Hexagonal and trigonal quasiperiodic tilings
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912505981304832 |
|---|---|
| author | Coates, Sam Koga, Akihisa Matsubara, Toranosuke Tamura, Ryuji Sharma, Hem Raj McGrath, Ronan Lifshitz, Ron |
| author_facet | Coates, Sam Koga, Akihisa Matsubara, Toranosuke Tamura, Ryuji Sharma, Hem Raj McGrath, Ronan Lifshitz, Ron |
| contents | Exploring nonminimal-rank quasicrystals, which have symmetries that can be found in both periodic and aperiodic crystals, often provides new insight into the physical nature of aperiodic long-range order in models that are easier to treat. Motivated by the prevalence of experimental systems exhibiting aperiodic long-range order with hexagonal and trigonal symmetry, we introduce a generic two-parameter family of 2-dimensional quasiperiodic tilings with such symmetries. We focus on the special case of trigonal and hexagonal Fibonacci, or golden-mean, tilings, analogous to the well studied square Fibonacci tiling. We first generate the tilings using a generalized version of de Bruijn's dual grid method. We then discuss their interpretation in terms of projections of a hypercubic lattice from six dimensional superspace. We conclude by concentrating on two of the hexagonal members of the family, and examining a few of their properties more closely, while providing a set of substitution rules for their generation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_11848 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hexagonal and trigonal quasiperiodic tilings Coates, Sam Koga, Akihisa Matsubara, Toranosuke Tamura, Ryuji Sharma, Hem Raj McGrath, Ronan Lifshitz, Ron Soft Condensed Matter Exploring nonminimal-rank quasicrystals, which have symmetries that can be found in both periodic and aperiodic crystals, often provides new insight into the physical nature of aperiodic long-range order in models that are easier to treat. Motivated by the prevalence of experimental systems exhibiting aperiodic long-range order with hexagonal and trigonal symmetry, we introduce a generic two-parameter family of 2-dimensional quasiperiodic tilings with such symmetries. We focus on the special case of trigonal and hexagonal Fibonacci, or golden-mean, tilings, analogous to the well studied square Fibonacci tiling. We first generate the tilings using a generalized version of de Bruijn's dual grid method. We then discuss their interpretation in terms of projections of a hypercubic lattice from six dimensional superspace. We conclude by concentrating on two of the hexagonal members of the family, and examining a few of their properties more closely, while providing a set of substitution rules for their generation. |
| title | Hexagonal and trigonal quasiperiodic tilings |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2201.11848 |