Christmas Ornaments

November 9, 2011 by staff 

Christmas Ornaments, One day, physicist Ho-Kei Chan of Trinity College Dublin was playing with steel ball bearings, trying to pack them into a little cylindrical tube in the most efficient way possible. It’s a tricky problem that can take even a powerful computer a week to calculate. But after thinking about it for a while, Chan has figured out a way to simplify the math. The advance could help engineers pack all sorts of spheres more efficiently, from nano-sized buckyballs to Christmas tree ornaments.

The challenge of packing as many spheres as possible into a cylinder comes up all the time. Microfluidics engineers grapple with it when they try to pack as many drug-delivery bubbles as they need into a tiny capillary tube, and manufacturers confront it when they try to cut shipping costs by packing as many bouncy balls into as small a package as possible. There are lots of possible packing patterns. The tennis ball-style single stack of balls in a tight-fitting cylinder is the simplest; pairs of balls stacked two by two in alternating directions is another. But as the cylinder gets wider, the possibilities spiral into mind-bogglingly complex helices and patterns. What’s the best way to pack them?

Chan realized he could solve the problem by imagining his cylinder full of ball bearings as a stack of disks, with a single layer of ball bearings on each disk. He then wrote a computer simulation to model it that way. The computer would lay spheres in a disk, and when it ran out of room, it would move up until it found enough space to fit another sphere. It would then rotate around fitting spheres on that level until there was no more room, moving up again, and repeating. Not all the spheres on a certain disk needed to be level; if a sphere could nestle down a little into a space created by two spheres on the disk below to get the tightest fit, it would. If the spheres below pushed it up a little higher than the other spheres on its disk, that was okay, too.

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