Packing Nonspherical Particles - Princeton University

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Dense <strong>Packing</strong>s of Icosahedra, Dodecahedra & Octahedra ASC scheme with many particles per cell yield densest lattice packings for centrally Platonic solids! Icosahedra Dodecahedra Octahedra φ = 0.836 φ = 0.904 φ = 0.947 Later showed octahedron packing leads to uncountably infinite number of tessellations by octahedra and tetrahedra (Conway, Jiao & Torquato 2010). . – p. 12/28
Superballs A d-dimensional superball is a centrally symmetric body in R d occupying |x1| 2p + |x2| 2p + · · · + |xn| 2p ≤ 1 (p: deformation parameter) Superdisks Superballs Densest packings are lattices and behave quite differently from ellipsoid packings! Jiao, Stillinger & Torquato, PRL (2008); PRE (2009) . – p. 13/28
Page 1 and 2: Packing Nonspherical Particles: All
Page 3 and 4: Geometric Structure Approach to Jam
Page 5 and 6: 3D Hard Spheres in Equilibrium Torq
Page 7 and 8: Dense Packings of Nonspherical Part
Page 9 and 10: Definitions A periodic packing is o
Page 11 and 12: Hyperuniformity for General Point P
Page 13 and 14: Packings of the Platonic and Archim
Page 15 and 16: Adaptive Shrinking Cell Optimizatio
Page 17: Kepler-Like Conjecture for a Class
Page 21 and 22: Conjecture 2: Another Organizing Pr
Page 23 and 24: Packings of Truncated Tetrahedra Th
Page 25 and 26: Maximally Dense Ellipsoidal Packing
Page 27 and 28: Generalizations of the Organizing P
Page 29 and 30: φ J 0.74 0.72 0.7 0.68 0.66 0.64 Z
Page 31 and 32: MRJ Packings of Nontiling Platonic
Page 33 and 34: Generalization of Hyperuniformity t

Packing Nonspherical Particles - Princeton University

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