To start things off, I finally got my first research paper from Duke published in a peer-reviewed journal — a mere 17 months after defending. Behold “Response to perturbations for granular flow in a hopper!” (Please note, the exclamation point is within the quotation marks only to conform to a grammatical rule I don’t agree with, and not to indicate that the actual title is exclaimed, although that would have been cool.) The paper is published in Physical Review E, which has an impact factor of something like 3, meaning that though I am an author, even I am unlikely to ever see it there since they publish a great, great many papers on non-linear and statistical physics. Instead, I will do what I expect everyone else will do, and just download it from the preprint server when I need it.
The gist of the paper is that we have carefully monitored the flow of sand in a large, conical hopper to observe how the flow changes as we perturbed the hopper by tilting it. The reason we care is that even though sand is composed of millions of discrete particles, their interaction with each other forces them to act as a collective whole. What we are testing are equations designed by civil engineers who were interested in keeping industrial materials (corn, coal, etc.) flowing out of hoppers.
These empirical, engineering equations describe the collective behavior of the sand as a continuum and ignore the complicated discreteness of the sand. In this way they are somewhat like the equations that successfully describe water as a continuum even though it is actually made of of billions of independent molecules. In the case of water, however, temperature acts to jitter everything around making it quite easy to average out the behavior of any individual molecule. In slow granular flows, there is no corresponding jitter, meaning that one grain can have a huge influence (the final snowflake that causes the avalanche). In this respect, granular materials are an analog for all sorts of systems where any constituent can have a large effect, whether it is a single cell that turns cancerous in the liver or a civil rights leader that starts changing minds. The beauty of sand in a hopper is that it is (mostly) controllable and (mostly) reproducible in ways that allow experiments that couldn’t be performed with organs or voters.
What is exciting about these dusty old civil engineering approaches for dealing with sand is that they seem to capture something about the collective behavior of the sand without getting bogged down in describing each and every grain of sand. There turn out to be many different sets of equations, but a group of them all (correctly) predict that in a untilted hopper full of grains with an opening in the bottom that the grains will move radially — straight toward the opening. Two of my co-authors, mathematicians at NC State, found that if the hopper was tilted that the equations predicted different behaviors, including complicated swirling of the sand (somewhat like a toilet bowl flushing except with two, counter-rotating vortices). Unfortunately, the swirling effect is much smaller than the overall downward flow, so we had to make very precise measurements to detect it. Once we found it, however, we were able to determine which set of equations actually did a pretty decent job of describing the response to perturbations of the all the grains collectively — a small victory for trying to describe the collective behavior of millions of interacting particles. Of course, as the t-shirt said, “Never underestimate the power of stupid people in large groups.”