Salvatore Torquato, a PRISM faculty member and a professor in the Department of Chemistry along with Yang Jiao, a graduate student in the Department of Mechanical and Aerospace Engineering reported in the cover story of the Aug. 13, 2009 issue of Nature to have beaten the present world record for packing the most tetrahedra into a volume. Using computer simulations, Torquato and Jiao were able to fill a volume to 78.2 percent of capacity with tetrahedra thereby improving upon previous 77.8 percent record for filling of the space.
In addition beyond making a new world record, Torquato and Jiao have devised an approach that involves placing pairs of tetrahedra face-to-face, forming a "kissing" pattern that, viewed from the outside of the container, looks strangely jumbled and irregular. Another striking outcome of their approach when applied to other Platonic solids with central symmetry is that the highest-density packings of such solids turn out to be their optimal Bravais lattice packings. Subsequent theoretical analysis further leads to the apparent optimality of the Brava is lattice packings for the centrally symmetric Archimedean solids.
The conclusions of this research are not at all obvious, and it took the development of a complex computer program and theoretical analysis to achieve their ground breaking results. Fundamental understanding into these so-called packing problems have produced deep mathematical ideas and led to practical applications as well.
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