Optimal Packings of Superdisks and the Role of Symmetry Export

@article{torquato08, abstract = {Almost all studies of the densest particle packings consider convex particles. Here, we provide exact constructions for the densest known two-dimensional packings of superdisks whose shapes are defined by |x1|2p+|x2|2p1 and thus contain a large family of both convex (p0.5) and concave (0\<p\<0.5) particles. Our candidate maximal packing arrangements are achieved by certain families of Bravais lattice packings, and the maximal density is nonanalytic at the \“circular-disk\” point (p=1) and increases dramatically as p moves away from unity. Moreover, we show that the broken rotational symmetry of superdisks influences the packing characteristics in a nontrivial way.}, author = {Jiao, Y. and Stillinger, F. H. and Torquato, S.}, citeulike-article-id = {3023271}, citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000100000024245504000001&idtype=cvips&gifs=yes}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRL/v100/e245504}, citeulike-linkout-2 = {http://dx.doi.org/10.1103/PhysRevLett.100.245504}, doi = {10.1103/PhysRevLett.100.245504}, journal = {Physical Review Letters}, keywords = {rcp}, number = {24}, posted-at = {2008-07-21 00:50:17}, priority = {0}, publisher = {APS}, title = {Optimal Packings of Superdisks and the Role of Symmetry}, url = {http://dx.doi.org/10.1103/PhysRevLett.100.245504}, volume = {100}, year = {2008} }

TY - JOUR ID - torquato08 L3 - citeulike-article-id:3023271 N2 - Almost all studies of the densest particle packings consider convex particles. Here, we provide exact constructions for the densest known two-dimensional packings of superdisks whose shapes are defined by |x1|2p+|x2|2p1 and thus contain a large family of both convex (p0.5) and concave (0<p<0.5) particles. Our candidate maximal packing arrangements are achieved by certain families of Bravais lattice packings, and the maximal density is nonanalytic at the “circular-disk” point (p=1) and increases dramatically as p moves away from unity. Moreover, we show that the broken rotational symmetry of superdisks influences the packing characteristics in a nontrivial way. IS - 24 JF - Physical Review Letters TI - Optimal Packings of Superdisks and the Role of Symmetry PB - APS VL - 100 KW - rcp AU - Jiao, Y AU - Stillinger, FH AU - Torquato, S PY - 2008/// UR - http://dx.doi.org/10.1103/PhysRevLett.100.245504 ER -