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Alexey Andreanov
복잡계 이론물리 연구단
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Locally Optimal 2-Periodic Sphere Packings

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Title
Locally Optimal 2-Periodic Sphere Packings
Author(s)
Alexei Andreanov; Yoav Kallus
Publication Date
2020-01
Journal
DISCRETE & COMPUTATIONAL GEOMETRY, v.63, no.1, pp.182 - 208
Publisher
SPRINGER
Abstract
The sphere packing problem is an old puzzle. We consider packings with m spheres in the unit cell (m-periodic packings). For the case m = 1 (lattice packings), Voronoi proved there are finitely many inequivalent local optima and presented an algorithm to enumerate them, and this computation has been implemented in up to d = 8 dimensions. We generalize Voronoi’s method to m > 1 and present a procedure to enumerate all locally optimal 2-periodic sphere packings in any dimension, provided there are finitely many. We implement this computation in d = 3, 4, and 5 and show that no 2-periodic packing surpasses the density of the optimal lattices in these dimensions. A partial enumeration is performed in d = 6. © Springer Science+Business Media, LLC, part of Springer Nature 2019
URI
https://pr.ibs.re.kr/handle/8788114/6684
ISSN
0179-5376
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > Journal Papers (저널논문)
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