Magnetic groups are applied to three-dimensional fluid flows with chirality, which are called Beltrami flows (or force-free fields in plasma physics). First, six Beltrami flows are derived so that their symmetries and antisymmetries are described by six different hexagonal magnetic groups. The general Wyckoff positions are used to derive the flows. Special Wyckoff positions are shown to be useful for finding the zero points of the flows. Tube-like surfaces called invariant tori are observed to interlace and form various crystal-like structures when streamlines winding around the surfaces are numerically plotted. Next, two simpler hexagonal Beltrami flows are derived, and their zero points and invariant tori are studied. Some families of the invariant tori have arrangements similar to those observed in materials science.

中文翻译：

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六角形情况下具有手性的三维流体流动的晶体学

磁群应用于具有手性的三维流体流，称为贝尔特拉米流（或等离子体物理学中的无力场）。首先，推导出六个贝尔特拉米流，以便通过六个不同的六角形磁群来描述它们的对称性和反对称性。一般威科夫位置用于推导流量。特殊的威科夫位置对于寻找流动的零点非常有用。当以数值方式绘制围绕表面的流线时，观察到称为不变环面的管状表面交错并形成各种晶体状结构。接下来，推导了两个更简单的六边形贝尔特拉米流，并研究了它们的零点和不变环面。一些不变环面家族的排列与材料科学中观察到的相似。