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.

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.

Funny Journal Content

1. A candidate for the funniest journal title/paper graphic…
Here’s a cute paper: rolling a single molecular at the atomic scale. The authors look at C₄₄H₂₄, a molecule possessing two triptyene ‘wheels’ (with three ‘paddles’, each) and thus two intramolecular degrees of freedom when adsorbed on a metal surface (the independent rotation of each wheel), and push it along with an STM tip. Interestingly, the STM current is a good indicater of what kind of motion the molecule is undergoing (’rolling’ versus ‘hopping’). What I find most amusing is that the molecule was previously used to construct a ‘molecular wheelbarrow’, a result which was published in Tetrahedron Letters - probably the funniest journal title I’ve come across - and includes the following priceless graphic:

2. Can a biologist fix a radio? Or, what one scientist learned while studying apoptosis
Speaking of funny papers, this paper by Yuri Lazebnick (via Structure+Strangeness) is great. Here’s an excerpt, dealing with the question of how would a biologist fix a radio, knowing only that it is a box meant to play music?

How would we begin? First, we would secure funds to obtain a large supply of identical functioning radios in order to dissect and compare them to the one that is broken. We would eventually find how to open the radios and will find objects of various shape, color, and size. We would describe and classify them into families according to their appearance. We would describe a family of square metal objects, a family of round brightly colored objects with two legs, round-shaped objects with three legs and so on. Because the objects would vary in color, we will investigate whether changing the colors affects the radio’s performance. Although changing the colors would have only attenuating effects (the music is still playing but a trained ear of some people can discern some distortion), this approach will produce many publications and result in a lively debate.

3. Formation of a nematic fluid at high fields in Sr₃Ru₂O₇:
I had quite a lengthy post on electronic liquid crystals in 2-dimensional electron gases (e.g. GaAs/AlGaAs heterostructures) a while back, and briefly noted that:

Scientists in Europe have measured a large magnetoresistive anisotropy in the correlated electron oxide strontium ruthenate (Sr₃Ru₂O₇) near the ‘metamagnetic quantum critical point’, indicating the formation of a new quantum nematic phase. This is strikingly similar to the tranport anisotropy in 2DEGs I’ve been talking about… in particular, both show strong sensitivity to disorder - and the authors claim that the formation of this phase is tuned by the divergence in the quasiparticle effective mass near this critical point. One can only wonder what other kinds of systems could yield such behavior as well.

This European work is now one of the feature papers for the online Journal Club for Condensed Matter Physics, with a far more in-depth (yet very readable) commentary by Catherine Kallin of McMaster University in Canada.

Electronic Liquid Crystals

Systems dominated by long-range repulsive forces often exhibit a uniform phase, while those dominated by short-range attractive forces tend to exhibit phase separation into compact structures. Competition between these two kinds of forces often leads to spatially inhomogeneous and anisotropic phases (such as ‘stripe’ or ‘bubble’ phases, depending on the area fraction of the sample) in a number of physical situations. Classical examples abound, such as blockcopolymers, ‘pasta phases’ of the crusts of neutron stars or DNA-intercalated lipid bilayers. One of my favorites is stripe formation in ferrofluids (due to competition between dipole-dipole repulsions and the attractive surface tension):

The image and a really neat movie of the stripes forming can be found at Ken Cooper’s website at Caltech. The experiment strikes me as being remarkably simple - just press an immiscible mixture of ferrofluid and IPA between two glass disks, and apply a magnetic field! The really interesting thing is that recent work has indicated such phases in strongly correlated electron systems as well (such as stripe phases of cuprate superconductors or manganates/nickelates) in which repulsive Coulomb interactions compete with the effective short range attractive Pauli exchange interaction.

A striking example is in the transport measurements of figure 1 (click ‘Read on’ below to see it), indicating significant anisotropy in the resistivity of a two-dimensional electron gas (2DEG) in very clean MBE-fabricated GaAs/AlGaAs heterostructure samples in the presence of moderately large magnetic fields. I’ll only focus on the results of Lilly et al. [1] here, but this has been confirmed independently by another group as well [2]. Recent theoretical work by Dorsey, Fradkin, Kivelson, Oganesyan, Radzihovsky and undoubtedly many others [3-4] explains this phenomenon via considerations of an orientationally ordered Quantum Hall Nematic (QHN). This naturally gives rise to a broader notion of ‘electronic liquid crystals’ [5] – that is, quantum mechanical analogues of classical liquid crystal phases in which rotation and/or translational symmetry (as dictated by the point-group symmetry of the crystal) is spontaneously broken.