Microstructures and anti-phase boundaries in long-range lattice systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911873030422528 |
|---|---|
| author | Braides, Andrea Voglino, Edoardo Zanardini, Matteo |
| author_facet | Braides, Andrea Voglino, Edoardo Zanardini, Matteo |
| contents | We study the effect of long-range interactions in non-convex one-dimensional lattice systems in the simplified yet meaningful assumption that the relevant long-range interactions are between $M$-neighbours for some $M\ge 2$ and are convex. If short-range interactions are non-convex we then have a competition between short-range oscillations and long-range ordering. In the case of a double-well nearest-neighbour potential, thanks to a recent result by Braides, Causin, Solci and Truskinovsky, we are able to show that such a competition generates $M$-periodic minimizers whose arrangements are driven by an interfacial energy. Given $M$, the shape of such minimizers is universal, and independent of the details of the energies, but the number and shapes of such minimizers increases as $M$ diverges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06542 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Microstructures and anti-phase boundaries in long-range lattice systems Braides, Andrea Voglino, Edoardo Zanardini, Matteo Analysis of PDEs Optimization and Control 39A12, 34K31, 82B20, 49J45, 46E39 We study the effect of long-range interactions in non-convex one-dimensional lattice systems in the simplified yet meaningful assumption that the relevant long-range interactions are between $M$-neighbours for some $M\ge 2$ and are convex. If short-range interactions are non-convex we then have a competition between short-range oscillations and long-range ordering. In the case of a double-well nearest-neighbour potential, thanks to a recent result by Braides, Causin, Solci and Truskinovsky, we are able to show that such a competition generates $M$-periodic minimizers whose arrangements are driven by an interfacial energy. Given $M$, the shape of such minimizers is universal, and independent of the details of the energies, but the number and shapes of such minimizers increases as $M$ diverges. |
| title | Microstructures and anti-phase boundaries in long-range lattice systems |
| topic | Analysis of PDEs Optimization and Control 39A12, 34K31, 82B20, 49J45, 46E39 |
| url | https://arxiv.org/abs/2405.06542 |