Wednesday, August 05, 2020

The energy of the Beirut explosion

The shocking explosion in Beirut yesterday was truly awful and shocking, and my heart goes out to the residents.  It will be quite some time before a full explanation is forthcoming, but it sure sounds like the source was a shipment of explosives-grade ammonium nitrate that had been impounded from a cargo ship and (improperly?) stored for several years.

Interestingly, it is possible in principle to get a good estimate of the total energy yield of the explosion from cell phone video of the event.  The key is a fantastic example of dimensional analysis, a technique somehow more common in an engineering education than in a physics one.  The fact that all of our physical quantities have to be defined by an internally consistent system of units is actually a powerful constraint that we can use in solving problems.  For those interested in the details of this approach, you should start by reading about the Buckingham Pi Theorem.  It seems abstract and its applications seem a bit like art, but it is enormously powerful.  

The case at hand was analyzed by the British physicist G. I. Taylor, who was able to take still photographs in a magazine of the Trinity atomic bomb test and estimate the yield of the bomb.  Assume that a large amount of energy \(E\) is deposited instantly in a tiny volume at time \(t=0\), and this produces a shock wave that expands spherically with some radius \(R(t)\) into the surrounding air of mass density \(\rho\).  If you assume that this contains all the essential physics in the problem, then you can realize that the \(R\) must in general depend on \(t\), \(\rho\), and \(E\).  Now, \(R\) has units of length (meters).  The only way to combine \(t\), \(\rho\), and \(E\) into something with the units of length is \( (E t^2/\rho)^{1/5}\).  That implies that \( R = k (E t^2/\rho)^{1/5} \), where \(k\) is some dimensionless number, probably on the order of 1.  If you cared about precision, you could go and do an experiment:  detonate a known amount of dynamite on a tower and film the whole thing with a high speed camera, and you can experimentally determine \(k\).  I believe that the constant is found to be close to 1.  

Flipping things around and solving, we fine \(E = R^5 \rho/t^2\).  (A more detailed version of this derivation is here.)  

This youtube video is the best one I could find in terms of showing a long-distance view of the explosion with some kind of background scenery for estimating the scale.  Based on the "before" view and the skyline in the background, and a google maps satellite image of the area, I very crudely estimated the radius of the shockwave at about 300 m at \(t = 1\) second.  Using 1.2 kg/m3 for the density of air, that gives an estimated yield of about 3 trillion Joules, or the equivalent of around 0.72 kT of TNT.   That's actually pretty consistent with the idea that there were 2750 tons of ammonium nitrate to start with, though it's probably fortuitous agreement - that radius to the fifth really can push the numbers around.

Dimensional analysis and scaling are very powerful - it's why people are able to do studies in wind tunnels or flow tanks and properly predict what will happen to full-sized aircraft or ships, even without fully understanding the details of all sorts of turbulent fluid flow.  Physicists should learn this stuff (and that's why I stuck it in my textbook.)

Saturday, August 01, 2020

How long does quantum tunneling take?

The "tunneling time" problem has a long, fun history.  Here is a post that I wrote about this issue 13 years ago (!!).  In brief, in quantum mechanics a particle can "tunnel" through a "classically forbidden" region (a region where by simple classical mechanics arguments, the particle does not have sufficient kinetic energy to be there).  I've written about that more recently here, and the wikipedia page is pretty well done.  The question is, how long does a tunneling particle spend in the classically forbidden barrier?  

It turns out that this is not a trivial issue at all.  While that's a perfectly sensible question to ask from the point of view of classical physics, it's not easy to translate that question into the language of quantum mechanics.  In lay terms, a spatial measurement tells you where a particle is, but doesn't say anything about where it was, and without such a measurement there is uncertainty in the initial position and momentum of the particle.  

Some very clever people have thought about how to get at this issue.  This review article by Landauer and Martin caught my attention when I was in grad school, and it explains the issues very clearly.  One idea people had (Baz' and Rybochenko) is to use the particle itself as a clock.  If the tunneling particle has spin, you can prepare the incident particles to have that spin oriented in a particular direction.  Then have a magnetic field confined to the tunneling barrier.  Look at the particles that did tunnel through and see how far the spins have precessed.  This idea is shown below.
"Larmor clock", from this paper

This is a cute idea in theory, but extremely challenging to implement in an experiment.  However, this has now been done by Ramos et al. from the Steinberg group at the University of Toronto, as explained in this very nice Nature paper.  They are able to do this and actually see an effect that Landauer and others had discussed:  there is "back-action", where the presence of the magnetic field itself (essential for the clock) has an effect on the tunneling time.  Tunneling is not instantaneous, though it is faster than the simple "semiclassical" estimate (that one would get by taking the magnitude of the imaginary momentum in the barrier and using that to get an effective velocity).  Very cool.

Saturday, July 25, 2020

Kitchen science: insulated cups

An impromptu science experiment this morning.  A few months ago we acquired some very nice insulated tumblers (initially from causebox and then more from here).  Like all such insulated items, the inner and outer walls are made from a comparatively lousy thermal conductor, in this case stainless steel.  (Steel is an alloy, and the disorder in its micro and nanoscale structure scatters electrons, making it have a lower electrical (and hence thermal) conductivity than pure metals.)  Ideally the walls only touch at the very top lip of the cup where they are joined, and the space between the walls has been evacuated to minimize heat conduction by any trapped gas in there.  When working well, so that heat transfer has to take place along the thin metal wall, the interior wall of the cup tends to sit very close to the temperature of whatever liquid is in there, and the exterior wall tends to sit at room temperature.

We accidentally dropped one of the cups this morning, making a dent near the base.  The question was, did this affect the thermal insulation of that cup?  To test this, we put four ice cubes and four ounces of water from our refrigerator into each cup and let them sit on the counter for 15 minutes.  Then we used an optical kitchen thermometer (with handy diode laser for pointing accuracy) to look at the exterior and interior wall temperatures.  (Apologies for the use of Fahrenheit units.)  Check this out.

The tumbler on the left is clearly doing a better job of keeping the outside warm and the inside cold.  If we then scrutinize the tumbler on the right we find the dent, which must be deep enough to bring the inner and outer walls barely into contact.

The bottom line:  Behold, science works.  Good insulated cups are pretty impressive engineering, but you really should be careful with them, because the layers really are close together and can be damaged.

Thursday, July 23, 2020

Recently in the arxiv - van der Waals interfaces

Sometimes when looking at the pace of results coming out of the 2D material community, I am reminded of an old joke from Tom Lehrer about super-productive people:  "It's people like that who make you realize how little you've accomplished. It's a sobering thought, for example, that, when Mozart was my age, he had been dead for two years." (See here and then listen to the whole album - National Brotherhood Week has particular resonance this year.).

Recently in the arxiv, there were two different back-to-back preprint pairs uploaded by extremely strong collaborations in the trade of creating new condensed matter systems at the interfaces of stacked van der Waals materials (systems like graphene and mica, that can be exfoliated down to atomically thin layers).  

The first pair of papers (and my apologies if I missed others) were this one and this one.  In the former, the investigators take advantage of the energies of the bands in \(\alpha\)-RuCl3, and find that when it is layered stacked with various 2D materials (graphene, bilayer graphene, WSe2, electrons are spontaneously transferred from the 2D materials to the \(\alpha\)-RuCl3 (The normally empty conduction band of \(\alpha\)-RuCl3 lies at lower energy than the top of the valence band of the 2D material.)  This leads to very high hole concentrations within the graphene (etc.), with comparatively minimal disorder, reminiscent of modulation doping, the technique used to achieve outstanding charge mobility in 2D electron and hole gases.  The latter paper is complementary to the former:  the investigators use near-field optical techniques to look at both the plasmon properties of the graphene in such structures, and can back out the optical conductivity of the now-electron-doped \(\alpha\)-RuCl3.

The second pair of papers, this one and this one, show a whole hierarchy of insulating states that appear in moire bilayer structures made from twisted WS2/WSe2 bilayers.  As I've written before, putting together close but not identical lattices and/or twisting one layer relative to another leads to a moire pattern, and therefore superlattice for charge carriers at that interface.  Both groups find (the first using optical methods, the second using microwave techniques) that for a large number of rational fraction ratios between the number of charge carriers and the number of lattice sites, the system is very strongly insulating.  Each insulating state corresponds to a particular periodic arrangement of the charge carriers, trying to stay generally as far away from each other as possible to minimize their potential energy.  These can be analogous to Wigner crystals and charge density waves.

Very cool stuff.

Wednesday, July 22, 2020

APS Division of Condensed Matter Physics invited symposium nominations

While no one knows right now whether the 2021 March Meeting will be in person, online, or some hybrid form next spring, now is the time to put in your nominations for invited speakers and symposia for the Division of Condensed Matter Physics.  The deadline to nominate is August 17.  The whole community benefits from high quality invited talks, so if you're in a position to do this, please think about it.

To Members of the Division of Condensed Matter Physics:

APS is now accepting invited speaker and invited symposium nominations for the March Meeting in 2021. Here is the link to the APS website for submitting nominations.

The Meeting is planned for March 15 to 19, 2021. Join more than 11,000 physicists attending, presenting, and networking at the APS March Meeting 2021. Showcase your work to a global audience of physicists, scientists, and students representing APS units and committees and explore groundbreaking research from industry, academia, and major labs.

Note that the decision regarding a virtual or in-person March Meeting will be made later this summer.

Jim Sauls
DCMP Secretary/Treasurer

Monday, July 13, 2020

Quantum Coffeehouse and other physics videos

Who doesn't need more videos to watch these days?

Erica Carlson has started a new Quantum Coffeehouse video series, including interviews with practicing physicists (including yours truly).  She had also presented a "Great Course", "Understanding the Quantum World".

I'm also a fan of Physics Girl.  I really liked her recent video with supercooled sodium acetate.

Minute Physics is truly outstanding, including their look at N95 masks and how they use electrets to gather and trap polarizable particles.

Andrew Dotson is reliably funny and insightful.

For the musically inclined, acapellascience is engaging, including their particularly timely William Rowan Hamilton.

I also have to plug my colleague Jason Hafner's channel, which netted him an on-screen appearance in the new movie Palm Springs.  Also making an appearance in the movie is Jim Freericks' edx course, Quantum Mechanics for Everyone.

Wednesday, July 08, 2020

Brief items - updated

Some further items of note:
  • There is great anxiety and frustration over the latest pronouncement from DHS/ICE about international students in the US.  Let me give a little context.  For many years there has been a rule that international students studying in the US can take no more than 3 credits (or equivalent) per semester of purely online instruction. The point of that was to prevent many people from applying for F visas and then "studying" at online-only diploma mills while actually working. That is, it was originally a policy meant to encourage that student visas go to legitimate international students and scholars pursuing degrees at accredited universities.  In the spring when the pandemic hit and many universities transitioned to online instruction in the middle of the semester, DHS granted a waiver on this requirement.  Well, now they are trying to rescind that, and are doing so in a particularly draconian way: As written, if a university goes online-only, either from the start of the semester or even partway through due to public health concerns, the international students would face having to leave the US on short notice.   This is a terrible, stupid, short-sighted way to handle this situation, and it doesn't remotely serve the best interests of any constituency (student, university, or country).  Unsurprisingly, many many organizations are pushing back against this.  Hopefully there will be changes and/or workarounds.  UPDATE:  The administration appears to have backed down from this.  Hopefully that will stick.
  • On to science.  Quanta has an article about the origins of the rigidity of glass.  The discussion there is about whether there is a kind of hidden structural order in the glassy material.  Fundamentally (as I've written previously), rigidity in any solid results from a combination of very slow timescales for atomic motion (due to lack of thermal energy available to overcome "barriers") and the Pauli principle giving a hard-core repulsion between atoms.  Still, the question of the underlying nature of glassy systems remains fascinating.
  • The 2D materials experts at Columbia have shown clean fractional quantum Hall physics in a monolayer of WSe<sub>2</sub>.  The actual paper is here.  I have yet to come up with a really nice, generally accessible write-up of the FQH effect. The super short version:  Confine charge carriers in strictly two dimensions, and throw in a large magnetic field perpendicular to the plane (such that the energy associated with cyclotron motion dominates the kinetic energy). At certain ratios of magnetic field to number of charge carriers, the charge carriers can condense into new collective states (generally distinguished by topology rather than broken symmetries like the liquid-gas or nonmagnetic/ferromagnetic phase transitions).  The fractional quantum Hall states can have all sorts of unusual properties, but the key point here is that they are fragile.  Too much disorder (like missing atoms or charged impurities), and the energy associated with that disorder can swamp out the energy savings of condensing into such a state.  It's remarkable that the material quality of the monolayer transition metal dichalcogenide (and its encapsulating boron nitride surroundings) is so high.  Seeing how FQH states evolve in this example new material system with rich band structure should be interesting.
  • I feel bad for only now learning about this great series of talks about the state of the art in spintronics, trying to understand, engineer, and control the motion of spin.
  • For your animal video needs, get the behind-the-scenes story about Olive and Mabel here.