Seminar on Applied Mathematics
Riddles of the sphinx tilings
2024/11/20 (Wed.) 15:00~16:00
- Date : 2024/11/20 (Wed.) 15:00~16:00
- Location : Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
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Speaker : Greg Huber (University of California San Francisco)
- Host(s) : Shih-Hsien Yu (AS)
- Abstract : The sphinx tile is a simple, non-symmetrical shape composed of six triangles which possesses some unique and minimal properties. It comes in left and right enantiomers and we propose it as a chiral building block to explore chiral interactions in crowded 2d spaces. Tilings forced spatially by fixed boundaries may require tiles of both chiral forms to produce tilings — including crystalline, quasicrystalline, and fully disordered states. A succession of exact methods are devised to find these states. For large systems, the numbers of configurations become so large that statistical mechanics obtains and thermodynamic quantities can be calculated. A Monte Carlo (MC) method based on fundamental shapes (“f-polyads”) has been developed to sample typical tilings. These explorations into chiral interactions raise a number of new mysteries which will be discussed.
