Stability of Objective Structures: General Criteria and Applications
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913728849510400 |
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| author | Schmidt, Bernd Steinbach, Martin |
| author_facet | Schmidt, Bernd Steinbach, Martin |
| contents | We develop a general stability analysis for objective structures, which constitute a far reaching generalization of crystal lattice systems. We show that these particle systems, although in general neither periodic nor space filling, allow for the identification of stability constants in terms of representations of the underlying symmetry group and interaction potentials. Our main results provide general stability criteria and second order energy bounds for equilibrium configurations. In particular, a general computational algorithm to test objective structures for their stability is derived. By way of example we show that our method can be applied to verify the stability of carbon nanotubes with chirality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04849 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stability of Objective Structures: General Criteria and Applications Schmidt, Bernd Steinbach, Martin Analysis of PDEs Mesoscale and Nanoscale Physics Materials Science 70C20, 70J25, 74Kxx, 49K40 We develop a general stability analysis for objective structures, which constitute a far reaching generalization of crystal lattice systems. We show that these particle systems, although in general neither periodic nor space filling, allow for the identification of stability constants in terms of representations of the underlying symmetry group and interaction potentials. Our main results provide general stability criteria and second order energy bounds for equilibrium configurations. In particular, a general computational algorithm to test objective structures for their stability is derived. By way of example we show that our method can be applied to verify the stability of carbon nanotubes with chirality. |
| title | Stability of Objective Structures: General Criteria and Applications |
| topic | Analysis of PDEs Mesoscale and Nanoscale Physics Materials Science 70C20, 70J25, 74Kxx, 49K40 |
| url | https://arxiv.org/abs/2205.04849 |