Cool Papers 1: General

I’ve come across a number of pretty cool papers in the past few months. Some of them deal with particular phenomena (stay tuned for possible upcoming posts on molecules at surfaces, biomimetics, phononics, crystallization, nanoparticles, wetting phenomena, computational physics, etc. etc. - at some point), and so are probably better off getting their own blog posts. Here are a few papers that didn’t fall into specific categories…

1. Frictional Anisotropy on a Quasicrystal Surface
Along with ~10 other things, a subject that I’ve recently become interested in is nanoscale mechanics, broadly defined. A key experimental tool in this field is the use of local probes to push or pull on things controllably. Miquel Salmeron’s STM group at Berkeley does work on this and related subjects, and I finally got around to reading this paper of theirs from a few years back.

The idea is conceptually very simple: while friction unsurprisingly depends on commensurability (that is, if two surfaces in contact are structurally ‘complementary’, they will ‘lock in’ to each other and hence have high friction between them - an idea that apparently dates back to da Vinci), trying to think about friction using just this notion is unrealistic. For starters, most contacting surfaces are probably incommensurate, and other factors - such as periodicity(?) - contribute, as well.

This paper nicely singles out the role of periodicity by looking at different directions along Al-Ni-Co quasicrystal surfaces using STM (to image the surface and hence distinguish the periodic and aperiodic directions of atom ordering) and AFM (to measure the probe tip-surface friction along these directions) in ultra-high vacuum. The AFM friction data can be modeled using a classical model relevant to the experimental situation (the Derjaguin-Muller-Toporov or DMT model, which I need to learn more about), enabling key parameters to be derived from the measurements.

In particular, the authors find a larger friction force (8x) along the periodic direction than along the aperiodic direction. Unsurprisingly, they ascribe this to differences in energy dissipation via electron or phonon excitation+propagation along the different directions, although it is unclear to what extent each kind of excitation plays a role. Perhaps similar local-probe measurements of a different kind (e.g. ones sensitive to electrical versus mechanical properties) might be useful… At the end of the day, I like this paper because it is an elegant example of using a unique microstructure, in which just one variable (here periodicity) changes in ways that are well understood, to study something interesting as a function of just that variable.

2. Liquid Crystals and the Origins of Life
Noel Clark gave a great talk about this work here at Penn not too long ago. I won’t write too much about this since Randy has a nice description of it over at the condmat journal club.

Here’s the executive summary: according to extensions of Onsager’s rigid-rod model for the formation of liquid crystal phases, individual molecules must be sufficiently anisotropic (i.e. the aspect ratio has to be above a certain minimum) to form a liquid crystal (LC). Surprisingly, the authors of this paper observed LC phases consisting of single-stranded (ss) DNA molecules too short to satisfy this criterion. Optical and x-ray measurements indicate that this results from end-to-end stacking of duplexes of complementary short ss-DNA molecules (known as ‘living polymerization’) into larger rods that satisfy the Onsager criterion, even at low temperatures (in concentrated phases of duplexes separated from the isotropic phase of unpaired ss-DNA molecules).

This autocatalytic behavior is like positive feedback, in a sense, and is why this work is so interesting from a biological point of view: it provides a mechanism by which the right molecules can be ’selected’ out from a ’soup’, and ‘evolve’ into larger ones as part of an RNA world. It’s an interesting idea - definitely one that’s gotten a lot of press, it seems - and while this work doesn’t provide much hard evidence for it, I’ll be interested to see what it stimulates.

3. Suprafroth!
This is a very interesting paper out recently on the arxiv, I think to be published in Nature Physics. While I don’t understand all the details, I like this particularly because it’s a nice combination of ideas from soft- and hard-condensed matter physics, like electronic liquid crystals.

The authors used magneto-optical imaging, which I need to learn more about, to image the flux pattern of superconducting lead (a type-I superconductor). Turns out that the magnetic field on the edge of a disc-shaped sample of lead is larger than the actual applied field, and for large enough magnetic field some flux can penetrate the sample. This leads to a phase intermediate between the normal and superconducting phases, possessing a froth-like magnetic structure - specifically, the froth cell boundaries are superconducting, while the interiors are normal metal. This shows up very clearly in the magneto-optical images (see figures in the paper).

The nice thing is that, unlike ‘conventional’ froths, mass-transport processes like drying or drainage are not present here (as the authors point out, “this superconducting froth involves only electrons”). This means that the froth structure can be tuned reversibly using the applied magnetic field or temperature, and the nice magneto-optical images allow for quantitative analysis of the froth structure as a function of just these parameters.

This is philosophically similar (loosely speaking) to paper #1 - the friction measurements of quasicrystals: again, it is a very nice example of using a unique microstructure (here, a froth structure that doesn’t suffer from irreversible processes, and can be controlled by magnetic field or temperature) to study something interesting (here, the structure and dynamics of froths) as a function of just the variables that you can control.

4. Universality in Conference Registration
This is a cute correspondence recently sent to Nature Physics describing an intriguing social application of statistical mechanics.

The authors used registration data from two physics conferences (# of registrants as a function of time to the deadline), saw that they matched up remarkably well (after rescaling), and came up with a simple model to capture the observed phenomenon in which the ‘pressure’ felt by potential attendees to register varies inversely with respect to the time to the deadline. Also, incorporating a Boltzmann-like factor (instead of uniform probability to register over the period of time) leads to a prediction that agrees well with # of payments as a function of time to the deadline data.

Of course, there are a number of assumptions and fitting parameters floating around here, and I’m not entirely sure this work will change the world of physics, but I always find things like this fun.

A few thoughts

Clearly blogging has slowed down now that I’m back into the swing of research. Here are a few minor non-research things that have transpired…

Free coffee? While attempting to read a thesis by a professor here, I came across an interesting line in the acknowledgments in which he thanked “the labours of the coffee and tea pickers whose efforts kept me awake long enough to produce this document”. Here’s a thought: athletes and celebrities receive inordinate amounts of free stuff - and of course, money - to endorse certain products (I presume). Why can’t physicists and other scientists do the same? For example, if Red Bull or La Colombe ran full-page ads in Nature along the lines of “Ed Witten drinks Red Bull - do you?” or “Andrew Wiles: turning La Colombe coffee into theorems”, I’m sure their sales would increase significantly. (I venture that no other single demographic consumes more caffeine.) And of course, they could give the individual/individual’s department free coffee and/or funding in return. It’s a win-win situation.

De Gennes dies: There’s not much I can say that hasn’t already been said (see this NYT article, for example). I’ve had the pleasure of delving into two of his books, the seminal Physics of Liquid Crystals - note to self: learn more about the connections between superconductors and liquid crystals - and the perhaps lesser-known Petit Point: A Candid Portrait on the Aberrations of Science. The latter is a rather interesting book, with very short chapters describing fictional characters based on scientific individuals. The sole reviewer of the book on Amazon claims to be able to identify Benoit Mandelbrot, Brian Josephson and Bernd Matthias in the various characters; my own hunch is that the chapter on “Chazot” is autobiographical in nature (the last line, “…in the end, Chazot’s real vocation is perhaps to give talks to high school students”, pretty much gives it away).

Blog-related: Henry Cate of the Why Home School blog is kicking off a carnival of space, which is a great idea (don’t know what a blog carnival is? See here.) Here are the archives, here is this week’s carnival, here’s the announcement, and most importantly - here’s how to submit a post for inclusion. Go for it!

And, in other news, Arunn of n0noscience and Rod of Perfectly Reasonable Deviations have both tagged me as being a ‘thinking’ blogger, which is a wonderful honor. I’m supposed to link to five other blogs that make me think, but it’s tough; the best I can do is link to the list of blogs I follow when I can since they’re all interesting.

Information theory: Cover and Thomas’ Elements of Information Theory (2nd ed.) is a really, really good book. Sadly I haven’t been able to read as much of it as I’ve wanted to, but it’s been a fascinating fusion of mathematics, physics, and computer science.

Silicon Brains, Photonics, etc.

The semester is officially over, which is exciting: I finally get to get back into the swing of research (with the occasional GRE study break, of course). As such, blogging will tend to be lighter; but before I lock myself in the lab, here are a few things that came to pass while I was busy finishing up the semester…

Building Brains in Silicon
Among other things, I wrote a paper for my computational neuroscience class on – you guessed it – some really cool work coming out of Kwabena Boahen’s group (formerly here at Penn, now at Stanford) on silicon-based artifical neural systems. This is sometimes classed as ‘neuromorphic engineering’, a term (coined by Carver Mead in the 1980’s) which has come to refer to a relatively recent interdisciplinary paradigm dealing with the development and study of artificial neural systems, drawing on principles from such fields as physics, biology, and computer/electrical engineering to design electronic-based analogues of biological systems. A number of people are using this to try to design new VLSI-based systems based on biological systems.

Some others are trying to reverse this scenario: while ‘real’ neural systems are experimentally studied by neurobiologists while grossly simplified ones are modeled by computational neuroscientists, groups like Boahen’s are trying to bridge these modes of inquiry by exploiting similarities between electronic and neural circuits. Mahowald and Douglas wrote a seminal paper in 1991 describing the first ‘silicon neuron’, and a good deal of work has gone on since then. For example, a number of ‘thermodynamic’ models of ion channels have been developed, building on concepts like Hodgkin/Huxley-type models. Anyway, by exploiting the beautiful similarity between ion channels and metal-oxide-semiconductor (MOS) transistors as two-state systems (simplistically, ion channels are either open or closed, with the energy barrier – and hence the transition rate – between the two states being modulated via, for example, a voltage; on the other hand, a voltage applied across the source and the drain of a MOSFET causes charges to diffuse through the ‘conduction channel’, with the effective barrier to this diffusion being modulated by a gate voltage), Boahen and his graduate student Kai Hynna have recently taken an important step toward ‘building a brain in silicon’. Using an approach that combines the advantages of experiment and artificial modeling, they have developed a simple electronic circuit that replicates the nonlinear dynamics of the gating particles of voltage-dependent ion channels.

References:
- Hynna and Boahen’s recent paper: K. M. Hynna and K. Boahen, Neural Computation 19, 327 (2007).
- 1991 silicon neuron paper: M. Mahowald and R. Douglas, Nature 354, 515 (1991).
- Thermodynamic models of ion channels: A. Destexhe and J. R. Huguenard, J. Comput. Neurosci. 9, 259 (2000).

Update: I guess Tech Review thought this stuff is cool, too: the latest issue has an article on Boahen’s work. It takes a broader view of his work than I have above - I just focused on one particular aspect.

Quasicrystals and Complex Materials as 3D Photonic Structures
I wrote another paper for my modern optics class, based on this recent experimental paper by Man, Megens, Steinhardt and Chaikin on three-dimensional quasicrystals as complete photonic bandgap materials. Here’s the deal: since Schrödinger’s wave equation and the electromagnetic wave equation are formally similar (neglecting spin statistics), it isn’t all that surprising that a number of analogies exist between electronic waves and light. In particular, electromagnetic waves can propagate in structures of periodic dielectric constant, and interference due to multiple Bragg reflections from these interfaces leads to directional-dependent energy band gaps. A major goal is to try to develop artificial structures to act as complete, omnidirectional photonic bandgap (PBG) crystals with bandgaps in the visible regime (wavelength ~ 400-700nm), and a lot of effort has gone into this. Interestingly, recent innovations in materials science and the study of complex materials – such as quasicrystals (QC), liquid crystals (LCs), and colloidal self-assembly – have breathed new life into this quest.

References:
- Experimental confirmation of the almost-spherical effective Brillouin zone (and hence the potential of developing a 3D PBG structure) of a macroscopic 3D icosahedral photonic QC: W. Man, M. Megens, P. J. Steinhardt and P. M. Chaikin, Nature 436, 993 (2005).
- Experimental approach towards assembling 3D analogues of the QC structures studied by Man et al. on a smaller scale using holographic optical trapping: Y. Roichman and D. G. Grier, Opt. Exp. 13, 5434 (2005).
- Another experimental approach, using a novel 7-beam optical interference holography technique: W. Y. Tam, Appl. Phys. Lett. 89, 251111 (2006).
- Using nematic liquid crystals in ‘inverse opal’ structures as PBG materials (tuned by parameters such as an external electric field) – for example, since liquid crystals are birefringent, modulating their orientational order using a field can influence their optical properties (a principle on which liquid crystal displays are based): K. Busch and S. John, Phys. Rev. Lett. 83, 967 (1998).
- Recent computational work has indicated a feasible method of fabricating 3D visible PBG crystals with two different types of lattice structure using self-assembly of a mixture of colloidal spheres of two different sizes: A. P. Hynninen, J. H. Thijssen, E. C. Vermolen, M. Dijkstra, and A. van Blaaderen, Nature Mater. 6, 202 (2007).

Talks Part 1: Modeling Cells

I always enjoy attending good talks, and we’ve had quite a few lately: they’ve either been relevant to my current research, interesting applications of concepts I’ve encountered before, or just plain cool. (And of course, going to talks - or blogging, for that matter - is always a good way of taking a break from working all the time i.e. staying sane.) The material presented is always a good springboard for learning more. Here are a few summaries and references for the talks that stuck out the most, mainly because they dealt with things that I hadn’t directly encountered before.

Modelling Cell Motion and Morphogenesis: Mark Alber (Notre Dame)
Although this was billed as an applied math talk, it felt more like a physics talk: the speaker focused on trying to convey what was actually going on and less on the mathematical details involved in modeling it, which was refreshing. I’ve been to too many math talks where the speaker gets hung up on mathematical details, and the big picture somehow gets left out. Anyway, Prof. Alber is an applied mathematician at Notre Dame who spends a good deal of time modeling cells and biological processes at various scales (hence the term multiscale modeling) using ideas from statistical mechanics. The point is this: different modeling methods have their advantages and disadvantages. For example, macroscopic continuum methods abstract away many (often crucial) things and can miss different kinds of phenomena, while microscopic cell-level models - in which stochasticity is very important - can be computationally very intensive. This is particularly important in biological systems, where important processes take place at pretty much all scales; ideally, one would be able to construct a 3-dimensional model of a system and be able to zoom in and out with ease. This is what Alber et al. have been working on, in two different ways.

The first method is a 3D stochastic model of myxobacteria dynamics based on a lattice-gas cellular automata model, and using this, they’re able to study experimentally-observed phenomena like rippling, the formation of things like ’streams’ and ‘traffic jams’, and cell swarming/aggregation. The second method treats the cells as extended objects and goes off the philosophy that “while individual organisms and organs have very different structures and behaviors, many of the underlying interactions and components are the same.” In particular, it is an implementation of the Cellular Potts Model (CPM) of statistical mechanics, a non-equilibrium variant of the Ising model, coupling this to a continuum reaction-diffusion model for morphogen production/diffusion and a set of conditions dictating how genes are regulated. In particular, each cell is represented as a cluster of pixels in the CPM (with a multidimensional index indicating the type of cell) and interacts with other cells via a pairwise adhesion, and the cool thing is that they can use this to model - to a certain extent - limb formation in things like growing chicken embryos.

Further reading…
- Modeling myxobacteria dynamics: O. Sozinova et al., “A Three-Dimensional Model of Myxobacterial Aggregation by Contact-mediated Interactions“, PNAS 102 11308 (2005) and D. Kaiser, “Coupling Cell Movement to Multicellular Development in Myxobacteria“, Nature Reviews Microbiol. 1 45 (2003).
- Modeling limb formation: R. Chaturvedi et al., “On Multiscale Approaches to 3-Dimensional Modeling of Morphogenesis“, J. R. Soc. Interface 2 237 (2005).
- Somewhat related: D. A. Beysens et al., “Cell Sorting is Analogous to Phase Ordering in Fluids“, PNAS 97 9467 (2000) and W. Zeng et al., “Non-Turing Stripes and Spots: a Novel Mechanism for Biological Cell Clustering“, Physica A 341 482 (2004). In particular, I find the similarities between figure 2 of the latter reference and this picture of stripe formation in ferrofluids in one of my previous posts on electronic liquid crystals are striking.

High-Energy Materials Science

Someone I know recently asked me about this recent New Scientist article, and honestly, I’m not sure what to make of it. To summarize the article, ‘string-net condensation‘ (a model in which “electrons are not really elementary, but are formed at the ends of long ’strings’ of other, fundamental particles”) predicts interesting new phases of matter in certain spin models, and recent experiments on the amusingly-named Herbertsmithite may be a signature of one such phase of matter.

The subject matter is definitely interesting, although I am in no position to comment on the actual science (especially the theory, because I don’t understand it - my very little exposure to renormalization group theory so far has been in the context of statistical mechanics). On the experimental side, there is no doubt that recent work studying material properties of this system (such as looking at the specific heat or the temperature-dependence of the magnetic susceptibility, as well as using inelastic neutron scattering) is yielding some very cool physics. And of course on the theory side of things, it is clear that being able to come up with a unified theory from which electrons and photons are emergent is a Big Deal. The problem I have is that while the New Scientist article makes it sound like these measurements are a clear signature of a new phase of matter as predicted by string-net condensation, I can’t really discern the degree to which the link between the theory and experiments is scientifically rigorous, at least from reading the relevant papers. Rather, the article strikes me as being yet another example of really bad sensationalist journalism (see this post by Doug Natelson for more).

However, I find this to be a nice example of how things like high-energy physics theories of string-net condensation or quantum electrodynamics are becoming increasingly important in the study of materials. The ‘hot’ material for this kind of thing these days is obviously graphene, the “new bridge between condensed matter physics and quantum electrodynamics“. Another surprising example of this, for example, is this recent paper connecting SU(2) Yang-Mills theory in the low-temperature phase to nematic liquid crystals (who’d have thought? Certainly not me - I found it amusing that the only equations in the paper I actually understood were 18-20, the ones relating to liquid crystals).

And of course, this Herbertsmithite stuff is an example of another big thing in condensed matter physics - namely, ‘discovering’ new states of matter (at least theoretically). A lot of interesting physics is coming out of this effort, such as this recent work by Shoucheng Zhang at Stanford.