Geodesic fibrations for packing diabolic domains

Randall D. Kamien, Thomas J Machon

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)


We describe a theory of packing hyperboloid “diabolic” domains in bend-free textures of liquid crystals. The domains sew together continuously, providing a menagerie of bend-free textures akin to the packing of focal conic domains in smectic liquid crystals. We show how distinct domains may be related to each other by Lorentz transformations and that this process may lower the elastic energy of the system. We discuss a number of phases that may be formed as a result, including splay–twist analogues of blue phases. We also discuss how these diabolic domains may be subject to “superluminal boosts,” yielding defects analogous to shock waves. We explore the geometry of these textures, demonstrating their relation to Milnor fibrations of the Hopf link. Finally, we show how the theory of these domains is unified in four-dimensional space.
Original languageEnglish
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number39
Publication statusPublished - 15 Sept 2020


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