Entropy and chirality in sphinx tilings
As a toy model of chiral interactions in crowded spaces, we consider sphinx tilings in finite regions of the triangular lattice. The sphinx tiles, hexiamonds composed of six equilateral triangles in the shape of a stylized sphinx, come in left and right enantiomorphs. Regions scaled up from the unit...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.013227 |
| _version_ | 1797210229583118336 |
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| author | Greg Huber Craig Knecht Walter Trump Robert M. Ziff |
| author_facet | Greg Huber Craig Knecht Walter Trump Robert M. Ziff |
| author_sort | Greg Huber |
| collection | DOAJ |
| description | As a toy model of chiral interactions in crowded spaces, we consider sphinx tilings in finite regions of the triangular lattice. The sphinx tiles, hexiamonds composed of six equilateral triangles in the shape of a stylized sphinx, come in left and right enantiomorphs. Regions scaled up from the unit sphinx by an integer factor (Sphinx frames) require tiles of both chiral forms to produce tilings, including crystalline, quasicrystalline, and fully disordered tilings. For frames up to order 13, we describe methods that permit exact enumeration and computation of partition functions using accelerated backtracking, seam, and dangler algorithms. For larger frames, we introduce a Monte Carlo method to sample typical tilings. The key to the latter is the identification of fundamental shapes (polyads) that admit multiple tilings and which allow a rejection-free MC simulation. |
| first_indexed | 2024-04-24T10:07:17Z |
| format | Article |
| id | doaj.art-55d4bd70478444ad8fd2a47b09305462 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:07:17Z |
| publishDate | 2024-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-55d4bd70478444ad8fd2a47b093054622024-04-12T17:39:58ZengAmerican Physical SocietyPhysical Review Research2643-15642024-03-016101322710.1103/PhysRevResearch.6.013227Entropy and chirality in sphinx tilingsGreg HuberCraig KnechtWalter TrumpRobert M. ZiffAs a toy model of chiral interactions in crowded spaces, we consider sphinx tilings in finite regions of the triangular lattice. The sphinx tiles, hexiamonds composed of six equilateral triangles in the shape of a stylized sphinx, come in left and right enantiomorphs. Regions scaled up from the unit sphinx by an integer factor (Sphinx frames) require tiles of both chiral forms to produce tilings, including crystalline, quasicrystalline, and fully disordered tilings. For frames up to order 13, we describe methods that permit exact enumeration and computation of partition functions using accelerated backtracking, seam, and dangler algorithms. For larger frames, we introduce a Monte Carlo method to sample typical tilings. The key to the latter is the identification of fundamental shapes (polyads) that admit multiple tilings and which allow a rejection-free MC simulation.http://doi.org/10.1103/PhysRevResearch.6.013227 |
| spellingShingle | Greg Huber Craig Knecht Walter Trump Robert M. Ziff Entropy and chirality in sphinx tilings Physical Review Research |
| title | Entropy and chirality in sphinx tilings |
| title_full | Entropy and chirality in sphinx tilings |
| title_fullStr | Entropy and chirality in sphinx tilings |
| title_full_unstemmed | Entropy and chirality in sphinx tilings |
| title_short | Entropy and chirality in sphinx tilings |
| title_sort | entropy and chirality in sphinx tilings |
| url | http://doi.org/10.1103/PhysRevResearch.6.013227 |
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