like sands through the hour glass…

…so are the Days of our Llives.

It is my hope that by being shameless enough to go first, that everyone else will start blogging their publications as they come along. I want to know all about reaction-diffusion systems, nuclear field theory, granular matter, and whatever else comes up. At least, I want to know as much about them as fits into an interesting blog post. And who knows, maybe one of the world’s Nelly Furtado fans (she is the Matron Saint of Lunchtime! visitors) will be inspired to read a research paper…

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.

Our simulations predict two swirling vorticesWhat 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.”


8 Responses to like sands through the hour glass…

  1. brianbunton says:

    It’s about damn time. Congratulations, John, I know what an ordeal it was for you. I’ll buy you a beer next time I see you.

    (Really? Nelly Furtado? What happened to naked Dutch cyclists?)

  2. mfkidd says:

    Yay, congrats!

    Also, I disagree with that grammar rule too.

  3. bpt2 says:

    Congrats, John, nice work!

    BTW, I’m now the proud owner of a 10 minute hourglass.

    And Nelly Furtado kicks naked Dutch cyclists’ asses. Brian Bunton’s mix CDs are probably responsible for 75% of traffic to the blog. John’s post on Andy Samberg and the Bentals Stormtrooper are also popular, along with Brad’s trivia posts.

    Me? I contribute nothin’.

    But Mary already name-dropped Paris Hilton, so I foresee great things for her.

  4. adawes says:

    Congrats! Having just submitted to PRA, maybe I’ll have one to post in a couple years đŸ™‚

    Just to help you avoid future grammatical dissonance, the rule is only for periods and commas. For exclamation points and question marks, the usage should follow the quoted material, i.e. if a question is being quoted, the mark goes inside:

    He just said “What was the rule again?”

    If a question is being asked of a quote, the mark goes outside:

    Didn’t he just say “What a stupid rule”?

    Same holds for exclamation points. And, as an aside, Britain does it backwards: commas and periods always outside (equally stupid in many opinions).

  5. mfkidd says:

    Good to know, Andy…I can rest easy now!

    It actually looks like a couple of people came here from my offhand Jude Law comment, and not Paris.

  6. bmarts says:

    I was taught that the reason the period goes inside the quote is that on old-time printing presses it stayed in place better that way. I’m not sure if I still believe that (though I have no reason not to, I’m just a bigger jerk now than before), but if it is true it’s a lousy reason to stick with a rule.

  7. bmarts says:

    John, isn’t there another paper to come out of your grad work, one with JESS as an author?

    Anna and I did publish our period doubling result in August, but I don’t think that deserves its own post. None of the prettiest pictures made the paper because it’s too hard to make them look pretty in black and white.

  8. jwambaugh says:

    I have two more papers “in the pipeline” with Bob, and one of them is the mysterious JESS paper. Don’t hold your breath…

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