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| Main Authors: | , |
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| Format: | Preprint |
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2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1901.00319 |
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| _version_ | 1866910047585435648 |
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| author | Headley, Francis Cox, Simon |
| author_facet | Headley, Francis Cox, Simon |
| contents | We present conjectured candidates for the least perimeter partition of a disc into $N \le 10$ regions which take one of two possible areas. We assume that the optimal partition is connected, and therefore enumerate all three-connected simple cubic graphs for each $N$. Candidate structures are obtained by assigning different areas to the regions: for even $N$ there are $N/2$ regions of one area and $N/2$ regions of the other, and for odd $N$ we consider both cases, i.e. where the extra region takes either the larger or the smaller area. The perimeter of each candidate is found numerically for a few representative area ratios, and then the data is interpolated to give the conjectured least perimeter candidate for all possible area ratios. At larger $N$ we find that these candidates are best for a more limited range of the area ratio. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_00319 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Least-perimeter partition of the disc into $N$ regions of two different areas Headley, Francis Cox, Simon Soft Condensed Matter We present conjectured candidates for the least perimeter partition of a disc into $N \le 10$ regions which take one of two possible areas. We assume that the optimal partition is connected, and therefore enumerate all three-connected simple cubic graphs for each $N$. Candidate structures are obtained by assigning different areas to the regions: for even $N$ there are $N/2$ regions of one area and $N/2$ regions of the other, and for odd $N$ we consider both cases, i.e. where the extra region takes either the larger or the smaller area. The perimeter of each candidate is found numerically for a few representative area ratios, and then the data is interpolated to give the conjectured least perimeter candidate for all possible area ratios. At larger $N$ we find that these candidates are best for a more limited range of the area ratio. |
| title | Least-perimeter partition of the disc into $N$ regions of two different areas |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/1901.00319 |