Hard tetrahedron model: Difference between revisions
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The '''hard tetrahedron model'''. | The '''hard tetrahedron model'''. | ||
==Maximum packing fraction== | ==Maximum packing fraction== | ||
<math>\phi=0.8503</math><ref>[http://dx.doi.org/10.1038/nature08641 Amir Haji-Akbari, Michael Engel, Aaron S. Keys, Xiaoyu Zheng, Rolfe G. Petschek, Peter Palffy-Muhoray and Sharon C. Glotzer "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra", Nature '''462''' pp. 773-777 (2009)]</ref> | It has recently been shown that regular tetrahedra are able to achieve packing fractions as high as <math>\phi=0.8503</math><ref>[http://dx.doi.org/10.1038/nature08641 Amir Haji-Akbari, Michael Engel, Aaron S. Keys, Xiaoyu Zheng, Rolfe G. Petschek, Peter Palffy-Muhoray and Sharon C. Glotzer "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra", Nature '''462''' pp. 773-777 (2009)]</ref> (the [[hard sphere model |hard sphere]] packing fraction is <math>\pi/(3 \sqrt{2}) \approx 74.048%</math> <ref>[http://dx.doi.org/10.1038/26609 Neil J. A. Sloane "Kepler's conjecture confirmed", Nature '''395''' pp. 435-436 (1998)]</ref>). This is in stark contrast to work as recent as in 2006, where it was suggested that the "...regular tetrahedron might even be the convex body having the smallest possible packing density"<ref>[http://dx.doi.org/10.1073/pnas.0601389103 J. H. Conway and S. Torquato "Packing, tiling, and covering with tetrahedra", Proceedings of the National Academy of Sciences of the United States of America '''103''' 10612-10617 (2006)]</ref>. | ||
==References== | ==References== | ||
<references/> | <references/> | ||
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The hard tetrahedron model.
Maximum packing fraction
It has recently been shown that regular tetrahedra are able to achieve packing fractions as high as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi=0.8503} [1] (the hard sphere packing fraction is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \pi/(3 \sqrt{2}) \approx 74.048%} [2]). This is in stark contrast to work as recent as in 2006, where it was suggested that the "...regular tetrahedron might even be the convex body having the smallest possible packing density"[3].
References
- ↑ Amir Haji-Akbari, Michael Engel, Aaron S. Keys, Xiaoyu Zheng, Rolfe G. Petschek, Peter Palffy-Muhoray and Sharon C. Glotzer "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra", Nature 462 pp. 773-777 (2009)
- ↑ Neil J. A. Sloane "Kepler's conjecture confirmed", Nature 395 pp. 435-436 (1998)
- ↑ J. H. Conway and S. Torquato "Packing, tiling, and covering with tetrahedra", Proceedings of the National Academy of Sciences of the United States of America 103 10612-10617 (2006)
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