Divide and Conquer: A Distributed Approach to Five Point Energy Minimization
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929676083003392 |
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| author | Schwartz, Richard Evan |
| author_facet | Schwartz, Richard Evan |
| contents | This work rigorously verifies the phase transition in 5-point energy minimization first observed by Melnyk-Knop-Smith in 1977. More precisely, we prove that there is a constant S = [15+24/512,15+25/512] such that the triangular bi-pyramid is the energy minimizer with respect to the s-power law potential for all s in (0,S) and some pyramid with square base is the unique minimizer for all s in (S,15+512/25]. Taking s=1 gives another solution to Thomson's 5 electron problem from 1904. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05090 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Divide and Conquer: A Distributed Approach to Five Point Energy Minimization Schwartz, Richard Evan Metric Geometry This work rigorously verifies the phase transition in 5-point energy minimization first observed by Melnyk-Knop-Smith in 1977. More precisely, we prove that there is a constant S = [15+24/512,15+25/512] such that the triangular bi-pyramid is the energy minimizer with respect to the s-power law potential for all s in (0,S) and some pyramid with square base is the unique minimizer for all s in (S,15+512/25]. Taking s=1 gives another solution to Thomson's 5 electron problem from 1904. |
| title | Divide and Conquer: A Distributed Approach to Five Point Energy Minimization |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2301.05090 |