Maximum parametric soft density of lattice configurations of balls
In 2018, Edelsbrunner and Iglesias-Ham defined a notion of density, called first soft density, for lattice packings of congruent balls in Euclidean 3- space, which penalizes gaps and multiple overlaps. In their paper, they showed that this density is maximal in a 1-parameter family of lattices, call...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
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| Sorozat: | Acta scientiarum mathematicarum
87 No. 3-4 |
| Kulcsszavak: | Geometria, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-020-483-y |
| Online Access: | http://acta.bibl.u-szeged.hu/75858 |
| Tartalmi kivonat: | In 2018, Edelsbrunner and Iglesias-Ham defined a notion of density, called first soft density, for lattice packings of congruent balls in Euclidean 3- space, which penalizes gaps and multiple overlaps. In their paper, they showed that this density is maximal in a 1-parameter family of lattices, called diagonal family, for a configuration of congruent balls whose centers are the points of a face-centered cubic lattice. In this note we extend their notion of density, which we call first soft density of weight t, and show that it is maximal in the diagonal family for some family of congruent balls centered at the points of a face-centered cubic lattice, for every t ≥ 1, and at the points of a body-centered cubic lattice for t = 0.5. |
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| Terjedelem/Fizikai jellemzők: | 615-647 |
| ISSN: | 2064-8316 |