Fun with fluids: Hydraulic jump

We usually think of shock waves as exotic - something that happens when a huge explosion goes off, or when a supersonic plane flies by.  A shock in a gas is a relatively abrupt boundary between relatively cold gas moving faster than the speed of sound in the gas (that is, with a Mach number \(M \equiv v/c_{s} > 1\), where \(c_{s}\) is the sound speed and \(v\) is the speed of the gas) and warmer gas moving slower than sound (\(M < 1\)).  A shock that moves on its own relative to a stationary environment is a shock wave, while one that remains fixed in place relative to its surroundings is a "standing shock".   The details of the gas motion within the shock itself are very complicated, but the constraints of mass and momentum conservation make it possible to understand a lot about the relationship between upstream and downstream gas conditions even without knowing the nitty gritty.

  

It turns out that you have very likely seen a fluid analog of a standing shock in your sink!   Run the tap so that a stream of water hits the flat bottom of a typical kitchen sink.  You will see a disk-shaped region with a radius of a few cm (depending on flow rate) where the water is fast-moving but thin, surrounded by a turbulent ring, outside of which the water layer is thicker but slower-moving.   This is called a hydraulic jump.   The fast-moving water has a speed \(v\) greater than the speed of gravity-driven ripples in a thin fluid layer, \(\sqrt{g h}\), where \(g\) is the gravitational acceleration and \(h\) is the fluid depth.  The Froude number \(Fr \equiv v/\sqrt{gh}\) is greater than one on the fast-moving side of the jump, and less than one on the slow moving side.  Like the gas shock case, the boundary is a mess, but mass and momentum conservation can let you calculate the flow speed and fluid depth downstream if you know the flow speed and fluid depth upstream.   

The receding floodwaters in my neighborhood Tuesday provided me with a great example of a hydraulic jump, shown in the brief video clip above.  I still think it's cool that you can see an analog of a sonic boom in your sink, or in a nearby street if you're unlucky.

Storms are powerful heat engines!

Storms are incredibly powerful (on human scales) heat engines - driven by the sun, the fluxes of mass and energy are simply enormous.  To see just how big, let's take a look at the big thunderstorm system that flooded large parts of the city of Houston last night (hence why I'm blogging and unable to get to campus until the waters recede).   A large storm system dumped about 20 cm of rain (!) over a land area of approximately 4000 km² between 10:00pm and about 4:00am.   That's 8 x 10¹¹ kg of water!

The bottom of the rain clouds was maybe 0.5 km above ground level.  That's a lower bound on how far all that rain had to fall.  Using \(g \approx \)10 m/s², that's about 4 x 10¹⁵ J of energy, deposited in about 20000 sec, for an average power delivered of 2 x 10¹¹ Watts, as much as 100 municipal-scale power stations.   That doesn't even account for the energy contained in the wind and the lightning discharges.

Remember, this is all being driven by the sun, through temperature differences that are at most 20 K.  Thermodynamics tells us that the most efficient this process could possibly be is something like 1 - (300 K/320 K) = 1/16.  That means that the total energy involved had to be at least 6.4 x 10¹⁶ J = about 18 billion kW-h, and that's only one part of a big storm system.  This is why engineering the weather is a non-starter!

What is band theory? (car analogy)

One of the commenters on my previous post asked how I could explain band theory to a nonscientist, an artist in particular.  Here's a shot.  By necessity, when trying to give an explanation that avoids math almost completely, I'm forced to lean heavily on analogy, which means sacrificing accuracy to some degree.  Still, I think this is a useful exercise - it certainly makes me think hard about what I consider to be the important elements of a concept.  (This must be what Randall Munroe had to do many times for his upcoming book!  If you haven't read his first one, what have you been waiting for?)

The electronic properties of many crystalline materials are well described by "band theory".  At its heart, band theory comes down to three important ideas that I'll explain more in a minute:  Electrons in solids can only have certain states (to be defined below); those states are determined by the arrangement of the atoms in the solid; and each state can only hold two electrons, no more.   To describe this, I'm going to have to mix metaphors a bit, but bear with me.

In a very American mode, we're going to picture the electronic states as individual lanes in a verrrrrry wide, multi-lane highway.  Each lane has a different speed limit (each state has a particular kinetic energy), with the slowest traffic off to the driver's right (in this US-centric analogy) and speed limits increasing progressively to the driver's left.   Each lane can only hold at most two cars (each state can only hold two electrons, one of each kind of "spin").   Here's where the analogy becomes more of a reach:  Not all speed limits (electron kinetic energies) are allowed.  Speeds in adjacent lanes are separated by a small amount (energy level spacings are set by the size of the crystal), and some lanes are missing altogether (some energies are outright forbidden, determined by the type and arrangement of atoms in the crystal).  So, there are "bands" of lanes, separated from each other by "gaps".

Now we start adding cars to the highway with the restriction that cars can only drive at the speed limit of their lane, and (in an un-American twist) the drivers want to go the minimum possible speed.  This is going to tell us the "ground state", the slowest/lowest energy configuration of the system.  The first two cars (electrons) go into the slowest lanes waaaaay over on the driver's right.  The next two cars go into the second-slowest lane, and so forth.  We keep adding in cars (electrons) until we run out of inventory (until we have kept track of all of the electrons).  The more cars we put in, the faster the top speed of the fastest cars!

Cars can only merge into lanes that are open (or only partly occupied).  If the last car added ends up in a lane in the middle of a band of lanes, so that it can easily merge into an adjacent unoccupied lane, this situation corresponds to a material that is a metal.  If the last car ends up right against the guard rail of a band of lanes, so that there just is no adjacent lane to the driver's left available, then this situation corresponds to a "band insulator".   (If the gap to the next band of lanes is large, we call such materials "insulators"; if it's not too big, we call those materials "semiconductors".)

One point that even this very imperfect analogy can highlight:  The speed of the fastest cars (electrons) in a block of copper is actually about 0.5% of the speed of light (!), or more than 6,000,000 kph.  For metals with even more electrons, the fastest movers can be going so quickly that relativistic effects become important!

This was a very rough cut.  I'll try to return to this later, with other ways of thinking about it.

Book recommendations: Stuff Matters and The Disappearing Spoon

I've lamented the lack of good popularizations of condensed matter/solid state physics.  I do, however, have recommendations for two relatively recent books about materials and chemistry, which is pretty close.

The Disappearing Spoon, by Sam Kean, is a fun, engaging stroll across the periodic table, exploring the properties of the various chemical elements through the usually fascinating, sometimes funny, occasionally macabre histories of their discoveries and uses.  The title references joke spoons made from gallium that would melt (and fall to the bottom of the cup) when used to stir tea.  The tone is light and anecdotal, and the history is obscure enough that you haven't heard all the stories before.  Very fun.

Stuff Matters, by Mark Miodownik, is similar in spirit, though not quite so historical and containing more physics and materials science.  The author is a materials scientist who happens to be a gifted author and popularizer as well.  He's done a BBC three-episode series about materials (available here), another BBC series about modern technologies, and a TED lesson about why glass is transparent.

A matter of gravity

Gravity remains an enduring challenge in physics.  Newton had the insight that he could understand many phenomena (e.g., the falling of an apple, the orbit of Halley's comet) if the gravitational interaction between two objects is an attractive force proportional to the product of the objects' masses, and inversely proportional to the square of the distance between them ( \(F = - G M_{1}M_{2}/r^{2}\) ), and acts along the line between the objects.  The constant of proportionality, \(G\), is Newton's gravitational constant.   About 225 years later, Einstein had the insight that in more generality one should think of gravity as actually distorting space-time; what looks like a force is really a case of freely falling objects moving in the (locally) straightest trajectories that they can.  (Obligatory rubber sheet analogy here.)  In that theory, general relativity (GR), Newton's constant \(G\) again appears as a constant of proportionality that basically sets the scale for the amount of space-time distortion produced by a certain amount of stress-energy (rather than just good old-fashioned mass).  GR has been very successful so far, though we have reasons to believe that it is the classical limit of some still unknown quantum theory of gravity.  Whatever that quantum theory is, \(G\) must still show up to set the scale for the gravitational interaction.

It makes sense that we would like to know the numerical value of \(G\) as accurately and precisely as possible - seems like the first thing you'd like to understand, right?  The challenge is, as I've explained before, gravity is actually an incredibly weak force.  To measure it well in absolute numbers, you need an apparatus that can measure small forces while not being influenced by other, faaaaaar stronger forces like electromagnetism, and you need to do something like measure the force (or the counter-force that you need to apply to null out the gravitational force) as a function of different configurations of test masses (such as tungsten spheres). 

I'm revisiting this because of a couple (1, 2) of interesting papers that came out recently.  As I'd said in that 2010 post, the challenge in measuring \(G\) is so difficult that different groups have obtained nominally high precision measurements (precise out to the fourth decimal place, such as \(G = 6.6730 \pm 0.00029 \times 10^{-11}\) Nm²/kg²) that are mutually inconsistent with each other.  See this plot (Fig. 1 from arxiv:1505.01774).  The various symbols correspond to different published measurements of \(G\) over the last 35 years (!).  The distressing thing is that there does not seem to be much sign of convergence.  The recent papers are looking to see whether there is actually some periodicity to the results (as hinted by the sinusoid on the plot).  To be clear:  The authors are not suggesting that \(G\) really varies with a several year period - rather, they're exploring the possibility that there might be some unknown systematic effect that is skewing the results of some or all of the various measurement approaches.  As both teams of authors say, the best solution would be to come up with a very clean experimental scheme and run it, undisturbed, continuously for years at a time.  That's not easy or cheap.  It's important to note that this is what real, careful measurement science looks like, not some of the stuff that has made web headlines lately.

People you should've heard about: John Bardeen

If you ask the average person to name a physicist, chances are they'll mention Einstein, Hawking, and possibly Sheldon Cooper.  Maybe Richard Feynman, Brian Greene or (*sigh*) Michio Kaku.  I'd like to have an occasional series of posts pointing out people that should be well-known, but for some reason are not.  High up on that list:  John Bardeen, who is the only person one of only two people to win two Nobel prizes in the same field.

Bardeen, like many of his contemporaries, followed what would now be considered a meandering, unconventional trajectory into physics, starting out as an undergrad engineer at Wisconsin, working as a geophysicist, enrolling as a math grad student at Princeton, and eventually doing a doctoral thesis with Wigner worrying about electron-electron interactions in metals (resulting in these two papers about how much energy it takes to remove an electron from a metal, and how that can be strongly affected by the very last layer of atoms at the surface - in the 1980s this would be called "surface science" and now it would be called "nanoscience").

Bardeen was a quiet, brilliant person.  After WWII (during which he worked for the Navy), he went to Bell Labs, where he worked with Walter Brattain to invent the point contact transistor (and much more disagreeably with William Shockley), explaining the critical importance of "surface states" (special levels for the electrons in a semiconductor that exist at the surface, where the periodic potential of the lattice is terminated).  Shockley is viewed in hindsight as famously unpleasant as a co-worker/boss - Bardeen left Bell Labs in large part because of this and ended up at Illinois, where seven years later he worked with Bob Schrieffer and Leon Cooper to produce the brilliant BCS theory of superconductivity, earning his second Nobel.  (Shockley's borderline abusive management style is also responsible for the creation of modern Silicon Valley, but that's another story.)

During and after this period, Bardeen helped build the physics department of UIUC into a condensed matter physics powerhouse, a position it continues to hold.  He was very interested in the theory of charge density waves (special states where the electrons in a solid spontaneously take on a spatially periodic density), though according to Lillian Hoddeson's excellent book (see here, too) he had lost the intellectual flexibility of his youth by this time.  

Bardeen contributed greatly to our understanding and advancement of two whole classes of technologies that have reshaped the world (transistors and superconductors).  He was not a flamboyant personality like Feynman (after all, he was from the Midwest :-) ), and he was not a self-promoter (like Feynman), but he absolutely deserves greater notoriety and appreciation from the general public.

Bad science, bad science journalism: the EmDrive

No, NASA has not discovered warp drive.  There is a huge amount of media attention (here, here, here, for examples of relatively mainstream media) being given to a claim that a NASA team has successfully tested a gadget called the EmDrive.  The claim is that one can take a conical microwave resonator (picture the cavity that is your microwave oven, only shaped like a truncated cone rather than a rectangular box), fire up microwaves to drive the resonant modes, and the cone will experience a steady thrust in one direction (the direction of the fat end of the cavity).  There are multiple alleged explanations for this, ranging from botched thinking about special relativity to really bizarre word-salad about virtual particles, the quantum vacuum, and "warp fields".

Let me explain why this is bad science, terrible science journalism, and highly problematic.

First, the science.  Our theory of electricity and magnetism is arguably the best understood, most precisely tested theory we have, both in its classical limit (the limit relevant for your microwave oven) and in its quantum limit (the limit relevant for things like calculating the magnetic moment of the electron, something that we can do to more than 14 decimal places!  According to that theory, a closed microwave resonator does not generate thrust (surprise surprise).  Given over 100 years of tests of classical E&M, it's going to take more than one poorly documented experiment, not published, to convince scientists that something exotic is going on.  Extraordinary claims require extraordinary evidence, and this just isn't it.  Moreover, claims that exotic quantum vacuum effects or "warp fields" are somehow relevant here are just on their face absurd!  The energy densities, the materials involved, none of this couples to exotic quantum vacuum physics any more than my microwave oven does.  This is like arguing that by accelerating a simple dielectric like a piece of plastic, I should see electron-positron pair production and warped spacetime.  It's nonsense.

What would it take to convince me?  How about a thoroughly documented experiment done by someone with credibility in precision measurement, for a start.

As for science journalism:  The number of outlets who uncritically pass along something like this is appalling.  What's worse, they distort it even more - the third link up top not only claims that this is a reactionless drive, but that it will allow faster-than-light travel.  What the hell?  (Yes, I know that the Daily Fail is third-rate fish-wrap.)  I fully expect to see a CNN story about this, and it will be terrible.  This will propagate in the media for several days, and they will portray it as some underdog inventors showing that the Scientific Establishment is wrong, or they'll present this as an actual scientific controversy, when in fact the burden is all on the experimenters to show that their work (which flies in the face of decades of contrary evidence) is right.  Hey, IFLS:  You should be ashamed of yourselves for your coverage of this.  Good grief - I thought part of your message was that people should, I don't know, think critically!

Why is this problematic?  It's an issue because people don't trust science, in part because they end up reading uncritical bull like this and come away thinking that science is either a dodge, a scam, or entirely a matter of opinion, when in fact it's an approach to thinking critically about the world that has made possible all of modern technology and medicine.

Anecdote 2: Life in a lab - the Demon Liquefier From Hell

I know this will come as a shock to many of you (ahem), but when I was a kid I watched a lot of Star Trek reruns.  Even in middle school one story-telling trope that seemed phony to me was the way Scotty (and Kirk) could tell just from the sound and feel of the ship whether something was wrong with the engines or environmental controls.   Years later, as a grad student in the Osheroff lab, I realized that this was actually one of the more realistic bits of writing and characterization in the show.

Our lab focused on ultralow temperature physics.  We ran experiments using dilution refrigerators (also see here), and these each required multiple vacuum pumps running continuously (in our case, each fridge needed a helium-leak-tight, sealed, mechanical "roughing" pump, a big conventional mechanical pump (for the "1K pot"), and a large diffusion pump as a "booster").   The mechanical pumps were housed in a cabinet in a room one floor below the main lab, and even with that kind of distance and insulation they provided a continuous background hum to the room.  That basement room also contained our group's helium liquefier, an ancient beast of a machine (a twin is shown here) that took in recycled helium gas from our experiments, cooled it by using pistons to drive a big flywheel, and then liquefied it by squirting it through a tiny, cold orifice.  The liquefier provided something between a wheeze and a heartbeat to the lab, a steady state "pachooka pachooka" sound with a repetition period of around one second when it was working well.  The muffled version of this noise also permeated the lab.  After being in the group for a few months, I understood completely where Scotty was coming from.  It was deeply disturbing to walk into the lab and realize that something, somewhere was amiss because the sound or extremely subtle floor vibrations felt "off".  

The liquefier (officially the Demon Liquefier From Hell [DLFH], or The Liquef--ker) was a formative part of our lab's grad school experience.  Running the system, which predated any serious automated controls, required some amount of fiddling in the best of times, interpreting half a dozen cryptic gauges ("inches of water" as a pressure unit?  Really?), with the only useful diagnostic being whether the liquid level in the big helium storage dewar is increasing or not.  A period preventative maintenance every few months meant replacing press-fit bearings, cleaning amazingly stinky phenolic parts, and worrying that we would bend a cam "wrist" and be out hundreds of dollars for a spare as well as having the system be down for a week.  Even before helium prices rose dramatically, recycling helium was a good idea if you could do it.   One of the most depressing calculations you could do as a student in our lab, as you were listening to the intake purifier blow moisture like a sad sneeze and wondering why the hell the DLFH wasn't making liquid, was to compare the cost of your time, recycled helium, and externally purchased helium, and realize that it was clearly financially smart for your adviser to use you to maintain the system.

The DLFH was certainly educational.  I learned a lot about engines and big mechanical systems.  I learned that it is only marginally cheaper to build a heavy crate and ship via an express carrier than it is just to buy a plane ticket for a 130 kg flywheel.  I learned what it feels like to take a jolt of 208 V (not recommended) and that yelped curses from that room could still be heard up in the lab.  To this day I still reflexively shudder a bit when I hear that "pachooka" sound when I visit a place with a similar gadget.  

Anecdote 1: The Qual

A key aspect of a good graduate education is realizing, more than ever, that to be competitive you'll have to raise your game.

My cohort of physics grad students arrived at Stanford in a sunny, dry September of 1993, and we were an interesting bunch.  Four out of the twenty of us were Russian (or from the recently former Soviet Union), and for this story it's important to understand that these folks were incredibly well-prepared in terms of academic physics training.  Growing up in the Soviet system, they basically decided for you when you were something like 14 years old if you were going to be trained as a physicist.  We all got together at a mixer in a crummy graduate apartment, and I still remember a bunch of us standing around the drinks table, chatting about our undergrad schools and what we'd studied.  One person had been a kicker for the Northwestern football team!  One person had been into rock climbing and had done a fun summer program at Los Alamos.  Then one of the Russians said that he'd studied conformal field theory.  For fun.  Kind of set the stage a bit.

At the time the department had a "qualifying exam" that was one of a series of tasks students had to complete in order to (eventually) receive doctoral candidacy.  In this case, the qual was a two-day, six hours each day, written exam with a total of eight problems, basically on advanced Stanford-level undergrad material, administered early in the fall quarter.  Two of the questions were "general physics", meant to test your ability to think on the fly and reason quantitatively as a physicist - these tended to be hard, since they didn't really seem like the kinds of questions you're usually asked in a standard undergrad physics class.  As I later learned from serving as the student rep on the department's qual committee, the point of the test was not to act as a filter to weed out weak students, or some kind of check on admissions.  The intent, at least for the 30% of the faculty who really thought this was a good idea, was that this was an assessment tool.  For example, if you passed overall but did badly on the quantum question, you would be strongly encouraged to think about taking (or grading) the undergrad quantum course.  You had two tries to pass the written exam, and if you were well prepared, you were strongly encouraged to give it a shot as soon as you got started in the program - why wait?  A strong showing on the qual could also ease the process of finding a rotation slot with a would-be thesis adviser.  Still, like any formal exam when the stakes are high, the process was fraught with tension.

Getting a really good qual exam together is very challenging, particularly if you want the problems to be solvable yet not be rehashed from books or other common sources.  This particular year, Bob Laughlin was chairing the qual committee, and he had lost patience with some of his colleagues and decided to put together much of the exam himself.   (Laughlin is a well-known, larger-than-life person who figures in a couple of other stories I may get around to telling.)  The previous year he'd written a question about heat capacity and thermal conductivity involving the cooking of a pot roast.  This problem was sufficiently infamous that he thought it would be funny to write another problem our year about pot roast (though he spelled it "potroast", prompting one Russian to ask, "Vot is this 'po-tro-ast'?").  He wrote a question spoofing "Brilliant Pebbles" (pdf!), a missile defense concept that he found completely ridiculous and impractical.  The exercise was about "brilliant pot roast", with the idea of de-orbiting 2 kg pieces of beef as kinetic kill weapons to take out missiles.   This included giving your opinion and a physics justification of whether the pot roast would splatter on the outside of the missile or punch a cartoonish pot roast-shaped hole through the missile.  He concluded the problem by saying "Don't worry if the numbers you find for this are absurd.  We'll just delete them and replace them with happier numbers.  This is called 'government science'."

We took the test in a big lecture room in one of the buildings ringing Stanford's main quad.   Chalkboards up front, lots of wood, afternoon sunlight slanting through narrow windows near the high ceiling.  The room had somewhat shallow tiered seating and long, curved tables rather than desks, so that everyone taking the exam (probably 30 people or so) could spread out and have plenty of room.   Stanford's honor code meant that the exam was unproctored, but Laughlin was sitting outside doing some reading, in case we had questions about the wording of the test.

Around 5 hours into day 1 (if I recall correctly), Laughlin came into the room, looking somewhat agitated.  "May I have your attention please?  It's been brought to my attention that there is a typographical mistake on the exam."

[groan from frustrated, tired students]

"On the time-dependent quantum problem, these two frequencies \( \omega_{0} \) and \( \omega \) are both supposed to be \( \omega_{0} \).  It may not be analytically solvable as written."

[angry muttering from bitter, aggravated students who had been wasting critical time on this]

"No," says a clear, Russian-accented voice from the back of the room, the same fellow who had studied conformal field theory, "Is difficult, but can be solved.  Have done."

[combination of disbelief, resignation, and semi-desperate laughter from the crowd]

Welcome to physics grad school.

Anecdotes from grad school and beyond

I've been thinking about what a more general audience likes to read in terms of science writing beyond descriptions of cool science.  Interesting personalities definitely have appeal.  Sure, he was a Nobel Laureate, but my guess is that much of Feyman's popularity originates from the fact that he really was a "curious character" and a great story-teller.  I'm not remotely in the same league, but in my scientific career, going back to grad school, I've been ridiculously fortunate to have had the chance to meet and interact with many interesting people.  Some of the stories might give a better slice-of-life feel for graduate science education and a scientific career than you'd get from The Big Bang Theory.  I'm going to start trying to write up some of these anecdotes - my apologies to friends who have heard some of these before....

Several items - SpaceX, dark matter, Dyson spheres, Bell Labs, and some condensed matter articles

There are a number of interesting physicsy science stories out there right now:

• SpaceX came very very close to successfully landing and recovering the first stage of their Falcon 9 rocket yesterday.  It goes almost without saying that they are doing this because they want to reuse the booster and want to avoid ruining the engines by having them end up in salt water.  I've seen a number of well-intentioned people online ask, why don't they just use a parachute, or set up a big net to catch it if it falls sideways, etc.  To answer the first question:  The booster is designed to be mechanically happy in compression, when the weight of the rocket is pushing down on the lower parts as it sits on the pad, and when the acceleration due to the engines is pushing it along its long axis.  Adding structure to make the booster strong in tension as well (as when it gets yanked on from above by parachute drogue lines) would be a major redesign and would add mass (that takes away from payload).  For the second question:  The nearly empty booster is basically a thin-walled metal tube.  If it's supported unevenly from the side, it will buckle under accelerations (like hitting a net).  Good luck to them!
• It would appear that there is observational evidence that dark matter might interact with itself through forces that are not just gravitational.  That would be very interesting indeed.  Many "simple" ideas about dark matter (say photinos) are not charged, so real dark-dark interactions beyond gravity could limit the candidates to consider.  I'm sure there will be papers on the high energy part of the arXiv within days claiming that string theory predicts exactly this, regardless of what "this" is.
• A Penn State group did a study based on WISE data, and concluded after surveying 100000 distant galaxies that there are only about 50 that seem to emit "too much" in the infrared relative to expectations.   Why look for this?  Well, if there were galaxy-spanning civilizations capable of stellar-scale engineering projects, and if they decided to use that capability to build Dyson spheres to try to capture more than 10% of the star-radiated power in the galaxy, and if those civilizations liked temperature ranges near ours, then you would expect to see an excess of infrared.  So.  Seems like galaxy-spanning civilizations that like to do massive building of Dyson spheres and similar structures are very rare.  I can't say that I'm surprised, but I am glad that creative people are doing searches like this.
• Alcatel-Lucent, including Bell Labs, is being purchased by Nokia.  If anyone knows what this means for Bell Labs research at the combined company, please feel free to post below.  
• One interesting article I noticed in Nature Physics (sorry for the paywall) shows remarkably nice, clean fractional quantum Hall effect (FQHE) physics in ZnMgO/ZnO heterostructures.  The FQHE tends to be "fragile" - the 2d electron system has to be in a material environment so clean and perfect that not only can an electron make many cyclotron orbits before it scatters off any impurities or defects, but that kind of disorder has to be weak compared to some finicky electron-electron interactions that are at milliKelvin scales.   The new data shows FQHE signatures at "filling fractions" (ratios of magnetic field to electron density) that correspond to some comparatively exotic collective states.  Neat.
• There is a special issue of Physica C coming out in honor of the remarkable (and very nice guy) Ted Geballe, a pioneer in superconductivity research.  I really don't like Elsevier as a publisher, so I am not going to link to their journal.  However, I will link to the arXiv versions of all the articles I've found from that issue:  "What Tc Tells", "Unconventional superconductivity in electron-doped layered metal nitride halides", "Superconductivity of magnesium diboride", "Superconducting doped topological materials", "Hole-doped cuprate high temperature superconductors", "Superconductivity in the elements, alloys, and simple compounds", "Epilogue:  Superconducting materials, past, present, and future", and "Superconducting materials classes:  Introduction and overview".  Good stuff by some of the big names in the field.

The Leidenfrost Effect, or how I didn't burn myself in the kitchen

The transfer of heat, the energy content of materials tied to the disorganized motion of their constituents, is big business.  A typical car engine is cooled by conducting heat to a flowing mixture of water and glycol, and that mixture is cooled by transferring that heat to gas molecules that get blown past a radiator by a fan.  Without this transfer of heat, your engine would overheat and fail.  Likewise, the processor in your desktop computer generates about 100 W of thermal power, and that's carried away by either a fancy heat-sink with air blown across it by a fan, or through a liquid cooling system if you have a really fancy gaming machine.

Heat transfer is described quantitatively by a couple of different parameters.  The simplest one to think about is the thermal conductivity \(\kappa_{T}\).  If you have a hunk of material with cross-sectional area \(A\) and length \(L\), and the temperature difference between the hot side and the cold side is \(\Delta T\), the thermal conductivity (units of W/m-K in SI) tells you the rate (\(\dot{q}\), units of Watts) at which thermal energy is transferred across the material:  \( \dot{q} = \kappa_{T} A \Delta T/L\).

Where things can get tricky is that \(\kappa_{T}\) isn't necessarily just some material-specific number - the transport of heat can depend on lots of details.  For example, you could have heat being transferred from the bottom of a hot pot into water that's boiling.  Some of the energy from the solid is going into the kinetic energy of the liquid water molecules; some of that energy is going into popping molecules from the liquid and into the gas phase.  The motion of the liquid and the vapor is complicated, and made all the more so because \(\kappa_{T}\) for the liquid is \(>> \kappa_{T}\) for the vapor.  (There is a generalized quantity, the heat transfer coefficient, that is defined similarly to \(\kappa_{T}\) but is meant to encompass all this sort of mess.)  If you think about \(\dot{q}\) as the variable you control (for example, by cranking up the knob on your gas burner), you can have different regimes, as shown in the graph to the right (from this nice wikipedia entry).  

At the highest heat flux, the water right next to the pan flashes into a layer of vapor, and because that vapor is a relatively poor thermal conductor, the liquid water remains relatively cool (that is, because \(\kappa_{T}\) is low, \(\Delta T\) is comparatively large for a fixed \(\dot{q}\)).    This regime is called film boiling, and you have seen it if you've ever watched a droplet of water skitter over a hot pan, or watched a blob of liquid nitrogen skate across a lab floor.  The fact that the liquid stays comparatively cool is called the Leidenfrost Effect.   This comparatively thermal insulating property of the vapor layer can be very dramatic, as shown in this Mythbusters video, where they show that having wet hands allows you to momentarily dip your hand in molten lead (!) without being injured. Note that this demo was most famously performed by Prof. Jearl Walker, author of the Flying Circus of Physics, former Amateur Scientist columnist for SciAm, and inheritor of the mantle of Halliday and Resnick.  The Leidenfrost Effect is also the reason that I did not actually burn my (wet) hand on the handle of a hot roasting pan last weekend.

This heat transfer example is actually a particular instance of a more general phenomenon.  When some property of a material (here \(\kappa_{T}\)) is dramatically dependent on the phase of that material (here liquid vs vapor), and that property can help determine dynamically which phase the material is in, you can get very rich behavior, including oscillations.  This can be seen in boiling liquids, as well as electronic systems with a phase change (pdf example with a metal-insulator transition, link to a review of examples with superconductor-normal metal transitions ).  

submerged due to grant deadline

Fear not, a new post is coming soon, but for now I'm trying to finish off a proposal.

America's "obsession with STEM education" is neither an obsession, nor is it dangerous

I'm late to the party about Fareed Zakaria's piece in the Washington Post titled "Why America's Obsession with STEM Education is Dangerous".  Zakaria is a smart guy, and I recognize that he has a book to sell, but this article is rhetorically frustrating:  He demolishes a serious straw man.  He wants people to be aware of the importance of a broad-based education, and he is apparently worried (or claiming to be for the sake of getting attention) that the US is culturally too focused on STEM and not enough on the other things, like creativity, the arts, and teaching people how to write well.

He is absolutely right that a broad-based education is generally a good idea, and that teaching people actual critical thinking and writing skills and an appreciation for things beyond math and science is also good.  However, I don't think you'll find any reasonable person advocating for purely technical educations with no cultural appreciation and ignoring teaching people how to communicate.   It's easy to demolish an argument that no one is making.  I could write 500 words about how it's crazy for people to drive themselves into crushing debt to get degrees that fail to teach them anything beyond rudimentary writing skills, but that would not be an assault on liberal education.

In two key respects, Zakaria has missed the boat.  First, while there is basically zero chance that we are going to abandon broad-based education in the US, it does seem like there is a far more real danger that we are trending away from science and rationality (c.f. vaccines, evolution, climate science).  Second, and here he was much closer to right, there is a danger in viewing absolutely all public investment in people (via education) and research purely in terms of short-term economic benefit - essentially eschewing basic research or basic education in favor purely of applied research and vocational training of obvious economic benefit to the country.   Frankly, there are people out there who truly do not believe in public education, period, and that's much scarier to me than an imagined attack on the value of the humanities as a component of an education.

The physics of drying your hands

We've all been there:  You wash your hands after using the restroom facilities, and turn away from the sink only to find one of those sad, completely ineffectual, old-style hot-air hand dryers bolted to the wall.  You know, the kind with the info graphic shown to the right (image credit:  nyulocal.com).  Why do these things work so poorly compared to paper towels?  What insight did Excel and Dyson have that makes their systems so much better?

It all comes down to the physics of trying to dry your hands.  At a rough estimate, the surface area of your hands is around 430 cm².   If your hands, when wet, are coated on average by a layer of water 100 microns thick (seems not crazy), that's a total volume of water of 4.3 cm³.  How can you get that water off of you?  One approach, apparently the one pursued by the original hot air dryers, is to convert that water into vapor.  Clearly the idea is not to do this by raising the temperature of your hands to the boiling point of water.  Rather, the idea is to flow hot, dry air over your hands, with the idea that the water molecules in question will acquire the necessary latent heat of vaporization (the energy input required to pull water molecules out of the condensed (liquid) phase and into the vapor phase) from their surroundings - the dry air, your hands, etc.  This "borrowing" of energy is the principle behind evaporative cooling, why you feel cold when you step out of the shower.

[A digression in fancy thermodynamic language:  When liquid water is in contact with dry air, the chemical potential for the water molecules is much higher in the liquid than in the air.  While the water molecules are attracted to each other via hydrogen bonds and polar interactions, there are so many many more ways that the water molecules could be arranged if they were diluted out into vapor in the air that they will tend to leave the liquid, provided each molecule can, through a thermal fluctuation of some sort, acquire enough energy to sever its bonds from the liquid.  The departing molecules leave behind a liquid with a lower average total energy, cooling it.  Note that water molecules can come from the vapor phase and land in the liquid, too, depositing that same latent heat per molecule back into the liquid.  When the departure and arrival processes balance, the vapor is said to be at the "saturated vapor pressure", and evaporative cooling stops.  This is why sweating a whole bunch on a super humid day does not cool you off.]

Back to your hands.  Converting 4.3 cm³ of water into vapor requires about 9700 Joules of energy.  If you wanted to do this with the heat supplied by the hot air dryer, and to do it in about a minute (which is far longer than most people are willing to stand there rubbing their hands as some feeble fan wheezes along), the dryer would have to be imparting about 160 W of power into the water.  Clearly that's not happening - you just can't get that much power into the water without cooking your hands!  Instead, you give up in disgust and wipe your hands discreetly on your pants.

In contrast, paper towels use thermodynamics much more effectively.  Rather than trying to convert the water to vapor, paper towels take great advantage of (1) the very large surface area of paper towels, and (2) capillary forces, the fact that the liquid-solid surface interaction between water and paper towel fibers is so attractive that it's energetically favorable for the water to spread out (even at the cost of increasing more liquid-vapor interface) and coat the fibers, soaking into the towel.  [Bonus physics lesson:  the wet paper towel looks darker because the optical properties of the water layer disfavor the scattering processes on micron-scale bits of fluff that tend to make the towel look white-ish.]  Yes, it takes energy to make paper towels, and yes, they must then be disposed.  However, they actually get your hands dry!

What about Excel and Dyson?  They realized very clearly that trying to vaporize the water on your hands is a fool's errand.  Instead, they try to use actual momentum transfer from the air to the water to blow the water off your hands.  Basically they accelerate a stream of air up to relatively high velocity (400 miles per hour, allegedly, though that sounds high to me).  That air, through its viscosity, transfers momentum to the water and that shear force drives the water off your hands.  They seem to have found a happy regime where they can blow the water off your hands in 10-15 seconds without the force from the air hurting you.    The awesome spectacle of those good dryers just shows how sad and lame the bad ones are by comparison.

Cleanrooms - what is new and exciting?

Cleanrooms - basically climate-controlled, dust-mitigated environments filled with equipment useful for micro/nanoscale fabrication and associated characterization - are a staple of modern research universities.  What kind of tool set and facilities you need depends on what you're trying to do.  For example, if you want to teach/do research on the fabrication of high performance Si transistors or large-scale integrated circuits, you probably want a dedicated facility that deals primarily with Si CMOS processing.  That might include large-area photolithography or wafer-scale e-beam lithography or nanoimprint lithography tools, evaporators/sputtering systems/PECVD/RIE/ALD systems able to service 150 mm or 200 mm substrates, and you might want to keep non-Si-friendly metals like Au far far away.  On the flip side, if you are more interested in supporting microfluidics or MEMS work, you might be more interested in smaller substrates but diverse materials, and tools like deep etchers and critical point dryers.

We're about to embark on a cleanroom upgrade at my institution, and I would appreciate input from my relevant readers:  What in your view is the latest and greatest in micro/nanofab tools?  What can't you do without?  Any particularly clever arrangements of facilities/  Assume we are already going to have the obvious stuff, and that we're not trying to create a production line that can handle 200 mm substrates.  Conversely, if you have suggestions of particular tools to avoid, that would also be very helpful.  Insights would be greatly appreciated.

Brief items, public science outreach edition

Here are a couple of interesting things I've come across in terms of public science outreach lately:

• I generally f-ing love "I f-ing love science" - they reach a truly impressive number of people, and they usually do a good job of conveying why science itself (beyond just particular results) is fun.  That being said, I've started to notice lately that in the physics and astro stories they run they sometimes either use inaccurate/hype-y headlines or report what is basically a press release completely uncritically.  For instance, while it fires the mind of science fiction fans everywhere, I don't think it's actually good that IFLS decided to highlight a paper from the relatively obscure journal Phys. Lett. B and claim in a headline that the LHC could detect extra spatial dimensions by making mini black holes.  Sure.  And SETI might detect a signal next week.  What are the odds that this will actually take place?  Similarly, the headline "Spacetime foam discovery proves Einstein right" implies that someone has actually observed signatures of spacetime foam.  In fact, the story is the exact opposite:  Observations of photons from gamma ray bursts have shown no evidence of "foaminess" of spacetime, meaning that general relativity (without any exotic quantumness) can explain the results.   A little improved quality control on the selection and headlines particularly on the high energy/astro stories would be great, thanks.
• There was an article in the most recent APS News that got me interested in Alan Alda's efforts at Stony Brook on communicating science to the public.  Alda, who hosted Scientific American Frontiers and played Feynman on Broadway, has dedicated a large part of his time in recent years to the cause of trying to spread the word to the general public about what science is, how it works, how it often involves compelling narratives, and how it is in many ways a pinnacle of human achievement.  He is a fan of "challenge" contests, where participants are invited to submit a 300-word non-jargony explanation of some concept or phenomenon (e.g., "What is a flame?", "What is sleep?").  This is really hard to do well!  
• Vox has an article that isn't surprising at all:  Uncritical, hype-filled reporting of medical studies leads to news articles that give conflicting information to the public, and contributes to a growing sense among the lay-people that science is untrustworthy or a matter of opinion.  Sigh.
• Occasionally deficit-hawk politicians realize that science research can benefit them by, e.g., curing cancer.  If only they thought that basic research itself was valuable.

"Flip chip" approach to nanoelectronics

Most people who aren't experts in the field don't really appreciate how amazing our electronic device capabilities are in integrated circuits.  Every time some lithographic patterning, materials deposition, or etching step is performed on an electrically interesting substrate (e.g., a Si chip), there is some amount of chemical damage or modification to the underlying material.  In the Si industry, we have gotten extremely good over the last five decades at either minimizing that collateral damage, or making sure that we can reverse its effects.  However, other systems have proven more problematic.  Any surface processing on GaAs-based structures tends to reduce the mobility of charge in underlying devices, and increases the apparent disorder in the material.  For more complex oxides like the cuprate or pnictide superconductors, even air exposure under ambient conditions (let alone much lithographic processing) can alter the surface oxygen content, affecting the properties of the underlying material.

However, for both basic science and technological motivations, we sometimes want to apply electrodes on small scales onto materials where damage from traditional patterning methods is unavoidable and can have severe consequences for the resulting measurements.  For example, this work used electrodes patterned onto PDMS, a soft silicone rubber.  The elastomer-supported electrodes were then laminated (reversibly!) onto the surface of a single crystal of rubrene, a small molecule organic semiconductor.  Conventional lithography onto such a fragile van der Waals crystal is basically impossible, but with this approach the investigators were able to make nice transistor devices to study intrinsic charge transport in the material.  

One issue with PDMS as a substrate is that it is very squishy with a large thermal expansion coefficient.  Sometimes that can be useful (read this - it's very clever), but it means that it's very difficult to put truly nanoscale electrodes onto PDMS and have them survive without distortion, wrinkling, cracking of metal layers, etc.  PDMS also really can't be used at temperatures much below ambient.  A more rigid substrate that is really flat would be great, with the idea that one could do sophisticated fab of electrode patterns, and then "flip" the electrode substrate into contact with the material of interest, which could remain untouched or unblemished by lithographic processes.

In this recent preprint, a collaboration between the Gervais group at McGill and the CINT at Sandia, the investigators used a rigid sapphire (Al2O3) substrate to support patterned Au electrodes separated by a sub-micron gap. They then flipped this onto completely unpatterned (except for large Ohmic contacts far away) GaAs/AlGaAs heterostructures.  With this arrangement, cleverly designed to remain in intimate contact even when the device is cooled to sub-Kelvin temperatures, they are able to make a quantum point contact while in principle maintaining the highest possible charge mobility of the underlying semiconductor.  It's very cool, though making truly intimate contact between two rigid substrates over mm-scale areas is very challenging - the surfaces have to be very clean, and very flat!  This configuration, while not implementable for too many device designs, is nonetheless of great potential use for expanding the kinds of materials we can probe with nanoscale electrode arrangements.

Tunneling two-level systems in solids: Direct measurements

Back in the ancient mists of time, I did my doctoral work studying tunneling two-level systems (TLS) in disordered solids.  What do these words mean?  First, read this post from 2009.   TLS are little, localized excitations that were conjectured to exist in disordered materials.  Imagine a little double-welled potential, like this image from W. A. Phillips, Rep. Prog. Phys. 50 (1987) 1657-1708.

The low temperature thermal, acoustic, and dielectric properties of glasses, for example, appear to be dominated by these little suckers, and because of the disordered nature of those materials, they come in all sorts of flavors - some with high barriers in the middle, some with low barriers; some with nearly symmetric wells, some with very asymmetric wells.   These TLS also "couple to strain" (that's how they talk to lattice vibrations and influence thermal and acoustic properties), meaning that if you stretch or squish the material, you raise one well and lower the other by an amount proportional to the stretching or squishing.

When I was a grad student, there were a tiny number of experiments that attempted to examine individual TLS, but in most disordered materials they could only be probed indirectly.   Fast forward 20 years.  It turns out that superconducting structures developed for quantum computing can be extremely sensitive to the presence of TLS, which typically exist in the glassy metal oxide layers used as tunnel barriers or at the surfaces of the superconductors.  A very cool new paper on the arxiv shows this extremely clearly.  If you look at Figure 2d, they are able to track the energy splittings of the TLS while straining the material (!), and they can actually see direct evidence of TLS talking coherently to each other.  There are "avoided crossings" between TLS levels, meaning that occasionally you end up with TLS pairs that are close enough to each other that energy can slosh coherently back and forth between them.   I find this level of information very impressive, and the TLS case continues to be an impressive example of theorists concocting a model based on comparatively scant information, and then experimentalists validating it well beyond the original expectations.   From the quantum computing perspective, though, these little entities are not a good thing, and demonstrate a maxim I formulated as a grad student:  "TLSs are everywhere, and they're evil."

(On the quantitative side:  If the energy difference between the bottoms of the two wells is \(\Delta\), and the tunneling matrix element that would allow transitions between the two wells is \(\Delta_{0}\), then a very simple calculation says that the energy difference between the ground state of this system and the first excited state is given by \(\sqrt{\Delta^{2} + \Delta_{0}^{2}}\).  If coupling to strain linearly tunes \(\Delta\), then that energy splitting should trace out a shape just like the curves seen in Fig. 2d of the paper.)

Table-top particle physics

We had a great colloquium here today by Dave DeMille from Yale University.   He spoke about his group's collaborative measurements (working with John Doyle and Gerry Gabrielse at Harvard) trying to measure the electric dipole moment of the electron.  When we teach students, we explain that as far as we have been able to determine, an electron is a truly pointlike particle (infinitesimal in size) with charge -e and spin 1/2.  That is, it has no internal structure (though somehow it contains intrinsic angular momentum, but that is a story for another day), and that means that attempts to probe the charge distribution of the electron (e.g., scattering measurements) indicate that its charge is distributed in a spherically symmetric way.

We know, though, that from the standpoint of quantum field theory like quantum electrodynamics that we should actually think of the electron as being surrounded by a cloud of "virtual" particles of various sorts.   In Feynman-like language, when an electron goes from here to there, we need to consider not just the direct path, but also the quantum amplitudes for paths with intermediate states (that could be classically forbidden), like spitting out and reabsorbing a photon between here and there.   Those paths give rise to important, measurable consequences, like the Lamb shift, so we know that they're real.  Where things get very interesting is when you wonder about more complicated corrections involving particles that break time reversal symmetry (like B and K mesons).  If you throw in what we know from the Standard Model of particle physics, those corrections lead to the conclusion that there actually should be a non-zero electric dipole moment of the electron.  That is, along its axis of "spin", there should be a slight deficit of negative charge at the north pole and excess of negative charge at the south pole, corresponding to a shift of the charge of the electron by about \(10^{-40}) cm.  That is far too small to measure.

However, suppose that there are more funky particles out there (e.g., dark matter candidates like the supersymmetric particles that many people predict should be seen at the LHC or larger colliders).  If those particles have masses on the TeV scale (that'd be convenient), there is then an expectation that there should be a detectable electric dipole moment.  DeMille and collaborators have used extremely clever atomic physics techniques involving optical measurements on beams of ThO molecules in magnetic and electric fields to look, and they've pushed the bound on any such moment (pdf) to levels that already eliminate many candidate theories.

Two comments.  First, this talk confirmed for me once again that you really have to have a special kind of personality to do truly precision measurements.  The laundry list of systematic error sources that they considered is amazing, as are the control experiments.  Second, I love this kind of thing, using "table-top" experiments (for certain definitions of "table") to get at particle physics questions.   Note that the entire cost of the whole experiment over several years so far as been around $2M.  That's not even a rounding error on the LHC budget.  Sustained investing at a decent level in this kind of work may have enormous bang-for-the-buck compared with building ever-larger colliders.