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arXiv · 2503.12555

Density-Functional Theory and Triply-Periodic Minimal Surfaces

Mengdi Yin·Jing Zhang·Dimitri D Vvedensky
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Abstract

Several authors have suggested that the surfaces of vanishing potential generated by the electrostatic fields from a distribution of point charges resemble triply periodic minimal surfaces (TPMS) corresponding to the positions of the point charges. We provide a theoretical basis for this phenomenological comparison by starting with the Boltzmann equation to show that the surface corresponding to zero charge density is a minimal surface. We then use density-functional calculations for elemental materials that differ electronically and structurally, Na, Cu, and Al, to show that surfaces of vanishing charge density converge to the corresponding TPMS.

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Mengdi Yin, Jing Zhang, Dimitri D Vvedensky. 2025-03-16. Density-Functional Theory and Triply-Periodic Minimal Surfaces. https://arxiv.org/abs/2503.12555

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