Update: I definitely wasn’t expecting this! It’s nice to see something applied win the prize.

So Nobel Prize season is upon us once again. It’s always fun to try to guess who the winners will be — and because I know nothing about Medicine, Peace, or Economics, I’ll stick to making predictions on the Physics and Chemistry prizes. I happened to pick 2007’s Physics winners correctly by sheer luck: maybe it’ll happen again?

Actually, I don’t know Chemistry as a field broadly enough to make any reasonable predictions, either. Just for fun, I’m going to guess Richard Zare will win this year, for the extensive work he has done using lasers for all sorts of spectroscopy — in particular, he developed laser-induced fluorescence spectroscopy. The only problem with picking Zare is that his work might (?) be too closely related to that of last year’s Chemistry picks (Shimomura, Chalfie and Tsien) for their discovery and development of green fluorescent protein.

This year I’m guessing that the Physics prize will go to Aharanov and Berry for their work on quantum topological and geometrical phases (see, for example, the Aharonov-Bohm effect or Berry phase). There are a number of reasons for this guess. Every physics student learns about how a charged particle moving in a region of zero electric and magnetic field is still affected by the potentially non-zero electromagnetic vector potential A – that is, its wave function picks up a phase shift given by integrating A along its path. This is an incredibly deep and fundamental result of quantum mechanics: unlike in classical electrodynamics, in quantum electrodynamics the effects of this potential can be felt. For example, as Aharonov and Bohm proposed in 1959, two charged particles going in opposite directions around a circle encircling a solenoidal magnetic field interfere when they are recombined — in particular, their phase difference (which can be measured) is directly proportional to the magnetic flux penetrating the circle, even though they feel zero magnetic field along the path they traverse!

Indeed, this effect has been verified in numerous measurements since. The earliest example that I am aware of is this elegant experiment by Chambers in 1960, using an electrostatic “biprism” consisting of an aluminized quartz fiber flanked by two grounded metal plates (schematic here) to interfere two beams of electrons.  This was followed up by further electron holography measurements using toroidal ferromagnets, as well as by work studying oscillations in the resistance of tiny metal rings as a function of the magnetic field being applied through their core. More recently, these magnetoresistance oscillations have been observed in individual carbon nanotubes with the field applied parallel to the tube axis, which I think is pretty cool. I remember when I first learned about this effect: it was one of the first times I was truly, genuinely, acutely thrown by quantum mechanics. And it has profound consequences — namely, it suggests that the electromagnetic vector potential is in some sense more “real” than the electric or magnetic fields on their own.

in 1984, Berry went one step further, pointing out that the Aharonov-Bohm effect is a particular example of geometric phase, and that a geometric phase often arises in many quantum situations. In particular, if a quantum system is changed very slowly (that is, adiabatically) such that it is eventually brought back to its initial conditions in parameter space, it turns out that it remembers the path it took: it picks up a phase factor that depends on the geometry of the path it took through parameter space. For example, if you subject a fixed electron to a constant magnetic field that changes in direction — say the magnetic field vector sweeps out an arbitrary closed loop on the surface of a sphere centered on the electron — it turns out that the electron state picks up a Berry’s phase proportional to the solid angle subtended by the path relative to the origin. That’s it. Isn’t that crazy?

The idea of a Berry phase (and the way in which it links physical effects to topological quantities) is quite general, and has found applications in many physical systems. For example, the quantum Hall effect can be understood as an example of Berry’s phase applied to 2D electronic systems, while the anomalous Hall effect for dilute magnetic semiconductors has recently been linked to Berry’s phase, as well. Graphene is a nice recent experimental system for studying Berry’s phase for electrons in two dimensions: electrons in graphene can be understood using the Dirac equation for spin-1/2 particles, and are characterized by “pseudospin”. Just as in the Berry phase example I gave earlier, an electron in graphene that completes a cyclotron orbit in an applied magnetic field has its pseudospin rotated by 360 degrees, and thus picks up a phase shift of pi in its wavefunction. The consequences of this have recently been observed in quantum Hall measurements of monolayer and bilayer graphene.  In related work, topological insulators and the quantum spin Hall effect have recently begun receiving a huge amount of attention from the physics community, because of their unusual properties — while they are insulating in the bulk, they can support unique “surface states”. I don’t fully understand the theory of these, but the main framework within which they appear to be studied is by describing them as topologically ordered states, characterized by topological invariants such as Chern numbers and a non-trivial Berry phase.

An interesting side note: in all of these Aharonov-Bohm/Berry phase experiments, the quantum phase is measured through some kind of interference process. Recently, Manoharan’s group at Stanford has done some pretty cool STM experiments to directly measure quantum phase information, by comparing the STM signal of physically different but electronically identical quantum corral-type nanostructures.

One potential problem: the Aharonov-Bohm effect was apparently previously predicted by Ehrenberg and Siday ten years earlier, and Berry phase was apparently discussed by Pancharatnam some 28 years before Berry’s paper! On the other hand, history suggests that this may not be enough to deter the prize committee.

Update: apparently Thomson Reuters agrees with my pick for Physics…

As some readers may already know, 2009 is the International Year of Astronomy, commemorating 400 years since Galileo raised his telescope to the stars and Kepler put forward his laws of planetary motion in his treatise Astronomia Nova. This put the Copernican idea of heliocentrism on a more rigorous scientific footing, and would eventually pave the way for Newton to formulate his theory of gravity.

Even aside from these achievements, Kepler is particularly fascinating character in the history of science. His work always seemed to be strongly guided by a Platonic view of a perfectly structured, geometrically harmonic universe. For example, in his Mysterium Cosmographicum – a lesser-known precursor to Astronomia Nova – Kepler devised an elegant, if incorrect, model of the six known planets as following orbits along spheres inscribed within and circumscribed around five platonic solids. Another example is his extensive exploration of tesselations and sphere-packings, which he often used to explain the structure of various materials, such as snowflakes.

A well-known result of this is Kepler’s conjecture on sphere packings – namely, that the maximum possible volume fraction of a container that can be filled by equally-sized spheres is that of face-centered cubic packing, slightly more than 74%. This was only proved by Thomas Hales recently, using a good deal of computational machinery.

A related problem – part of Hilbert’s list of some of the most important problems in mathematics – involves finding the densest packings of regular polyhedra. While cubes and truncated octahedra can tile space (so their densest packing has a volume fraction of 100%), it turns out that none of the other five Platonic solids or thirteen Archimedean solids can. A good deal of recent work has focused on trying to find the densest possible packing of regular tetrahedra, mainly by construction. In two very nice recent papers, however, Sal Torquato and his student Yang Jiao have come up with a computational scheme for generating very, very dense packings of polyhedra, calculating the densest known packings of the Platonic and Archimedean solids. I won’t go into the details of the algorithm – the follow-up paper does a very nice job of explaining it. The basic idea is to start with a randomized ‘dilute’ configuration of the polyhedra in a box of some shape and either randomly move a randomly chosen polyhedron by a small amount, or deform the box by some amount, only allowing changes that increase the volume fraction while still preventing polyhedra from overlapping. One can imagine that iterating this many times would result in very, very dense packings — the hope, of course, is that these are the densest possible polyhedral packings. This remains to be proven.

The cool thing that Torquato and Jiao found is that for all the Platonic and Archimedean solids possessing central symmetry, the densest possible packings they found had volume fractions equal to the volume fractions of Bravais lattice packings of the same solids, to within a few hundredths of a percent. A nice Kepler-style argument using inscribed spheres gives upper bounds on the volume fractions of these densest possible packings – these are larger by only ~3-13%. Taken together, these results hint at a possible “Kepler Conjecture” for polyhedral packings: namely, that the densest packings of the centrally symmetric Platonic and Archimedean solids are given by their corresponding optimal lattice packings. Very cool — this suggests that quite complicated polyhedral packings might be able to be understood using some very simple rules.

On the other hand, Torquato and Jiao found that for the two polyhedra not possessing central symmetry — the tetrahedron and the truncated tetrahedron — the volume fractions of the densest lattice packings grossly underestimated the volume fractions of the densest packings they found using simulations. This leads to a converse conjecture: in particular, that the densest possible packing of any convex, congruent polyhedron without central symmetry is not a Bravais lattice packing — rather, it is significantly more complicated. (A nice side result is that the densest packing they found possesses no long-range order — more on this later.) It is not clear at this point what rules, if any, would dictate what the densest possible packing of these polyhedra look like.

One word of caution: as I mentioned before, because this approach is computational, none of these densest-known packings has been proved to be the densest-possible. Because the algorithm requires some choice of the starting ‘dilute’ configuration, it is possible that this choice will influence the final structure the algorithm settles at. In fact, Torquato and Jiao already found this to be the case in their search for the densest possible tetrahedral packing, as they note in their second paper — using a different initial condition, they found a densest packing ~4% more dense than the one they initially reported in the first paper.

While they don’t mention it, I think these results are particularly interesting in the context of amorphous systems, such as glasses. For example,why can a simple liquid metal be supercooled below its freezing point without crystallizing, potentially forming a glass? F. C. Frank put forward a very nice explanation for this. Considering the atoms of the liquid metal as spheres interacting via a non-directional Lennard-Jones potential, it turns out that the local energy density can be minimized by forming “locally-preferred” tetrahedral clusters. These then come together to form polytetrahedral Frank-Kasper phases, because forming these clusters requires less energy than forming crystalline clusters. The only problem with these phases is that they cannot tile space and are geometrically ‘frustrated‘ — the system is not in the crystalline state of lowest possible free energy, but is rather trapped a local free energy minimum in phase space. A significant amount of work has focused on trying to understand these kinds of structures, and connecting the geometric frustration inherent in these phases to the physical properties of supercooled liquids and glasses. It is not too surprising, then, that definitively finding the densest possible packing of tetrahedra (and analyzing the physical properties of such a structure) could help flesh out these connections — and Torquato and Jiao’s work seems to point the way.

While Steven Wolfram may not the most, um, orthodox figure in the scientific community (see, for example Steven Levy’s bio, or Cosma Shalizi’s review of the modestly-titled A New Kind of Science), I don’t think anyone doubts the usefulness of Mathematica and the various things associated with it (e.g. MathWorld and the Demonstrations Project). And now apparently his latest production – WolframAlpha, Wolfram’s new Mathematica-based search engine – will be released to the public this Monday. It looks quite interesting.

Finding useful information on the internet can be difficult and incredibly annoying, particularly for scientists or anyone in search of statistics of some sort. Google and Wikipedia, while useful, can often be inefficient or yield inadequate results. Many new search engines tailored to various interests seem to have emerged recently, but I am not aware of any current tools that satisfactorily tackle this particular (non-trivial) problem. One solution for anyone interested in biology is bionumbers, a searchable database of useful biological facts and data taken straight from the literature — but I think it’s quite clear that a more general and comprehensive solution (which WolframAlpha purports to be) would be very cool.

Judging from Wolfram’s promo video and reviews on pcworld, techreview and semantic universe, Alpha seems to be bionumbers made significantly more powerful and comprehensive. You probably won’t want to use it over google to find movie times or track your favorite celebrities’ lovelives; but you will want to use it to find various kinds of quantitative information: various metrics of the weather in Springfield, MA on the day David Ortiz was born, the location and sequence of some gene, the flowfield over a particular airfoil, the current position of the International Space Station, or data on blood cholesterol and potassium levels of middle-aged male smokers, for example. I look forward to pushing the limits of this tool, but it looks very useful.

Not be outmatched, Google recently announced plans to implement a similar kind of service using publicly-available data. I’m not sure when they will be releasing it, though, or how it will compare to WolframAlpha.

Here’s an interesting recent controversy. While I know absolutely nothing about the subject, the ideas and questions raised are interesting, so here’s a quick summary of the different opinions.

In one corner – Rao et al.
In a recent high-profile Brevia published in Science a week ago, Rao et al. suggest that

1. the degree of randomness in linguistic systems is significantly different from that of nonlinguistic systems, and
2. the degree of randomness of the script of the Indus civilization is similar to that of other linguistic systems – in particular, Sumerian and Old Tamil. (The similarity to Old Tamil is particularly striking because it seems to support the somewhat controversial opinion of some “that the Indus peoples spoke and wrote a Dravidian language” – here I’m quoting from Farmer et al.’s rebuttal.)

Based on this, their claim is that the Indus script encodes some kind of linguistic structure, in stark contradiction to some well-known work by Farmer et al. arguing that the Indus script is “a simple nonlinguistic sign system common in the ancient world”. Unsurprisingly, this has set off a number of critical responses, and it’s always fun to see discussion and debate of this sort go on.

The way Rao et al. quantify the degree of randomness of any given sequence of units, or “tokens” (for example, words or characters in English) is by computing the conditional entropy, a standard measure of randomness in information theory. Simplistically, this quantity is a measure of how flexibly different tokens can be ordered: in a nonlinguistic system where different tokens are ordered at random – what Rao et al. call a “Type 1 nonlinguistic system” – the conditional entropy is high, while in a nonlinguistic system where a given token must be followed by another specific token – a “Type 2 nonlinguistic system” – the conditional entropy is low. Intuitively, it is perhaps not surprising that linguistic systems fall somewhere in between: Rao et al. verify this by computing the conditional entropy for a few different linguistic systems, as well as two synthetic nonlinguistic systems (type 1 and type 2). They use this to support their first claim. Furthermore, they compute the conditional entropy for sequences of signs from the Indus script and – surprise, surprise – find that it falls somewhere in between the type 1 and type 2 nonlinguistic systems, just like the other linguistic systems they studied. They use this to support their second claim.

In the other corner – Farmer et al., Liberman, Pereira, Shalizi, Sproat, and others.
Farmer et al. – whose work Rao et al.’s contradicts – have written a pretty strong response to Rao et al.’s paper. Among other things, Farmer et al. claim that their original work from 2004 “awakened resistance from Indian nationalists and researchers whose entire careers have been linked to the Indus-script thesis, one of whom is listed as coauthor of [Rao et al.'s] study”; and, “if [Rao et al.'s] paper had been properly peer reviewed it would not have been published.” Ouch. Here are their main critiques of this work:

• Rao et al. used “synthetic” type 1 and type 2 nonlinguistic data in their calculations – that is, they created it according to certain rules. In a sense, these are designed to represent two different extremes on the “conditional entropy spectrum”, and as such it is not surprising that linguistic systems fall somewhere in between. Other nonlinguistic systems might, as well – so, claim #1 is unsubstantiated.
• The idea that the Indus signs are in some linguistic way related to Old Tamil does not make sense historically: for example, “the first attestation
  of Old Tamil came nearly two thousand years after the Indus civilization disappeared”.

Others have weighed in on this as well, including Mark Liberman, Fernando Pereira, Cosma Shalizi, and Richard Sproat. In particular, Liberman, Shalizi and Sproat have come up with simple counter-examples to Rao et al.’s data, showing instances of nonlinguistic datasets that show at least qualitatively similar behavior to Rao et al.’s linguistic datasets. It appears that at least for now, Pereira’s comment that language is “a system… carrying lots of specific information that cannot be captured by a single statistic” seems to hold.

Superconductors are generally classified as being type-I or type-II; Doug Natelson touched on this as part of his recent series of pedagogical posts explaining solid-state physics concepts. Type-I superconductors usually do not admit an external magnetic field in the superconducting state: they turn “normal” above a critical value of the field. Type-II superconductors do admit a magnetic field for some field strengths above the critical value, while still being able to superconduct: this is known as the “mixed” state.

In the presence of an externally-applied magnetic field, “vortices” form in a superconductor, with a normal nonsuperconducting core of size ~ (the “coherence length” over which Cooper pairs – quasiparticles consisting of pairs of ‘bound’ electrons – are extended). This is surrounded by a region of size ~ in which a supercurrent circulates (where is known as the penetration depth), and hence produces its own opposing magnetic field. Forming such a vortex requires some energy; straightforward calculations show that the interfacial energy per unit length associated with a vortex is proportional to . If , forming such vortices increases the free energy of the system, and vortices tend to attract and annihilate – as in the case of type-I superconductors. If , on the other hand, a “lattice” of repulsive vortices is formed – as in the case of the mixed state of type-II superconductors.

In some materials, electrons can exist in two different bands ( and ), reflecting different kinds of bonding. A classic example of this is graphite. The electrons in the highest occupied states in a structurally similar superconductor, MgB₂, are similarly - or -bonded. This can be thought of as resulting in two different kinds of Cooper pairs with two different values of and . The interesting thing is that in MgB₂, the quasiparticles associated with the electrons have (type-I), while the quasiparticles associated with the electrons have (type-II).

The coupling between these two different states is so weak that MgB₂ was predicted - and has now been found – to be a so-called “type-1.5″ superconductor — that is, one with behavior combining aspects of type-I and type-II superconductivity. In this case, the vortices repel each other (as in type-II superconductors) over short distances while they attract each other (as in type-I superconductors) over long distances. In a previous post, I noted that competition between long-range repulsive and short-range attractive forces often leads to spatially inhomogeneous and anisotropic phases in various systems: examples include “stripe” or “bubble” phases in blockcopolymers, “pasta phases” of the crusts of neutron stars or DNA-intercalated lipid bilayers, stripe formation in ferrofluids, and anisotropic phases in two-dimensional electron gases in the presence of moderately large magnetic fields. Similarly, one might expect the competition between short-range repulsive and long-range attractive forces between vortices to give rise to interesting pattern formation in MgB₂ at low applied fields.

This is what Moshchalkov et al. set out to explore. One way to visualize the flux vortices of a superconductor is using so-called ‘magnetic decoration’: that is, by sprinkling ferromagnetic powder onto the surface of the superconductor. The powder is then attracted by the vortex flux lines and forms a pattern representative of the flux vortices. Using this technique, Moshchalkov et al. found indeed that the vortices in MgB₂ were inhomogeneously distributed, often forming stripes separated by regions of ‘normal’ phase – thus confirming that MgB₂ is a type-1.5 superconductor.

Glasses have received a lot of attention because of their interesting structure and dynamics (indeed, Nobel Laureate Phil Anderson wrote that “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition.”) Unlike crystals, they do not possess long-range order — only short or medium-range order, like liquids. Unlike liquids, however, glasses have mechanical properties akin to those of solids. A number of different approaches have been explored to study the physics of glasses, including harnessing the technology of colloidal physics as many in our and other research groups do. Metallic glasses are also model glassy systems, formed when a molten liquid precursor is supercooled at a rate fast enough that glass formation wins over crystal formation.

Here’s a quick description of two recent papers that look at two different aspects of metallic glasses…

1. How easy is it to form a glass? (Li et al., Science 2008)
Intuitively, one might expect that if the liquid precursor to a metallic glass has higher packing density, the atomic subunits making up the liquid have less “free” volume to explore and hence have a lower probability of forming an ordered cluster to nucleate crystal formation: the glass is “easier” to form. (Note that because the density at the glass transition is continuous, unlike the transition between a liquid and crystal, the density of the liquid precursor and the density of the newly-formed glass are the same thing).

Surprisingly, it seems there is very little clear experimental demonstration of this correlation between the density of a metallic glass and the ease with which it is formed. In this paper, Li et al. show a very nice route towards this. They use microfabrication to produce an array of silicon nitride cantilevers, sputter-coated with differing compositions of the binary alloy Cu_xZr_1-x, a popular system for studying metallic glasses. They measure the density difference between the as-deposited glass and the crystal that results from thermal annealing their samples by measuring the deflection of the cantilevers before and after annealing (the density of the resulting crystalline state can be estimated using equilibrium thermodynamics). On the other hand, they measure the ease of glass formation for glasses of differing composition by casting them in wedge-shaped molds; a cross-section of the resulting solid shows a clear boundary between the glassy and the crystalline state, and the thickness of the lower (denser) glassy state is a standard metric for how easily it formed. The beauty of these experiments is that they are quite straightforward, and look at this particular system over a range of relative compositions.

Sure enough, Li et al. see very nice correlation between the glass/crystal density difference and the ease of glass formation over the range of compositions they study. Interestingly, three particular compositions seem to form the glassy state very easily — and surprisingly, only one can be predicted using existing models!

2. What is the medium-range structure of a glass? (Ma et al., Nature Materials 2008)
A good deal of work has focused on understanding the microscopic nature of short-range – that is, on the lengthscale of just a few atoms – order (SRO) in metallic glasses (e.g. Miracle, 2004). A relatively recent model, which is accumulating more and more experimental support, is that alloyed metallic glass are composed of small clusters of majority atoms surrounding a minority atom “seed”. If one is willing to believe this model, the next question is: how do we use this understanding to better understand the nature of medium-range order (MRO) in metallic glasses? It has been suggested that these clusters may closely pack to form the metallic glass. In this paper, Ma et al. suggest another idea: these clusters form a fractal network of dimension 2.31.

The evidence Ma et al. compile to support this notion is compelling. For starters, fractal networks are ubiquitous in materials of interesting microstructure (e.g. see the references in Ma et al.’s paper). One close example is quasicrystals, which also lack translational symmetry, and have been shown to also be described as fractal networks. Second, Raman and neutron-scattering experiments performed in the 1990s suggested the existence of frequency-dependent vibrational excitations in metallic glasses, with a crossover between the phonons that are characteristic of ordered crystals and “fractons”, vibrational excitations of a fractal network. (This is the first time I come across the idea of a “fracton”, and I will have to spend some time rigorizing how I think about them.) In this paper, Ma et al. present their own and others’ neutron and X-ray diffraction data of a number of metallic glasses of different compositions (including the Cu_xZr_1-x mentioned in the previous paper).

In crystalline materials, the momentum-space position of the first Bragg peak in a powder diffraction pattern () is inversely proportional to the largest distance between two atomic planes of the sample — small ’s probe large lengthscales. Representing the atoms making up the crystal as hard spheres of volume , this distance scales as (that is, constant). The key idea in Ma et al.’s paper is that while metallic glasses do not have well-defined Bragg peaks because of their disordered structure, the medium-range order does give rise to a few diffuse scattering “haloes”. Thinking about the atoms of the metallic glass as hard spheres as well, on expects that constant, where mass density/(avogadro’s number * molecular weight) and is the fractal dimension of the network making up the metallic glass. Strikingly, they see this kind of scaling behavior, with . Further analysis of the atomic pair distribution function of their samples (essentially, a measure of how correlated atoms at different distances from each other are) supports this notion of a fractal network over medium-range length scales. It’ll be interesting to see how future work builds on this idea. I’m a bit confused as to what the “atomic volume” as calculated in Ma et al.’s paper physically represents in these alloyed metallic glasses, something the authors don’t go into too much detail on. Naively I would guess this is somehow related to the size of the clusters making up the fractal network — perhaps it would be interesting to use this kind of data to pull out this information and see if it agrees with other work on the structure of these SRO clusters.

I’m back – posts will be much shorter and more paper-centered from now on, as classes and research continue to consume my life.

Three really cool papers recently, all dealing with particles in some kind of flow:

1. Effects of particles in chaotic flow (Ouellette et al., PRL 2008)
Small tracer particles are often used to ‘visualize’ fluid flows, by seeding them into the fluid. If the particles are small enough and have low enough density to match the fluid, they can be considered as infinitesimal fluid elements to a good approximation. This breaks down if the particles are (i) too large, or (ii) too dense. While the effect of having small but dense particles is pretty well studied (since the particles can be taken to be pointlike), the case of large particles is more complicated – one has to solve the relevant Navier-Stokes equation over the surface of each particle. How does a large tracer particle perturb fluid flow?

By imaging the motion of tracer particles of different sizes in a chaotic fluid flow, Ouellette et al. study the flow field around a large tracer particle as well as its own motion. (The smallest particles act as the ‘ideal’ infinitesimal fluid elements that follow the flow well.) The effect of tracer particles being too large or too dense is often thought to be captured by the Stokes number where and are the particle and fluid densities, and are the particle radius and characteristic flow length scale, and is the fluid Reynolds number. It is surprising, then, that the data in these experiments does not seem to solely depend on the Stokes or Reynolds numbers – these dimensionless parameters don’t appear to capture all of the physics associated with inertial effects. Weird.

2. Effects of particles in turbulent flow (Tanaka and Eaton, PRL 2008)
Ok, so the previous paper dealt with non-turbulent flow. This one deals with the case of how particles in a turbulent flow affect the turbulence. Do they make it more turbulent, make it less turbulent, or (unlikely) don’t affect the flow? Can these effects be captured by the Stokes or Reynolds number, unlike the previous case?

Tanaka and Eaton looked at data from many different experiments on this subject, finding (as in Ouellette et al.’s experiments) no systematic dependence on the Stokes or Reynolds numbers. Hm. Instead, they use some very beautiful dimensional analysis to come up with a new dimensionless parameter, what they call the particle momentum number Pa, which seems to capture more of the physics here – for very large and very small values of Pa, the particles augment turbulence, while for an intermediate range of Pa turbulence is attenuated. (Instead of attempting to write the two forms of Pa out, I’m just going to refer the reader to equations 14 and 15 in the paper). This is cool – finally a parameter that yields information about the physics of the situation!

Physically, is there a simple way of seeing what Pa actually means, versus just being a combination of Re, St, and various relevant variables? (The Reynolds number, for example, can be understood as telling one about the relative importance of inertial forces versus viscous forces on a tracer particle; the Stokes number on the other hand tells one about how ‘impactable’ a tracer particle is – it describes how independently the particle can move from the carrier flow.) I wasn’t fully able to decipher this.

Secondly, and I’m not sure if this even makes sense or not, but could this have any relevance to Ouellette et al.’s experiments, in which St or Re on their own were not enough to account for the effects of perturbations due to tracer particles? I did some mindless playing around with Ouellette et al.’s data from figure 4c-d, plotting it as a function of two such possible parameters. The first, ‘Pa1′, is inspired by Tanaka and Eaton’s particle momentum number, and is defined as ; the second, ‘Pa2′, is Tanaka and Eaton’s equation 15: . This is what I’m showing here:

Perhaps unsurprisingly, the two curves (for two tracer particle sizes) still don’t fall on a single curve. Oh well. Again, I’m not entirely sure if it makes sense to ask this question, but is there some combination of St and Re (similar to Pa) that is a more relevant dimensionless parameter for Ouellette et al.’s experiments?

3. Phonons in a 1D microfluidic ‘crystal’ (Beatus et al., Nature Physics 2008)
This is a cute paper that touches on many, many interesting ideas. The basic idea is straightforward: Beatus et al. produced a continuously-flowing array of uniformly-spaced oil drops in a microfluidic channel, surrounded by a continuous oil phase. The drops are disc-like in shape (they are confined in the z-direction), unconstrained in the x-direction (the direction of flow), and the constraint in y (i.e. the width of the channel) is varied, thus varying the friction on the drops.

The cool thing is that these researchers see interesting longitudinal and transverse fluctuations (it’s worth looking at the supplementary movies), and by fourier-transforming their data, they pull out dispersion relations that surprisingly show acoustic phonon propagation. The phonon propagation speed is much smaller than the speed of sound in the surrounding fluid, which leads them to hypothesize that these collective modes arise from dipole-like hydrodynamic interactions between droplets. Very pretty stuff.

Along with moving to a new institution for my Ph.D., I have decided to switch fields, moving from hard condensed matter/nanoscience to soft condensed matter/biological physics. This decision was totally unplanned – even when applying to and visiting graduate schools, I thought I wanted to do some variant of what I did as an undergrad. The thing is, as I visited more and more schools and learned about different people’s work, I found that what really captured my interest and got me excited was the soft matter side of things. Particularly in biological physics, things tend to be messier and less well understood – but this just means that there’s more to learn and quantify. I think physicists are well-positioned to bring something new and useful to the table.

(And recently, I’ve been shifting my focus more and more towards colloids and emulsions – they’re wonderful systems to work with, and allow for what I consider to be some very cool experimental statistical mechanics. My new interest in colloidal physics will have to wait for another post in the future, though.)

While in one sense my interest in soft condensed matter and biological physics has been steadily increasing over the past few years due to some really great classes I took as an undergrad, my interest in the biological side of things was really catalyzed by three key experiments/ideas:

1. Tensegrity and the structure of biological systems
Tensegrity is a mechanical design principle pioneered by Kenneth Snelson and Buckminster Fuller in the 1960’s, in which structures are designed such that the competition between forces – tension versus compression – throughout has a self-stabilizing effect. (A well-known example of this is the geodesic dome.) Among others, Don Ingber has spent a lot of time exploring the application of this idea to the structure of cells. Basically, the idea is that the cytoskeleton of the cell is composed of a network of interconnected units – the microfilaments, microtubules, and intermediate filaments – under tension and compression; that is, it is structured according to the principle of tensegrity. Many groups have explored this idea since it was first proposed, and other theories exist for understanding cellular structure; indeed, many groups, including the one I’m in, currently spend a lot of time trying to better understand the structure and physical properties of cells. (You can read more about this here.) I just thought the idea was so darn cool when I first came across it in this very nice Scientific American article written over a decade ago (look at the cell on page 54!). What’s more, this idea could be used to understand the structure of other assemblies at the micro- or nano-scale, such as buckyballs or nanotubes (e.g. see the chapter by Yakobson on “Carbon Nanotubes: Supramolecular Machines” in the Dekker Encyclopedia of Nanoscience and Nanotechnology), actuated nanocolumns, and even…

2. Viruses from a materials perspective
Yep – reading about tensegrity led to me to Caspar and Klug’s classical work in the 1960’s, in which they attempted to understand the structure of ’spherical’ viral capsids within a tensegrity-inspired framework. Since then, a number of physicists and engineers have spent a good deal of time trying to understand the structure of viral capsids. One framework in particular, developed by David Nelson and co-workers, really appeals to me: I think it’s an elegant combination of ideas from crystallography and continuum mechanics (what they call “spherical crystallography”). Basically, the idea is that if you try to pack a number of particles – be they beads, or the protein subunits of a viral capsid – on the surface of a sphere, the resulting assembly necessarily possesses crystallographic defects resulting from geometrical frustration. I wrote a small review of viral structure and mechanics focused on this work for a nanomechanics class not too long ago, which you can read here, if you want to explore this further. And this is just the tip of the iceberg – people are doing all sorts of crazy things with viruses: playing tug of war with them, watching them spit out their DNA, poking on them, shocking them, and filling them with various cargoes, among other things. Pretty cool stuff.

3. Hitting worms with laser pulses
Again, this is a very broad field in which a lot of great work has been (and continues to be) done. I don’t know enough about it. What first got me excited about biological neural networks and c. elegans was learning about this experiment by Mehmet Fatih Yanik. Basically, Yanik et al. used femtosecond laser pulses to cut single axons in c. elegans worms, observed the resulting phenotypic effects, and watched them grow back within 24 hours. This is pretty neat – after all, being able to perturb these affords researchers quite a lot of control, and could be used to study nerve regeneration processes one axon at a time, among other things. c. elegans is quite the model system, and I’m sure there’s a lot of other cool work going on trying to understand various processes and mechanisms in these worms. For example, in addition to Yanik’s work, my very little reading of research in this field has exposed me to some very interesting papers from Richard Morimoto’s, Ikue Mori’s, Aravi Samuel’s and William Bialek/William Ryu’s groups, to name a few off the top of my head. I still need to learn more about this field, particularly of what the biologists are doing – but again, this femtosecond laser stuff really got my attention when I first came across it.

It’s been a while since I last posted, and I’ve been up to quite a bit since then. For starters, I’m officially done with undergrad – apparently now I’m a bachelor of arts and a master of science.

In other news, I finally (!) decided on a grad school – this fall, I will be moving on from Penn and starting my Ph.D. in physics at Harvard. I actually packed up and moved to Cambridge a week ago, and have been getting settled and starting work in my new lab – I’m doing biophysics work in Dave Weitz’s group, which is really exciting. (More details later…)

Physics bloggers have actually been shuffling around quite a bit: for example, fliptomato has come back to the U.S. from the U.K., while in a happy coincidence Mark Trodden will be leaving Syracuse for… Penn!

A nice little sidenote is that one of my main papers stemming from some of the work I did while at Penn was accepted not too long ago – watch out for it in Nano Letters sometime soon…

And lastly, moving has given me a chance to organize some of the clutter in my life. In that spirit, I’ve decided to give my new personal webpage and this blog a quick makeover.

So, it looks like I’m part of a blog-meme. I normally wouldn’t do this, but I have some time to kill what with all this flying I’m doing (visiting grad schools). So, here goes, slightly modified…

1. Link to the person who tagged you. Done.

2. List 7 a few random things currently on your mind.

• Where should I go for grad school? I have it narrowed down to a few institutions, each of which has its own particular strengths and weaknesses – in terms of the projects I’m very excited about, equipment/facilities, funding, location, the size of the groups, the intellectual culture, etc. The spreadsheet has them dead even to within uncertainty, which means that I’ll have to keep taking data…

• Some of the research groups I’m interested in joining are quite large. This is often cited as a disadvantage, since it could translate into less “face-time” with the advisor, although to be fair – isn’t the more relevant parameter the (postdoc + senior grad student)/new student ratio rather than the faculty/new student ratio?

• Research – just thinking through the details of a number of experiments and simulations that I’m working on. The annoying thing with all this traveling is that it really punches a hole in my productivity (as well as means I’ll be missing the first half of the APS March Meeting!); but then again, talking to all these fascinating people and finding out about all the cool work going on at these different places is invaluable.

• Another thing that traveling makes difficult is staying on top of the literature. I have several tens of papers waiting to be read, and while long flights are great for plowing through them, the rate at which the to-read list grows is impressive.

• I came across this interesting NYT book review on a recent book, Intern by Sandeep Jauhar. The gist is Scrubs-ian in nature – it’s the story of a medical intern trying to deal with the imperfections of day-to-day hospital culture, the meaning of life, etc. – but what really got me was his physics background (he has a Ph.D. from Berkeley) and the analogies he makes: “Life on the wards was like the plasmons I had studied in condensed matter physics… where individual electrons, moving randomly, coalesced into something greater than the sum of their parts. There was a sort of synchronized buzz. … In the midst of this collective excitation, I kept thinking, Why am I so lonely?” Alright, so it’s kind of a stretch, but still – it’s physics.

3. Tag more people at the end of your blog and link to theirs. I’ll suggest Rod, Sam and Travis.

4. Let the tagged people know by leaving a note on their site. Done.