The physics of ornithopters

One thing that the new Dune film captures extremely well is the idea that the primary small-capacity air transportation mode on Arrakis is travel by ornithopter.  The choice of flapping wings as a lift/propulsion mechanism can be in-fictional-universe justified by the idea that jet turbines probably won't do well in an atmosphere with lots of suspended dust and sand, especially on take-off and landing.  Still, I think Frank Herbert decided on ornithopters because it just sounded cool.

The actual physics and engineering of flight via flapping wings is complicated.  This site is a good place to do some reading.  The basic idea is not hard to explain.  To get net lift, in the cyclical flapping motion of a wing, somehow the drag force pushing downward on the wing during the upstroke has to be more than balanced by the flux of momentum pushed downward on the wing's downstroke.  To do this, the wing's geometry can't be unchanging during the flapping.  The asymmetry between up and down strokes is achieved through the tilting (at the wing base and along the wing) and flexing of the wing during the flapping motion.  

The ornithopters in the new movie have wings on the order of 10 m long, and wing motions that look like those of a dragonfly, and the wings are able to flap up and down and an apparent frequency of a couple of hundred hertz (!).  If you try to run some numbers on the torque, power, and material strength/weight that would be required to do this, you can see pretty quickly why this has not worked too well yet as a strategy on earth.   (As batteries, motor technology, and light materials continue to improve, perhaps ornithopters will become more than a fun hobby.)  

This issue - that cool gadgets in sci-fi or superhero movies would need apparently unachievable power densities at low masses - is common (see, e.g., Tony Stark's 3 GW arc reactor that fits in your hand, weighs a few pounds, and somehow doesn't have to radiate GW of waste heat), and that's ok; the stories are not meant to be too realistic. Still, the ornithopter fulfills its most important purpose in the movie:  It looks awesome.  

Brief items - Sarachik, Feynman, NSF postdocs and more

 Here are several items of interest:

• I was saddened to learn of the passing of Myriam Sarachik, a great experimental physicist and a generally impressive person.  I was thinking about writing a longer piece about her, but this New York Times profile from last year is better than anything I could do.  This obituary retells the story to some degree. (I know that it's pay-walled, but I can't find a link to a free version.)  In the early 1960s, after fighting appalling sexism to get a doctorate and a position at Bell Labs, she did foundational experimental work looking at the effect of dilute magnetic impurities in the conduction of nonmagnetic metals.  For each impurity, the magnetic atom has an unpaired electron in a localized orbitals.  A conduction electron of opposite spin could form a singlet to fill that orbital, but the on-site Coulomb repulsion of the electron already there makes that energetically forbidden except as a virtual intermediate state for a scattering process.  The result is that scattering by magnetic impurities gets enhanced as \(T\) falls, leading to an upturn in the resistivity \(\rho(T)\) that is logarithmic in \(T\) at low temperatures.  Eventually the localized electron is entangled with the conduction electrons to form a singlet, and the resistivity saturates.  This is known as the Kondo Effect based on the theoretical explanation of the problem, but Sarachik's name could credibly have been attached.  Her family met with a personal tragedy from which it took years to recover.  Later in her career, she did great work looking at localization and the metal-insulator transition in doped semiconductors.  She also worked on the quantum tunneling of magnetization in so-called single-molecule magnets, and was a key player in the study of the 2D metal-insulator transition in silicon MOSFETs.  I was fortunate enough to meet her when she came through Rice in about 2003, and she was very generous in her time meeting with me when I was a young assistant professor.  Sarachik also had a great service career, serving as APS President around that time.  Heck of a career! 
• The audio recordings of the famous Feynman Lectures on Physics are now available for free to stream from Caltech.  You can also get to these from the individual lectures by a link on the side of each page.
• There is a new NSF postdoctoral fellowship program for math and physical sciences.  I would be happy to talk to anyone who might be interested in pursuing one of these who might want to work with me.  Please reach out via email.
• I've written before about the "tunneling time" problem - how long does quantum mechanical tunneling of a particle through a barrier take?  Here is an experimental verification of one of the most counterintuitive results in this field:  the farther "below" the barrier the particle is (in the sense of having a smaller fraction of the kinetic energy needed classically to overcome the potential barrier), the faster the tunneling.  A key experimental technique here is the use of a "Larmor clock", with the precession of the spin of a tunneling atom acting as the time-keeping mechanism.
• Did you know that it is possible, in Microsoft Word, to turn on some simple LaTeX-style symbolic coding?  The key is to enable "Math Autocorrect", and then typing \alpha will automatically be turned into \(\alpha\).  (I know act like doing scientific writing in Word is heretical, but not everyone in every discipline is facile with LaTeX/Overleaf.)

The Purcell effect - still mind-blowing.

The Purcell effect is named after E. M. Purcell, a Nobel-winning physicist who also was a tremendous communicator, author of one of the great undergraduate textbooks and a famous lecture about the physical world from the point of view of, e.g., a bacterium.  I've written about this before here, and in a comment I include the complete (otherwise paywalled) text of the remarkable original "paper" that describes the effect.

When we calculate things like the Planck black-body spectrum, we use the "density of states" for photons - for a volume \(V\), we are able to count up how many electromagnetic modes are available with frequency between \(\nu\) and \(\nu + \mathrm{d}\nu\), keeping in mind that for each frequency, the electric field can be polarized in two orthogonal directions.  The result is \( (8\pi/c^3)\nu^2 \mathrm{d}\nu\) states per unit volume of "free space".

In a cavity, though, the situation is different - instead, there is, roughly speaking, one electromagnetic mode per the bandwidth of the cavity per the volume of the cavity.  In other words, the effective density of states for photons in the cavity is different than that in free space.  That has enormous ramifications:  The rates of radiative processes, even those that we like to consider as fundamental, like the rate at which electrically excited atoms radiatively decay to lower states state, can be altered in a cavity.  This is the basis for a lot of quantum optics work, as in cavity quantum electrodynamics.  Similarly, the presence of an altered (from free space) photon density of states also modifies the spectrum of thermal radiation from that cavity away from the Planck black-body spectrum.  

Consider an excited atom in the middle of such a cavity.  When it is going to emit a photon, how does it "know" that it's in a cavity rather than in free space, especially if the cavity is much larger than an atom?  The answer is, somehow through the electromagnetic couplings to the atoms that make up the cavity.  This is remarkable, at least to me.   (It's rather analogous to how we picture the Casimir effect, where you can think about the same physics either, e.g., as due to altering local vacuum fluctuations of the EM field in the space between conducting plates, or as due to fluctuating dipolar forces because of fluctuating polarizations on the plates.)

Any description of a cavity (or plasmonic structure) altering the local photon density of states is therefore really short-hand.  In that approximation, any radiative process in question is tacitly assuming that an emitter or absorber in there is being influenced by the surrounding material.  We just are fortunate that we can lump such complicated, relativistically retarded interactions into an effective photon density of states that differs from that in free space. 

Spin glasses and the Nobel

The Nobel Prize in physics this year was a bit of a surprise, at least to me.  As one friend described it, it's a bit of a Frankenprize, stitched together out of rather disparate components.  (Apologies for the slow post - work was very busy today.)  As always, it's interesting to read the more in-depth scientific background of the prize.  I was unfamiliar with the climate modeling of Manabe and Hasselmann, and this was a nice intro.

The other prize recipient was Giorgio Parisi, a statistical mechanician whose key cited contribution was in the theory of spin glasses, but was generalizable to many disordered systems with slow, many-timescale dynamics including things like polymers and neural networks.  

The key actors in a spin glass are excess spins - local magnetic moments that you can picture as little magnetic dipoles. In a generic spin glass, there is both disorder (as shown in the upper panel of the cartoon, spins - in this case iron atoms doped into copper - are at random locations, and that leads to a broad distribution of spin-spin interactions in magnitude and sign) and frustration (interactions such that flipping spin A to lower its interaction energy with spin B ends up raising the interaction energy with spin C, so that there is no simple configuration of spins that gives a global minimum of the interaction energy).  One consequence of this is a very complicated energy landscape, as shown in the lower panel of the cartoon.  There can be a very large number of configurations that all have about the same total energy, and flipping between these configurations can require a lot of energy such that it is suppressed at low temperatures.  These magnetic systems then end up having slow, "glassy" dynamics with long, non-exponential relaxations, in the same way that structural glasses (e.g., SiO2 glass) can get hung up in geometric configurations that are not the global energetic minimum (crystalline quartz, in the SiO2 case).  

The standard tools of statistical physics are difficult to apply to the glassy situation.  A key assumption of equilibrium thermodynamics is that, for a given total energy, a system is equally likely to be found in any microscopic configuration that has that total energy.  Being able to cycle through all those configurations is called ergodicity.  In a spin glass at low temperatures, the potential landscape means that the system can get easily hung up in a local energy minimum, becoming non-ergodic.  

An approach that Parisi took to this problem involved "replicas", where one considers the whole system as an ensemble of replica systems, and a key measure of what's going on is the similarity of configurations between the replicas.  Parisi himself summarizes this in this pretty readable (for physicists) article.  One of Parisi's big contributions was showing that the Ising spin glass model of Sherrington and Kirkpatrick is exactly solvable.

I learned about spin glasses as a doctoral student, since the interacting two-level systems in structural glasses at milliKelvin temperatures act a lot like a spin glass (TLS coupled to each other via a dipolar elastic interaction, and sometimes an electric dipolar interaction), complete with slow relaxations, differences between field-cooled and zero-field-cooled properties, etc.  

Parisi has made contributions across many diverse areas of physics.  Connecting his work to that of the climate modelers is a bit of a stretch thematically - sure, they all worry about dynamics of complex systems, but that's a really broad umbrella.  Still, it's nice to see recognition for the incredibly challenging problem of strongly disordered systems.

Annual Nobel speculation thread

Once more, the annual tradition:  Who do people think will win the Nobel this year in physics or chemistry?  I have repeately and incorrectly suggested Aharonov and Berry for geometric phases.  There is a lot of speculation on social media about Aspect, Zeilinger, and Clauser for Bell's inequality tests.  Social media speculation has included quantum cascade lasers as well as photonic bandgap/metamaterials. Other suggestions I've seen online have included superconducting qubits (with various combinations of people) and twisted bilayer graphene, though both of those may be a bit early.