So I've made a movie to demonstrate the point. The movie shows two systems at criticality. On the left will be an Ising model for a magnet. Each site can be up or down (north or south) and neighbouring sites like to line up. The two phases at the critical point are the opposite magnetisations represented here by black and white squares.<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1eD4e5rcMqUH1KRZ_CzbR4OTq2thOCTLizqHiqs0m18WC2gR3hu-QY_KSLmE7FQkWKtWIVagYJKh4sHDzxJz3RSjvMHJPkhUKrtCQf5c93LdUXAPpTYJBs-UJRfUwoGGTX3fAXSfl26Xw/s1600/ising_uni.png" imageanchor="1" style=""><img border="0" height="200" width="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1eD4e5rcMqUH1KRZ_CzbR4OTq2thOCTLizqHiqs0m18WC2gR3hu-QY_KSLmE7FQkWKtWIVagYJKh4sHDzxJz3RSjvMHJPkhUKrtCQf5c93LdUXAPpTYJBs-UJRfUwoGGTX3fAXSfl26Xw/s200/ising_uni.png" /></a></div>On the right will be a Lennard-Jones fluid. This is a model for how simple atoms like Argon interact. Atoms are attracted to one another at close enough range but a strong repulsion prevents overlap. The two phases in this case are a dense liquid and a sparse gas.<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH37iDJxJzr2i59k36fIW0B22vklDp2HFnKega1sgtgvmZyKxcqUWyKWybTxG33vYAVXpiG6_t6z5ee8u7HLjKJEj8Jo6ONJEJW1AY-xh-gNW51RsVoexwT2fxETHlC6BmTqIcCuWXX2j4/s1600/lennard_uni.png" imageanchor="1" style=""><img border="0" height="199" width="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH37iDJxJzr2i59k36fIW0B22vklDp2HFnKega1sgtgvmZyKxcqUWyKWybTxG33vYAVXpiG6_t6z5ee8u7HLjKJEj8Jo6ONJEJW1AY-xh-gNW51RsVoexwT2fxETHlC6BmTqIcCuWXX2j4/s200/lennard_uni.png" /></a></div><br />
One of these systems lives on a lattice, the other is particles in a continuous space that are free to move around. Very different as you can see from the pictures. However, what happens when we look on a slightly bigger length scale? Role the tape!<br />
<iframe width="425" height="349" src="http://www.youtube.com/embed/Kd4UvhUsBAU" frameborder="0" allowfullscreen></iframe><br />
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At the end of the movie (which you can view HD) the scale is about a thousand particle diameters across containing about 350,000 particles and similar for the magnet. At this distance you just can't tell which is which. This demands an important point: These pictures I've been making don't just show a critical Ising model, they pretty much show you what <i>any</i> two-dimensional critical system looks like (isotropic, short range...). Even something complicated from outside of theory land. And this is why the theory of critical phenomena is so powerful, something that works for the simplest model we can think of applies exactly - not approximately - to real life atoms and molecules, or whatever's around the kitchen.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com1tag:blogger.com,1999:blog-5457514384557268934.post-29999987735289953642011-06-15T16:28:00.001+01:002011-06-15T17:57:43.909+01:00Meeting is goodOnce again I find myself making some excuse as to why it's been over a month since my last post. My first reason is I'm finishing up my current postdoc. My other reason is I've been doing lots of travelling. This is much more exciting as I've been finding out more about all the cool soft matter / stat-mech work that is going on in the UK. Some of which I will blog about in time. I've also learned that half the people in soft matter in the UK have worked at some point in the Netherlands, which is handy because I'm moving to the Netherlands!<br />
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<h4>Getting to the point</h4>All this travelling is related to the topic I wanted to get to today - the value of meeting. I was started off thinking about this thanks to <a href="http://www.timeshighereducation.co.uk/story.asp?storyCode=416433&sectioncode=26">Alice Bell's article in the THE</a> on the value of the seminar. Here Alice calls for seminars to be posted online, something I agree with very much, as a way to reach more people (and to improve the standard a bit). From my experience I've had to use hundreds of pounds of grant money touring the country giving the same seminar. While I value that experience - meeting the people in the groups, direct interaction and so on - it's a shame that people at other universities can't see the talk as well.<br />
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Of course if people knew it was online they may not turn up, but hopefully not. I might start sticking mine up here.<br />
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The more efficient way of way of reaching many like-minded academics is of course the conference. A good conference can do wonders for your creativity and enthusiasm, it can give you an instant snapshot of the state-of-art and you can meet future employers/collaborators.<br />
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But they can be a bit stuffy and long. And expensive. So I'd like to fly the flag for a third kind of academic interaction, the informal science "retreat". Not long ago we had our annual Cornish Soft Matter weekend. A small group of physicists and chemists from a couple of universities got together for a more relaxed meeting. Talks were projected onto a sheet, we were sitting on sofas or the floor, and the start of a talk would be delayed due to people making a last minute cup of tea (usually this was me). All this in a really nice setting.<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQgKXCmu7OWLMGw2PkoVDtgHNVhnmHisiAmf6AR6WM0HYPEqmYVNHNsuLA0fsHguTn5wBgXs3DWQAf501NHG6aa_Wsw4tfrjEdMe_brfSBlQHQmVzbhdasnm4fQ_8krtm1mGL_-FZg44A9/s1600/IAmBWh.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQgKXCmu7OWLMGw2PkoVDtgHNVhnmHisiAmf6AR6WM0HYPEqmYVNHNsuLA0fsHguTn5wBgXs3DWQAf501NHG6aa_Wsw4tfrjEdMe_brfSBlQHQmVzbhdasnm4fQ_8krtm1mGL_-FZg44A9/s200/IAmBWh.jpg" width="200" /></a></div>The demographic was largely PhD students and postdocs, and everyone had to give a short talk. If it overran, fine, if people had questions they'd asked them right away. Students were encouraged to ask as many questions as possible and academics resisted the urge to tear anyone to bits with their sharpened critical skills.<br />
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Scientifically it's great. I got to hear from the people who make all these synthetic colloids that I always cite. Their concerns weren't always about phase diagrams or dynamic arrest, sometimes it was simply how much stabiliser or chemical X do I need to get the polydispersity down. These are problems I don't usually get to hear about and it's particularly nice to get it from the people at the coal face.<br />
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Because the atmosphere is more relaxed you can give a different kind of talk. In a conference you're so worried about being jumped on that you tend to take out all the personality from a talk, all the wild speculation and, well, then fun side of science. Here we could kind of let rip. If we wanted.<br />
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Socially it is also a good thing. It's easy to get a little isolated with your own little problem, especially when your doing a PhD, so it's nice to mix a bit. Science, like most jobs, requires a degree of networking. While I hate this word and all that it implies, these informal gatherings are a much better way to get to know people than conferences. People at conferences are always trying to look smart and generally suck up to the established professors. Makes me shiver just thinking about it.<br />
<h4>A snappy conclusion</h4>The main thing that made this meeting nice was the atmosphere. I highly recommend anyone to organise something similar if it's possible. Sure, it was no Copenhagen, but the science was good and it helped create that sense of being in a scientific community.<br />
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While it's not free it's a lot cheaper than a conference. I guess you don't need to go all the way to Cornwall but it is nice to get out the department for a couple of days - especially when you usually sit at a desk all the time.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-76554813078470680602011-04-27T17:43:00.001+01:002011-04-28T09:07:31.157+01:00An early look at simulationWhile I was putting together the <a href="http://www.kineticallyconstrained.com/2011/04/paper-review-hexatic-phases-in-2d.html">post on 2D disks</a> I came across a <a href="http://dx.doi.org/10.1103/PhysRev.127.359">lovely paper</a> from 1962 on 2D melting by Alder and Wainwright. From there I found this paper from 1959: <a href="http://link.aip.org/link/doi/10.1063/1.1730376">Studies in Molecular Dynamics. I. General Method</a> by the same authors.<br />
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They describe the "event driven" molecular dynamics (MD) algorithm. Normally, with MD you calculate forces, and thus accelerations, and update this way. Hard disks or spheres behave more like snooker balls, the forces are more or less instantaneous impulses that conserve momentum so it's better to deal with collision <i>events</i> and leave out the acceleration part.<br />
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The paper gives a fascinating insight into the early days of computer simulation (they still refer to them as "automatic computers"), what their limitations were and what details were worth worrying about. To give you an idea, in 1959 they say:<br />
<blockquote>With the best presently available computers, it has been possible to treat up to five hundred molecules. With five hundred molecules it requires about a half-hour to achieve an average of one collision per molecule.<br />
</blockquote>So in their case it was CPU speed that was the problem, they get about thousand collisions per hour. To put that in perspective, a modern event-driven simulation of a similar system will maybe hit about a <i>billion</i> collisions per hour on a reasonable desktop [<a href="http://dx.doi.org/10.1103/PhysRevE.80.056704">source</a>]. I don't say this to mock their efforts, these are the giants on whom's shoulders we stand. I'll come back to why that number is so comparatively big these days, first I want to look at visualisation.<br />
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<h4>Visualistion</h4>In 1959 there were no jpegs or postscripts and certainly no <a href="http://www.povray.org/">Povray</a> or <a href="http://www.ks.uiuc.edu/Research/vmd/">VMD</a>, I'm not sure they even had printers. So how do you visualise your simulation? Well they had a rather elegant answer to that. They could output the current state of the system to a cathode-ray tube as a bunch of dots in the positions of the particles. Then they pointed a camera at the screen and left the shutter open while they ran a simulation. What you get is these beautiful images below showing the particle trajectories. Firstly in a crystal phase you can see the particles rattling around their lattice sites<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHM6yA16vPKZdbanVLR2jnFZsM9BKJHXjTmdMdcPWEuADlzmf129_XNJSwKOIDL0Lcqrk-0CL2XGOcFkKC7QOXxz00mTjlMLy6dTPl05yU-YNQXiQuvcj_CWiBiB7vbKi8i-CufrDvaBuj/s1600/alder_crystal.jpg" imageanchor="1" style=""><img border="0" height="382" width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHM6yA16vPKZdbanVLR2jnFZsM9BKJHXjTmdMdcPWEuADlzmf129_XNJSwKOIDL0Lcqrk-0CL2XGOcFkKC7QOXxz00mTjlMLy6dTPl05yU-YNQXiQuvcj_CWiBiB7vbKi8i-CufrDvaBuj/s400/alder_crystal.jpg" /></a></div><br />
This is a projection of the FCC lattice (the squares confused me at first). In the fluid phase they do a little bit of cage rattling and then start to wander off.<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbDMMhfcOGhoDlOqH8WDzeXHUKupsY4BDPAz5qrgI0wmmIpl4F1sYvAqtb86OvDNUIs7RB1amLUMWrdlGs0xowzSjOcWa6g0Dg2zA7Q8Y2DCroprAA0vdP16zmrieHYNocbPNtSe3FMo-S/s1600/alder_fluid.jpg" imageanchor="1" style=""><img border="0" height="396" width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbDMMhfcOGhoDlOqH8WDzeXHUKupsY4BDPAz5qrgI0wmmIpl4F1sYvAqtb86OvDNUIs7RB1amLUMWrdlGs0xowzSjOcWa6g0Dg2zA7Q8Y2DCroprAA0vdP16zmrieHYNocbPNtSe3FMo-S/s400/alder_fluid.jpg" /></a></div>[Figures reprinted with permission <a href="http://link.aip.org/link/doi/10.1063/1.1730376">Alder and Wainwright, J. Chem. Phys.</a> <strong>31</strong>, 459 (1959). Copyright 1959, American Institute of Physics].<br />
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I honestly couldn't show it better today. Some people dismiss visualisations as pretty pictures that only exist to attract attention. Perhaps this is sometimes true but it only takes one look at this to see how they can stir the imagination and shape the intuition – and that's what creates new ideas.<br />
<h4>Algorithms</h4>I'd quickly like to come back to the speed difference between 1959 and today. A lot of the difference can be put down to Moore's law. After an annoying amount of Googling I can't really say how much faster modern CPUs are. A lot probably. However, I'd like to focus on an often overlooked factor – the development of algorithms.<br />
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A general event driven algorithm calculates the collision time for each pair of particles and, if it is under a cutoff, stores it in an event queue. It then fast forwards to the shortest time whereupon it will need to update the queue with new events that appear after the collision. Initially this requires checking all pairs, <a href="http://link.aip.org/link/doi/10.1063/1.1730376">Alder and Wainwright</a> call this the "long cycle", and this has complexity of order N-squared, O(N^2). This means that if you double the number of particles, N, then you have four times as many calculations to perform.<br />
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After a collision you only need to update events involving the particles that collided so you can get away with doing N updates. This is the "short cycle" and is O(N). It's not mentioned in this paper but I think there's an issue with sorting the event queue so this is probably still O(N^2). Either way, for their early simulations the total number of collisions per hour tanked as N was increased.<br />
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And this is where algorithms come in. You can use all sorts of tricks. In dense systems you can use a cell structure to rule out collisions between pairs far away. Modern algorithms focus largely on keeping the event queue properly sorted. A <a href="http://www.worldscinet.com/ijmpc/10/1007/S0129183199001042.html">binary tree</a> will sort with O(log(N)) and <a href="http://www.sciencedirect.com/science/article/B6WHY-4KNKH3H-3/2/64f6dd719cc8ac1219489539bec8c1a2">here</a> they claim to have it O(1). Of course the complexity is not the only important factor, there may be other more important overheads, but it gives an idea of the limitations.<br />
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In equilibrium statistical mechanics specialised computer algorithms have made a spectacular impact. Techniques such as the Wolff algorithm, Umbrella sampling, and many many more, have outstripped any speed up by Moore's law by many orders of magnitude. I could go on about algorithms for hours (maybe a post brewing), instead I'll just make the point that it doesn't always pay to just sit and wait for a faster computer.<br />
<h4>We've come a long way</h4>These early simulation studies weren't just important for developing methods, they were able to answer some serious questions that were hopelessly out of reach at the time. Since then simulation has firmly established itself in the dance between theory and experiment, testing ideas and generating new ones. And it shows no sign of giving up that position.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com2tag:blogger.com,1999:blog-5457514384557268934.post-44384808078284547522011-04-15T09:02:00.003+01:002011-04-15T09:04:00.642+01:00Lipid membranes on the arXivA while ago I discussed <a href="http://www.kineticallyconstrained.com/2009/08/biological-membranes.html">lipid membranes</a> and how they could exhibit critical behaviour. There were some lovely pictures on criticality on giant unilamellar vesicles (GUVs) which are sort of model cell walls. That work was done by Sarah Keller and friends in Seattle.<br />
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This morning on the arXiv I saw this new paper, also by Sarah:<br />
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<a href="http://arxiv.org/abs/1104.2613">Dynamic critical exponent in a 2D lipid membrane with conserved order parameter</a><br />
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They look at the critical dynamics of the GUV's surface. Being embedded in a 3D fluid does have its consequences so they've attempted to account for the effect of hydrodynamic interactions. I haven't poured over their model but the paper looks really nice.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-40691379647925340142011-04-13T17:40:00.002+01:002011-04-13T17:50:55.646+01:00Paper review: Hexatic phases in 2DI'm doing my journal club on this paper by Etienne Bernard and <a href="http://www.lps.ens.fr/~krauth/index.php/Main_Page">Werner Krauth</a> at ENS in Paris:<br />
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<a href="http://arxiv.org/abs/1102.4094">First-order liquid-hexatic phase transition in hard disks</a><br />
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So I thought that instead of making pen-and-paper notes I'd make them here so that you, my huge following, can join in. If you want we can do it proper journal club style in the comments. For now, here's my piece.<br />
<h4>Phase transitions in 2D</h4>Dimension two is the lowest dimension we see phase transitions. In one dimension there just aren't enough connections between the different particles – or spins, or whatever we have – to build up the necessary correlations to beat temperature. In three dimensions there are loads of paths between A and B and the correlations really get going. We get crisp phase transitions and materials will readily gain long range order. Interestingly, while it should be easier and easier to form crystals in higher dimensions there do exist pesky glass transitions that <a href="http://dx.doi.org/10.1103/PhysRevE.79.030201">get worse with increasing dimension</a>. But I digress.<br />
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In two dimensions slightly strange things can happen. For one thing, while we can build nice crystals they are never quite as good as the ones you can get in 3D. What do I mean by this? Well in 3D I can give you the position of one particle and then the direction of the lattice vectors and you can predict exactly where every particle in the box will sit (save a bit of thermal wiggling). In 2D we get close, if I give you the position and lattice vectors then that defines the relative position and orientation for a long way – but not everywhere.<br />
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By "a long way" I mean correlations decay algebraically (distance to the power something) rather than exponentially (something to the power distance), which would be short ranged. We can call it <i>quasi</i>-long ranged.<br />
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Never-the-less, this defines a solid phase and this solid can melt into a liquid (no long range order of any kind). What is very interesting in two dimensions is that this appears to happen in two stages. First the solid loses its positional order, then it loses it's orientational order as well. This is vividly demonstrated in Fig 3. of the paper. The phase in the middle, with quasi-long range orientational order but short range positional order, is known as the <i>hexatic phase</i>.<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_ZMaNlyI2BLgNh3tajuraXXlUE7JoKyR04445Vrofi1BorJvlnIzZEtw0Kpj2o-eK9yW9JNVgoK9KBT4SGu_dZHiOClQvM2FUVd56_KhpQ6mwArjqN_WHGksqN1Nr5I_tOS0WvDqgcHGw/s1600/hex.png" imageanchor="1" style=""><img border="0" height="225" width="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_ZMaNlyI2BLgNh3tajuraXXlUE7JoKyR04445Vrofi1BorJvlnIzZEtw0Kpj2o-eK9yW9JNVgoK9KBT4SGu_dZHiOClQvM2FUVd56_KhpQ6mwArjqN_WHGksqN1Nr5I_tOS0WvDqgcHGw/s320/hex.png" /></a></div>When the lattice is shifted a bit the orientation can be maintained but the positions become disordered.<br />
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<h4>A brief XY interlude</h4>Before we get on to hard disks it might help to understand a slightly simpler model. The XY model is similar to the Ising model, it's on a lattice but the spins are now continuous in the XY plane. This is basically enough to kill the phase transition we see in the Ising model (separation of up and down spins) because the XY spins can gradually rotate from up to down getting rid of a sharp interface.<br />
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So we lose any long range order, however, at low temperatures the XY model can hold quasi-long range order – just like the hexatic. Most importantly there is a phase transition from disordered to quasi-ordered. This transition, known as the Kosterlitz–Thouless (KT) transition, is a bit weird and it is related to topological defects in the vector field. Chapter 9 of <a href="http://books.google.co.uk/books?id=P9YjNjzr9OIC&lpg=PP1&dq=chaikin%20lubensky&pg=PP1#v=onepage&q&f=false">Chaikin and Lubensky</a> will blow your head off if you want to learn all there is to know about these things. To get a rough idea here is what these defects, or "vortices" can look like (nicked <a href="http://www.ibiblio.org/e-notes/Perc/xy.htm">from here</a>).<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWPFN5Q7CrNattMN5sBXsAOAz7L559Ma77LWRzsZhIX6ZY7FHkgDSqA-xzH8-u-_WG5jsnSCmDHBNu8zKVvqdhEqOf76QFByRkBvBbZ0eBeTYdzoFs4pyBMW381zgqP8JOmA-0A1RXrzqO/s1600/vertex.gif" imageanchor="1" style=""><img border="0" height="200" width="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWPFN5Q7CrNattMN5sBXsAOAz7L559Ma77LWRzsZhIX6ZY7FHkgDSqA-xzH8-u-_WG5jsnSCmDHBNu8zKVvqdhEqOf76QFByRkBvBbZ0eBeTYdzoFs4pyBMW381zgqP8JOmA-0A1RXrzqO/s320/vertex.gif" /></a></div><br />
These vortices cost free energy but at high enough temperature we can afford them. In turn they have affect of suppressing correlations in the director field. When the temperature drops such that we can't afford these defects, we develop quasi-long ranged order. The KT transition is continuous in nature (ie, you don't get interfaces) although it's not strictly second order.<br />
<h4>Back to disks</h4>Going back to particles, this hexatic picture appears to be fairly ubiquitous in 2D systems. To get something more concrete we now focus on one model, the simplest of all the off-lattice models, hard disks. Hard disks, like hard spheres, are very interesting because they are the basis of most liquid theories and are the simplest approximation to an atom we can think of. So how do they melt?<br />
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No one pretends (or pretended) to know for sure. Most people agree that there should be a (quasi) solid that melts to a liquid via a hexatic but the nature of the transition is hotly contested. One prediction is via KTHNY theory. This horribly named theory (I now pronounce either "kuthny" or I cough and wave my hands) can give two continuous, XY-esque, transitions: solid-[continuous]->hexatic-[continuous]-> liquid.<br />
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So we finally arrive at the paper. What Etienne and Werner are now saying is that the transition from liquid to hexatic is actually <i>first order</i>. The reason it is so difficult to say for sure is that you need a very big system to see it and, because it's so dense, you need a long time to equilibrate it. In this paper they have a huge system (10^6 particles) and they use a special Monte Carlo algorithm, the Event Chain algorithm, that is very efficient for hard disks. These together allow them to really see what the transition looks like.<br />
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To verify what they're seeing they first study the two phases in isolation, just above and below the coexistence region. By monitoring the pressure as they scan the coexistence region (in an infinite system it would be constant) they can see how the peak-to-peak pressure difference scales. The scaling is quite clean and consistent with a first order transition. The most vivid demonstration of the first order nature is the picture in Fig 1. that shows the interface between the liquid and the hexatic phase.<br />
<h4>First order then?</h4>So the journal club part of this is to ask how convinced you are? My brain is naturally attracted to pictures and that interface is pretty striking. I happen to know they've done simulations with 4x the area and it looks even better there. As it's shown here there's maybe a bit of ambiguity just by eye.<br />
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If you want to remember what a second order transition looks like there's always the <a href="http://youtu.be/fi-g2ET97W8?hd=1">super huge Ising model</a> (now in HD!).<br />
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The pressure measurements are probably the most convincing piece of evidence for me. It's certainly an impressive achievement, I definitely look forward to any follow-ups.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com2tag:blogger.com,1999:blog-5457514384557268934.post-55940969036286792542011-03-17T17:28:00.001+00:002011-03-20T13:42:56.096+00:00Six degrees - the documentary you can't seeA while back the BBC put on an documentary about networks called "Six Degrees". Normally when you see a documentary about a field that you're vaguely related to you feel a bit sick because they did it all wrong.<br />
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Well I have worked in networks a bit and I thought Six Degrees was excellent. It got a great balance of the historical study of networks and then it ran its own version of the Milgram experiment which was mostly used as a plot device to keep driving the story forwards. The people involved (Watts, Strogatz, Barabasi) were all very entertaining and successfully transmitted the excitement of scientific discovery.<br />
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Suffice to say it was great. I had planned to link to it and then discuss it a little bit. Annoyingly the BBC have switched off the <a href="http://www.bbc.co.uk/programmes/b00kdtvv">iPlayer</a> version of the programme and they now appear to have shutdown the version at <a href="http://topdocumentaryfilms.com/six-degrees-of-separation/">top documentaries</a>.<br />
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I know the beeb don't want to give away content for free but it strikes me that a resource this useful (I'd even recommend it to scientists new to the field) should be kept live. Instead it's buried away where it's now useless. Scientists are always told about public engagement, well unblock this film - engage!<br />
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I'm going to write to them an encourage them to let it free, then perhaps instead of a rant about the BBC we can talk about some science.<br />
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UPDATE:<br />
As you can see from the comments, the BBC didn't make the film so they can't keep it online. I can't work out how to get a DVD yet but when I find out I'll put up a link and then can get on talking about networks. In the mean time, <a href="http://books.google.co.uk/books?id=qfZaNQAACAAJ&dq=editions:QTWHAAAACAAJ&hl=en&ei=XwOGTeuEIMyChQeI-JWyBA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCoQ6AEwAA">this book</a>, "<a href="http://bookshop.blackwell.co.uk/jsp/welcome.jsp?action=search&type=isbn&term=075381689X">Small World</a>" by <a href="http://markbuchanan.net/">Mark Buchanan</a> is well worth a read.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com2tag:blogger.com,1999:blog-5457514384557268934.post-2112098472596789192011-03-10T18:08:00.000+00:002011-03-10T18:08:58.320+00:00Thoughts of a first-time peer reviewerMost of my time is spent tirelessly chipping away at the scientific rock face, probably bogged down fixing a bug in my code or staring at some noisy looking data. Every now and then it all comes together and I want to tell people about it. So I write up my results as best I can, spend hours tinkering with figures, another few hours getting the fonts right on the axes, and after drafts and re-drafts, eventually I'll send it away to a journal to be published. This is where I become caught up in the process of <i>peer review</i>.<br />
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Usually it goes like this: The editor of the journal will check that the paper is basically interesting and then send it out to two reviewers who are chosen for their expertise in your area. These reviewers, or referees, will then read the paper, check it for basic errors and then comment on its originality and its pertinence to the field. This is sent back to the editor who will decide whether or not to publish. Usually the referees make you fix something, sometimes nothing, sometimes you can have a right old ding dong.<br />
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The main point is that the process is anonymous and behind closed doors. This is good and bad. <a href="http://cameronneylon.net/">Better</a> <a href="http://alicerosebell.wordpress.com/">blogs</a> than this one discuss different options. It's not really my intention to criticise or support peer review, just to share my experiences.<br />
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Recently I was sent my first ever article to review. I can't say anything about the details, but it has been strange crossing over to the other side. I've had to ask questions that I have never thought much about before. So I wanted to put it down before I forget what all the fuss is about.<br />
<h4>Reviewed</h4>Up to now my only experience has been on the reviewed side of peer review. I've certainly had mixed experiences here. The first paper I had reviewed went through after lots of useful comments by the reviewers. It gave us more work but it made the paper better. Good experience. Another time a reviewer spotted a small error in our equations - also a good experience.<br />
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My worst experience involved two bad scenarios. Our first reviewer had not understood the paper, nor taken the time to follow the references that would allow him/her to do so. Instead of passing on to someone more qualified they just said it didn't make sense and was not interesting. The second referee had some interesting points but appeared to block it mainly on the basis that it didn't agree with other (presumably their) results. As you can see, I'm still bitter about this paper! It took 18 months to eventually get it through by which time it was thoroughly buried.<br />
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Of course, I'm biased, our paper could have been crap. Either way, the experience was bad enough that I was close to leaving science because of it. Receiving sneering anonymous reviews is a crushing blow to your ego - even if they're right.<br />
<h4>Reviewer</h4>So now I've reviewed my first paper. I won't say what I did, most of the questions I found myself asking would apply to any paper.<br />
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I'm quite used to reading other people's work, occasionally making a scoffing remark, or more likely not fully understanding it. The prospect of checking a paper for errors and assessing its quality filled me with dread. The only way I could deal with it was telling myself that it doesn't matter if I don't understand absolutely everything. The main thing is to check that they haven't done anything completely stupid.<br />
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This part of peer review I think is not too bad. There is an element of trust that someone has collected their data properly, but checking that it's not completely upside down is not too difficult or controversial.<br />
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Where it starts to get subtle is questioning the interpretation. Pulling someone up on their conclusion requires quite a bit of guts. Or I suppose an over inflated ego - of which there are many in science. This is related to another question, when should a scientific argument happen before publication and when should it happen afterwards? If the signal to noise ratio is to kept reasonably high then some things will need to be filtered out before hitting public view. I have not worked out an answer to this.<br />
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The final problem I had was with the question, "is this work of sufficient quality to be published in journal X?". Again this is really tricky, scientists can be real bitches when deciding what is or isn't interesting. On the other hand some scientists can try and get away with putting out any old crap just to lift their publication count. I found being asked to be the arbiter of quality quite stressful. Most results need to be on the scientific record somewhere, but should something be blocked for being too "incremental"? I suppose this is the journal's decision.<br />
<h4>Is it worth it?</h4>Apart from some initial stress I found the whole experience quite enjoyable. It makes you feel part of the scientific collective and it really tunes your critical skills. It will be interesting to see what becomes of peer review in the web 2.0 era, I would quite like to see it open up a little. I worry that unregulated, open anonymous comments, could be unhelpful. People are arseholes when they're anonymous, just ask a peer reviewer.Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-17633815643839384402011-02-22T15:30:00.000+00:002011-02-22T15:30:47.372+00:00New domainI've taken the domain name, kineticallyconstrained.com. For now don't change anything as the exact address might move about a bit. I haven't quite worked out what sub domains to use blah blah blah.<br />
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Eventually I plan to put some permanent content and develop the site a bit. For now, to be honest, I'm mostly testing that the RSS feed is still working!Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0tag:blogger.com,1999:blog-5457514384557268934.post-33850017663489537562011-02-03T19:18:00.000+00:002011-02-03T19:18:56.343+00:00Colloids are just rightAll being good it looks like I've secured employment for a tiny while longer. Hooray!<br />
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The place I'm moving to is a big place for synthetic colloids, so it seems like a good time to go through what I know about colloids. If nothing else it'll be interesting to compare this to what I'll know in a year's time! So, here is a theorists perspective on colloid science.<br />
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I'll spare the usual introduction about how colloids are ubiquitous in nature, you can go to <a bitly="BITLY_PROCESSED" href="http://en.wikipedia.org/wiki/Colloid">Wikipedia</a> for that. The type of colloids I'm interested in here are synthetic colloids made in the lab. They're usually made from silica or PMMA (perspex), you can make a lot of them, they can be made so they're roughly the same size and you'll have them floating around in a solution. By playing with the solution you can have them density matched (no gravity) or you can have them sinking/floating depending what you want to study.<br />
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The colloids that people make sit nicely in a sweet spot of size and density that make them perfect for testing our fundamental understanding of why matter arranges itself in the way it does. Colloids can undergo most of the same phase transitions that we get in molecular systems, but here we can actually <i>see</i> them. Take for example this beautiful electron microscope image of a colloidal crystal from the <a bitly="BITLY_PROCESSED" href="http://www.physics.nyu.edu/pine/Pine___Res___Clusters.html">Pine group at NYU</a>.<br />
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<div class="separator" style="clear: both; text-align: center;"><a bitly="BITLY_PROCESSED" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOHQSA0TgWT3Dk-k8YIbN8BOQ3fGXO_L-NDj6tB-o4hJjb2dNqzLtqfyI4wuXH5IRK6sARoAThyphenhyphenfe4T9LKQukW4f2hKZpFEtnPGApmalcqdgXbgdeeHaOwWp0xJwKuPSHm10ONZXL4zveM/s1600/Pine_Crystal.jpg" imageanchor="1"><img border="0" height="169" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOHQSA0TgWT3Dk-k8YIbN8BOQ3fGXO_L-NDj6tB-o4hJjb2dNqzLtqfyI4wuXH5IRK6sARoAThyphenhyphenfe4T9LKQukW4f2hKZpFEtnPGApmalcqdgXbgdeeHaOwWp0xJwKuPSHm10ONZXL4zveM/s320/Pine_Crystal.jpg" width="319" /></a></div><br />
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<h4>1. They're big enough to image</h4>Colloids are usually of the order a micron across. At this size it is still possible to use <a bitly="BITLY_PROCESSED" href="http://en.wikipedia.org/wiki/Confocal_microscopy">confocal microscopy</a> to image the particles. While nothing like the resolution of the electron microscope, the confocal can actually track the positions of individual particles in real time, in solution. It's almost like a simulation without the periodic boundary conditions! A confocal can take lots of 2D slices through the sample, such as below from the <a bitly="BITLY_PROCESSED" href="http://www.physics.emory.edu/%7Eweeks/">Weeks group</a>. The scale bar is 5 microns.<br />
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<div class="separator" style="clear: both; text-align: center;"><a bitly="BITLY_PROCESSED" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNsd8qq1fixAfgGHlze5zeMoAh4DUOTCnbTlwPrHomNP3qEMLCtOplt96s5eMWpK2fIu4ROiZQW-UfnEciN8_3Jak1bC_zVpOXkI60FaAW-pupyJ5QVkJ6uiaY-jlLCNMdzfFgDKYGk4Li/s1600/weekscrystal01.gif" imageanchor="1"><img border="0" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNsd8qq1fixAfgGHlze5zeMoAh4DUOTCnbTlwPrHomNP3qEMLCtOplt96s5eMWpK2fIu4ROiZQW-UfnEciN8_3Jak1bC_zVpOXkI60FaAW-pupyJ5QVkJ6uiaY-jlLCNMdzfFgDKYGk4Li/s320/weekscrystal01.gif" width="202" /></a></div><br />
If you do it quick enough then you can keep track of the particle moving before it loses its identity. The Weeks group did some very famous work <a bitly="BITLY_PROCESSED" href="http://www.physics.emory.edu/%7Eweeks/lab/bumpy.html">visualising dynamic heterogeneity</a> in liquids near the glass transition. (see their <a bitly="BITLY_PROCESSED" href="http://dx.doi.org/10.1126/science.287.5453.627">science paper</a> if you can).<br />
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If we want to think about colloids as model atoms, which we do, then there's another property apart from just their size that we need to be able to control.<br />
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<h4>2. You can control their interactions</h4>Being the size they are, if we didn't do anything to our colloids after making the spheres they would stick together quite strongly due to van de Waals forces - this is the attraction between any smooth surface to another, as used by clingfilm. To counteract this the clever experimentalists are able to graft a layer of polymers around onto the surface of the colloid.<br />
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It's like covering it with little hairs. When the hairs from two particles come into contact they repel, overcoming the van de Waals attraction. The particles are "stabilised". In this way it's possible to make colloids that interact pretty much like hard spheres. So not only can we use them as model atoms, but we can use them to test theoretical models as well!<br />
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Further to this the colloids can be charged and by adding salt to the solvent one can control the screening length for attraction or repulsion to other colloids. Finally there's the depletion interaction. I want to come back to this so for now I'll just say that by adding coiled up polymers into the soup we can create, and tightly control, attractions between the colloids. With this experimentalists can tune their particles to create a zoo of different behaviours.<br />
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<h4>3. They're thermal</h4>If the colloids are not too small to be imaged, why not make them bigger? If we made them, say 1cm, then we could just sit and watch them, right? Well not really. If you filled a bucket with ball bearings and solution, density matched them so they don't sink or float and then waited, you'd be there a long time. The only way to move them in a realistic amount of time is to shake them - this is granular physics.<br />
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Granular physics is great but it's not what we're doing here. Real atoms are subject to random thermal motions and they seek to fit the Boltzmann distribution. For this to work with colloids they need to be sensitive to temperature.<br />
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When a colloid is immersed in a fluid it subject to a number of forces. If it's moving then there will be viscous forces, and on an atomistic level it is constantly being bombarded by the molecules that comprise the fluid. In the interests of keeping this post to a respectable size I can't go through the detail, but suffice it to say that this is an old problem in physics - Brownian motion.<br />
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Under Brownian motion the large particle will perform a random walk that is characterised by its diffusion constant. The bigger this number the quicker it moves around. A more intuitive number is the time it takes for a particle to move a distance of one particle diameter. When you solve the equation of motion for a large particle in a Stokesian fluid you find that this time is given by<br />
<div class="separator" style="clear: both; text-align: center;"><a bitly="BITLY_PROCESSED" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6ueeEklCSQpPdnoLvThTmrQZh5w9H6am3ApfmwWdgRWaXdOu2-z-ZTOpHo9RvhbVfo-rh-rvxtGMt1E0t1P472AydjJDlftHnR_mj3tTWoBmCVQdxBQYlc8rNuhdwDpWvHuQ_XHM_72lq/s1600/tau-stokes.png" imageanchor="1"><img border="0" height="57" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6ueeEklCSQpPdnoLvThTmrQZh5w9H6am3ApfmwWdgRWaXdOu2-z-ZTOpHo9RvhbVfo-rh-rvxtGMt1E0t1P472AydjJDlftHnR_mj3tTWoBmCVQdxBQYlc8rNuhdwDpWvHuQ_XHM_72lq/s320/tau-stokes.png" width="111" /></a></div><br />
where <img align="middle" height="8" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheA9WbBEoxi1hsuvJKT777Ce5BIO0DSLeeVehJmMrCb7bN_xemPb21hyphenhyphenOqtWNSac1qexxEu2wh1MBy7zfH1wH7k3Y5OzWBPLsH-YodPcGVsTB1AhPEXgbK9ynQjupYbEKJMGMXt2X5C4cE/s320/eta.png" /> is viscosity, a is the particle diameter, and k_B T is Boltzmann's constant and temperature. Now this does get more complicated in dense systems and the properties of the fluid matter, but this is a good start. This could be a topic for another post.<br />
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For a typical colloidal particle, around a micron in size, you have to wait about a second for it to move its own diameter. For something only as big as a grain of sand you can be waiting hours or days. Even by 10 microns it's getting a bit too slow. But close to 1 micron, not only does it move about in an acceptable time frame, we can easily track it with our confocal microscope. If it's diffusing around then we can hope that it will be properly sampling the Boltzmann distribution - or at the very least be heading there. So once again, that micron size sweet spot is cropping up.<br />
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<h4>So what else?</h4>Hopefully this serves as a good starting point to colloids. Obviously there's a lot more to it. An area that I'm very interested in at the moment is what happens when the colloids are not spheres but some other shape. I'll be posting more about it in the coming months.<br />
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If you don't remember anything else just remember that colloids are the perfect size to test statistical mechanics and to be visible.<br />
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So well done colloids, you're just right size.<br />
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<div style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="100" src="http://www.youtube.com/embed/Ce7D-LqQHD4" title="YouTube video player" width="400"></iframe></div>Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com2tag:blogger.com,1999:blog-5457514384557268934.post-69265734049170226842011-01-19T17:46:00.001+00:002011-01-19T17:47:50.303+00:00It's been a whileBut I'm planning a dramatic comeback - just as soon as I've sorted my next job!<br />
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I've got some more critical-scaling stuff in the pipeline, some nice crystallisation videos and it may be time for some chat about self-assembly seeing as I'm now officially a self-assembler (self-assemblist?).<br />
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So don't delete Kinetically Constrained from your RSS reader just yet!Anonymoushttp://www.blogger.com/profile/10673953249469231273noreply@blogger.com0