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New twist on ancient math problem could improve medicine, microelectronics
Date:5/11/2012

the pattern change size and move around, depending on how many discs are allowed, but those over the traps are always the same. Phillips suspects that if a design uses enough discs, every trap will have a disc centered over it.

In their paper, published online today in Physical Review Letters, the researchers report the rules for how to find the ideal size and spacing of the discs that fill a shape. In the future, they expect to reveal an algorithm that can take the desired shape and the number of discs, or the shape and percentage of the area to be filled, and spit out the best pattern to fill it.

Extending the approach into three dimensions, Glotzer proposes that it could decide the placement of wireless routers in a building where the signal must not be available to a potential hacker in the parking lot. Alternatively, it could help demolition workers to set off precision explosions, ensuring that the blast covers the desired region but doesn't extend beyond a building's outer walls.

Phillips expects filling solutions to be scientifically useful as well. Glotzer's team developed the new problem by trying to find a way to represent many-sided shapes for their computer models of nanoparticles. In addition to nanotechnology, biology and medicine often need models for complex shapes, such as those of proteins.

"You don't want to model every single one of the thousands of atoms that make up this protein," Phillips said. "You want a minimal model that gives the shape, allowing the proteins to interact in a lock-and-key way, as they do in nature."

The filling approach may prove a perfect fit for a variety of fields.


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Contact: Katherine McAlpine
kmca@umich.edu
734-763-4386

Source:Eurekalert

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