Princeton University scientists set new world record in packing puzzle

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London, Aug 13 (ANI): Researchers at the Princeton University claim to have set a new record of packing the most tetrahedral - solid figures with four triangular faces - into a volume.

The cover story of the Aug. 13 issue of Nature reads that Salvatore Torquato, a professor in the Department of Chemistry and the Princeton Institute for the Science and Technology of Materials, and Yang Jiao, a graduate student in the Department of Mechanical and Aerospace Engineering, claim to have bettered the record set by Elizabeth Chen, a graduate student at the University of Michigan, in 2008.

Using computer simulations, Torquato and Jiao filled a volume up to 78.2 percent with tetrahedral while Chen had filled 77.8 percent of the space last year.

Not just that, Torquato and Jiao have also formulated a way of placing pairs of tetrahedra face-to-face, forming a "kissing" pattern which looks jumbled and irregular when seen from the outside of the container.

Torquato said: "We wanted to know this: What's the densest way to pack space? It's a notoriously difficult problem to solve, and it involves complex objects that, at the time, we simply did not know how to handle."

"From a scientific perspective, to know about the packing problem is to know something about the low-temperature phases of matter itself," he added.

The effective and efficient packing of solids is a vital part of the mathematics that goes into the error-detecting and error-correcting codes used for storing information on compact discs, as also to compress data for efficient transmission around the world.

The research could not only help in storing data on compact discs but also better the understanding of matter itself.

Torquato and Jiao used a complex computer program and theoretical analysis to achieve the feat. Earlier computer simulations had jammed virtual piles of polyhedra into in a virtual box and allowed them to "grow."

Torquato and Jiao, developed "an adaptive shrinking cell optimization technique, which shrivelled the box, thereby changing its shape.

Torquato said: "When you 'grow' the particles, it's easy for them to get stuck, so you have to wiggle them around to improve the density...Such programs get bogged down easily; there are all kinds of subtleties. It's much easier and productive, we found, thinking about it in the opposite way."

Torquato said his work was different than previous researches conducted as it showed "the best packings, period" in the case of the centrally symmetric Platonic and Archimedean solids.

Theoretical arguments - that the densest packings of these objects are likely to be their best lattice arrangements - also back the research.

"This is now a strong conjecture that people can try to prove," Torquato said. (ANI)

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