An efficient saddle search method for ordered phase transitions involving translational invariance
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917642996023296 |
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| author | Cui, Gang Jiang, Kai Zhou, Tiejun |
| author_facet | Cui, Gang Jiang, Kai Zhou, Tiejun |
| contents | In this work, we propose an efficient nullspace-preserving saddle search (NPSS) method for a class of phase transitions involving translational invariance, where the critical states are often degenerate. The NPSS method includes two stages, escaping from the basin and searching for the index-1 generalized saddle point. The NPSS method climbs upward from the generalized local minimum in segments to overcome the challenges of degeneracy. In each segment, an effective ascent direction is ensured by keeping this direction orthogonal to the nullspace of the initial state in this segment. This method can escape the basin quickly and converge to the transition states. We apply the NPSS method to the phase transitions between crystals, and between crystal and quasicrystal, based on the Landau-Brazovskii and Lifshitz-Petrich free energy functionals. Numerical results show a good performance of the NPSS method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07108 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An efficient saddle search method for ordered phase transitions involving translational invariance Cui, Gang Jiang, Kai Zhou, Tiejun Numerical Analysis 37M05, 49K35, 37N30 In this work, we propose an efficient nullspace-preserving saddle search (NPSS) method for a class of phase transitions involving translational invariance, where the critical states are often degenerate. The NPSS method includes two stages, escaping from the basin and searching for the index-1 generalized saddle point. The NPSS method climbs upward from the generalized local minimum in segments to overcome the challenges of degeneracy. In each segment, an effective ascent direction is ensured by keeping this direction orthogonal to the nullspace of the initial state in this segment. This method can escape the basin quickly and converge to the transition states. We apply the NPSS method to the phase transitions between crystals, and between crystal and quasicrystal, based on the Landau-Brazovskii and Lifshitz-Petrich free energy functionals. Numerical results show a good performance of the NPSS method. |
| title | An efficient saddle search method for ordered phase transitions involving translational invariance |
| topic | Numerical Analysis 37M05, 49K35, 37N30 |
| url | https://arxiv.org/abs/2310.07108 |