Porosity and topological properties of triply periodic minimal surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914849796128768 |
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| author | Ermolenko, Sergei Snopov, Pavel |
| author_facet | Ermolenko, Sergei Snopov, Pavel |
| contents | Triple periodic minimal surfaces (TPMS) have garnered significant interest due to their structural efficiency and controllable geometry, making them suitable for a wide range of applications. This paper investigates the relationships between porosity and persistence entropy with the shape factor of TPMS. We propose conjectures suggesting that these relationships are polynomial in nature, derived through the application of machine learning techniques. This study exemplifies the integration of machine learning methodologies in pure mathematical research. Besides the conjectures, we provide the mathematical models that might have the potential implications for the design and modeling of TPMS structures in various practical applications. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_16215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Porosity and topological properties of triply periodic minimal surfaces Ermolenko, Sergei Snopov, Pavel Differential Geometry Mathematical Physics Geometric Topology K-Theory and Homology Machine Learning Triple periodic minimal surfaces (TPMS) have garnered significant interest due to their structural efficiency and controllable geometry, making them suitable for a wide range of applications. This paper investigates the relationships between porosity and persistence entropy with the shape factor of TPMS. We propose conjectures suggesting that these relationships are polynomial in nature, derived through the application of machine learning techniques. This study exemplifies the integration of machine learning methodologies in pure mathematical research. Besides the conjectures, we provide the mathematical models that might have the potential implications for the design and modeling of TPMS structures in various practical applications. |
| title | Porosity and topological properties of triply periodic minimal surfaces |
| topic | Differential Geometry Mathematical Physics Geometric Topology K-Theory and Homology Machine Learning |
| url | https://arxiv.org/abs/2406.16215 |