Porosity and topological properties of triply periodic minimal surfaces

• URL: http://arxiv.org/abs/2406.16215v2
• Date: Wed, 26 Jun 2024 18:39:00 GMT
• Title: Porosity and topological properties of triply periodic minimal surfaces
• Authors: Sergei Ermolenko, Pavel Snopov,
• Abstract summary: Triple periodic minimal surfaces (TPMS) have garnered significant interest due to their structural efficiency and controllable geometry. This paper investigates the relationships between the porosity and entropy with the shape factor of TPMS.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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