A note on energy minimization in dimension 2
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910757429444608 |
|---|---|
| author | Faulhuber, Markus Shafkulovska, Irina Zlotnikov, Ilia |
| author_facet | Faulhuber, Markus Shafkulovska, Irina Zlotnikov, Ilia |
| contents | Proving the universal optimality of the hexagonal lattice is one of the big open challenges of nowadays mathematics. We show that the hexagonal lattice outperforms certain "natural" classes of periodic configurations. Also, we rule out the option that the canonical non-lattice rival -- the honeycomb -- has lower energy than the hexagonal lattice at any scale. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16266 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on energy minimization in dimension 2 Faulhuber, Markus Shafkulovska, Irina Zlotnikov, Ilia Classical Analysis and ODEs Mathematical Physics Metric Geometry 52C25, 74G65 Proving the universal optimality of the hexagonal lattice is one of the big open challenges of nowadays mathematics. We show that the hexagonal lattice outperforms certain "natural" classes of periodic configurations. Also, we rule out the option that the canonical non-lattice rival -- the honeycomb -- has lower energy than the hexagonal lattice at any scale. |
| title | A note on energy minimization in dimension 2 |
| topic | Classical Analysis and ODEs Mathematical Physics Metric Geometry 52C25, 74G65 |
| url | https://arxiv.org/abs/2306.16266 |