Minimal Twin Surfaces
Minimal Twin Surfaces
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DOI：
10.1080/10586458.2017.1413455
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发表时间：
2019-10-02
影响因子：
0.5
通讯作者：
Chen, Hao
中科院分区：
文献类型：
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作者：
Chen, Hao
我们报道了一些极小曲面，它们可以看作是平行镜面中反射相关的三周期极小曲面(TPMS)的副本。我们称它们为最小孪生表面，因为它们与孪晶相似。Brakke的曲面演化程序被用来构造各种经典的TPMS的孪晶，包括Schwarz的原始(P)和钻石(D)曲面，它们的菱面体变形(RPD)，以及Schoen的回转(G)曲面。我们的数值结果为材料科学家最近在实验中观察到的D孪晶和G孪晶的数学存在提供了强有力的证据。对于RPD双胞胎，我们通过注意以前由[Traizet 08]和[Fujimori and Weber 09]构造的示例来发展很好的理解。相比之下，我们对G双胞胎的了解非常有限。然而，我们的实验导致了D和G表面的新的三次多面体模型，受此启发，我们在Traizet框架下推测了新的TPMS变形。
We report some minimal surfaces that can be seen as copies of a triply periodic minimal surface (TPMS) related by reflections in parallel mirrors. We call them minimal twin surfaces for the resemblance with twin crystal. Brakke's Surface Evolver is employed to construct twinnings of various classical TPMS, including Schwarz' Primitive (P) and Diamond (D) surfaces, their rhombohedral deformations (rPD), and Schoen's Gyroid (G) surface. Our numerical results provide strong evidences for the mathematical existence of D twins and G twins, which are recently observed in experiment by material scientists. For rPD twins, we develop a good understanding, by noticing examples previously constructed by [Traizet 08] and [Fujimori and Weber 09]. Our knowledge on G twins is, by contrast, very limited. Nevertheless, our experiments lead to new cubic polyhedral models for the D and G surfaces, inspired by which we speculate new TPMS deformations in the framework of Traizet.