Crystallography of three‐dimensional fluid flows with chirality in hexagonal cases. Issue 6 (7th October 2019)

• Record Type: Journal Article
• Authors: Nishiyama, Takahiro
• Is Part Of: Acta crystallographica. Volume 75:Issue 6(2019:Nov.)
• Page Start: 798
• Page End: 813
• Publication Date: 2019-10-07
• Subjects: magnetic groups -- chirality -- hexagonal symmetry -- Beltrami flow -- invariant torus; Crystallography -- Periodicals; Condensed matter -- Periodicals; 548
• DOI: 10.1107/S205327331901146X
• Languages: English
• ISSNs: 2053-2733

Abstract

Abstract : Magnetic groups are applied to three‐dimensional fluid flows with chirality, which are called Beltrami flows. Eight Beltrami flows are derived and studied using Wyckoff positions. The crystal‐like structures of their tube‐like surfaces, called invariant tori, are numerically observed. Abstract : 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.