Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.01387 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918425141444608 |
|---|---|
| author | Hubert, Markus Combescure, Christelle Brenner, Renald Auffray, Nicolas |
| author_facet | Hubert, Markus Combescure, Christelle Brenner, Renald Auffray, Nicolas |
| contents | This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and is defined in terms of the spatial autocorrelation functions of the material under consideration. By using the representation of these autocorrelation functions in Fourier space, the space groups of both periodic and quasiperiodic materials can be obtained. In this context, an image processing methodology is proposed to identify the key characteristics of a material's space group (i.e its point group and its symmorphism) directly from the Fourier transform of the mesostructure. The method is validated on synthetic two-dimensional images of (quasi)periodic architectured materials and it is pointed out, as an illustrative example, that the rotational symmetry of the classical Penrose tiling is of order ten. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01387 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetries of (quasi)periodic materials: Superposability vs. Indistinguishability Hubert, Markus Combescure, Christelle Brenner, Renald Auffray, Nicolas Mathematical Physics This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and is defined in terms of the spatial autocorrelation functions of the material under consideration. By using the representation of these autocorrelation functions in Fourier space, the space groups of both periodic and quasiperiodic materials can be obtained. In this context, an image processing methodology is proposed to identify the key characteristics of a material's space group (i.e its point group and its symmorphism) directly from the Fourier transform of the mesostructure. The method is validated on synthetic two-dimensional images of (quasi)periodic architectured materials and it is pointed out, as an illustrative example, that the rotational symmetry of the classical Penrose tiling is of order ten. |
| title | Symmetries of (quasi)periodic materials: Superposability vs. Indistinguishability |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2604.01387 |