The discrete dislocation dynamics of multiple dislocation loops
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_ | 1866908300310740992 |
|---|---|
| author | Patrizi, Stefania Vaughan, Mary |
| author_facet | Patrizi, Stefania Vaughan, Mary |
| contents | We consider a nonlocal reaction-diffusion equation that physically arises from the classical Peierls-Nabarro model for dislocations in crystalline structures. Our initial configuration corresponds to multiple slip loop dislocations in $\mathbb{R}^n$, $n \geq 2$. After suitably rescaling the equation with a small phase parameter $\varepsilon>0$, the rescaled solution solves a fractional Allen-Cahn equation. We show that, as $\varepsilon \to 0$, the limiting solution exhibits multiple interfaces evolving independently and according to their mean curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The discrete dislocation dynamics of multiple dislocation loops Patrizi, Stefania Vaughan, Mary Analysis of PDEs 82D25, 35R09, 35R11, 74E15, 47G20 We consider a nonlocal reaction-diffusion equation that physically arises from the classical Peierls-Nabarro model for dislocations in crystalline structures. Our initial configuration corresponds to multiple slip loop dislocations in $\mathbb{R}^n$, $n \geq 2$. After suitably rescaling the equation with a small phase parameter $\varepsilon>0$, the rescaled solution solves a fractional Allen-Cahn equation. We show that, as $\varepsilon \to 0$, the limiting solution exhibits multiple interfaces evolving independently and according to their mean curvature. |
| title | The discrete dislocation dynamics of multiple dislocation loops |
| topic | Analysis of PDEs 82D25, 35R09, 35R11, 74E15, 47G20 |
| url | https://arxiv.org/abs/2406.14793 |