Hollywood, here they come! New computing techniques solve some old problems

Landsat image, February 8, 1974, of linear sand dunes encroaching on Nouakchott,
the capital of Mauritania.

After water, granular materials (such as sand, soil, snow...) are the most common material on earth.  We encounter them not only in nature, but in our engineered world: cereals, pharmaceuticals, road aggregate, gravel...  Many scientists consider them--after solid, liquid, and gas--to be a fourth state of matter (well, the plasma physicists would argue with that).  Granular materials sometimes act like a solid, sometimes like a gas, and other times like a liquid.  Modeling their behavior and creating graphic images showing this behavior has been a huge computational challenge. Thousands to millions of grains interact as they flow, and simulating the motion of each grain responding to contact and frictional forces with other grains is computationally prohibitive.

In a new paper posted on the WWW site of the university of North Carolina GAMMA group, Narain and others have unveiled a novel approach. The paper is to be published in the ACM SIGGRAPH conference proceedings; ACM is the Association for Computing Machinery; SIGGRAPH seems to mean Special Interest Group on Computer Graphics and Interactive Techniques. Narain et al. assume that the grains are so small that the precise motion of individual grains is unimportant, and they treat a granular material like a liquid, a so-called "continuum model". But, to avoid having the grains flow just like water or syrup, they impose other conditions.  The material maintains its volume when at rest, like a pile of sand, but disperses freely when perturbed. In fact, unlike a liquid, there may be no actual surface that defines the material once it starts moving: imagine throwing a ball into a pile of sand. Where does the pile of sand end, and the cloud of ejecta begin?  They choose a friction model that can counteract gravity and allow stable piles of grains in equilibrium.  The material responds to external forces (such as a push) and internal stresses (contact and frictional forces). Computationally they divide the simulation into two parts: they calculate the motion under the forces present and determine the internal stresses at a particular time.  Then, they integrate the motion of the material under these forces. Rather than tracking individual grains, they track moving "clumps" of matter.

"Fungus Among us"

Check out the video of their simulation results--amazing stuff! Unfortunately, it's a big file and may not play over slow connections. I can play it in my office at the University, but not at home. The link is http://gamma.cs.unc.edu/granular/narain-2010-granular.mov if you want to try it some other way.

The Feb. 18 issue of Science has images that won the science visualization contest this year. They are also available through Wired magazine here. Titled Fungus Among Us, by Kandis Elliot, Mo Fayyaz at the University of Wisconsin was the first prize winner in informational graphics.

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