Periodic sphere packings and the Wulff-shape
type: Item
instance of: scholarly article
title: Periodic sphere packings and the Wulff-shape
zbMATH Open document ID: 0960.52013
author: Uwe Schnell
published in: Beiträge zur Algebra und Geometrie
publication date: 2001-01-09T00:00:00Z
full work available at URL: https://eudml.org/doc/227385
full work available at URL: 10.html
review text: The asymptotic shape of large densest sphere packings in a lattice \(L\subset E^d\), \(d\geq 2\) is a polytope, the Wulff-shape, which in \(E^3\) models the shape of an ideal crystal in this special case. The density is measured by parametric density. The author shows that this also holds for the general case of periodic packings with spheres of different size. Although this case is much more general and more complicated, it still is a good model for the Wulff shape of crystals. This is underlined by 3 examples of different crystallographic type given in this paper. Besides these applications in 3-space the results hold for all \(d>3\).
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 82D25
Mathematics Subject Classification ID: 11H31
zbMATH DE Number: 1549692
zbMATH Keywords: lattice packings
zbMATH Keywords: sphere packings
zbMATH Keywords: Wulff-shape
zbMATH Keywords: crystals
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1549692