### Abstract

Twist-grain-boundary phases in smectics are the geometrical analogs of the Abrikosov flux lattice in superconductors. At large twist angles, the nonlinear elasticity is important in evaluating their energetics. We analytically construct the height function of a π 2 twist-grain-boundary phase in smectic-A liquid crystals, known as Schnerk's first surface. This construction, utilizing elliptic functions, allows us to compute the energy of the structure analytically. By identifying a set of heretofore unknown defects along the pitch axis of the structure, we study the necessary topological structure of grain boundaries at other angles, concluding that there exist a set of privileged angles and that the π 2 and π 3 grain boundary structures are particularly simple.

Original language | English (US) |
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Article number | 011702 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 75 |

Issue number | 1 |

DOIs | |

State | Published - Jan 26 2007 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*75*(1), [011702]. https://doi.org/10.1103/PhysRevE.75.011702